英文数学竞赛选择题（English）（第6/6卷）2020-2020年·本卷583题（第4001—4583题）说明：题目按年份倒序排列（近期→历年）。每题后附【答案】与【解析】，便于核对。1.Ten years ago,the sum of the ages of my mother and father was 71.What is the sum of their ages today?A.51 B.61 C.81 D.91【答案】D【解析】Ten years ago,the sum of the ages of my mother and father was.Each has aged years,so the sum of their ages is now.711091 2.The triplets Adam,Jan and Stas and their sister Marysia who is four years older than them were years old together three years ago.How old is Marysia today?(2001 Math Kangaroo Problem,Level 5-6,Question#18)24 A.5 B.8 C.9 D.12 E.15【答案】D【解析】Adam,Jan and Stas were years old three years ago.Marysia was years old.Thus,Marysia is years old.(24−4)÷4=55+4=99+3=12 3.A mother cut a cake into equal slices.Her four children had a slice each and she had one too.Later,a neighbour ate four slices.What percentage of the cake was left at the end of the day?12 A.5\textbackslash%B.10\textbackslash%C.25\textbackslash%D.35\textbackslash%E.50\textbackslash%【答案】C【解析】12−(4×1)−1−4=3312×100\textbackslash%=25\textbackslash%4.A worm is staying at the bottom of a well with a depth of metres.If it climbs up metres in the daytime and slips down metre at night,which day will it climb up to the ground?1341 A.The th day4 B.The th day5 C.The th day6 D.The th day7【答案】A【解析】It climbs up metres in the day time and slips down metre at night,so it climbs up metres in a whole day.For the first days,it climbs metres.During the day time of the forth day,it climbs metres and reaches the ground.Then it needs four days to climb up to the ground.413394 5.A bag of toffee is dollars,a bag of cotton candy is dollars,and a bag of orange candy is dollars.Now,the candy shop decides to mix bags of toffee,bags of cotton candy,and bags of orange candy for bags of assorted candy.What should be the price of the assorted candy in dollars to keep the total revenue unchanged?7615405010100 A.7.3 B.8 C.9.5 D.10 E.12【答案】A【解析】Total revenue:dollars A bag of assorted candy:dollars40×7+50×6+10×15=730730÷100=7.3 6.A drawer contains yellow socks,blue socks and pink socks.Bella picks socks from the drawer without looking.What is the smallest number of socks she must pick to make sure she has at least one sock of each colour?1084 A.3 B.4 C.18 D.19【答案】D【解析】10+8+1=19 7.Peter has some toy cars,and Paul has more toy cars than Peter.Altogether they have toy cars.How many toy cars does Paul have?436 A.16 B.48 C.20 D.12【答案】C【解析】Paul has toy cars.(36+4)÷2=20 8.There is an equation with all integers in the upper squares,and the answer on the right side is only the approximation of after rounding off.The numbers in each of the three upper squares of the equation are}in order.◻3+◻5+◻7≈1.16 A.1,2,3 B.1,3,5 C.1,4,3 D.2,1,2 E.2,3,5【答案】A【解析】NA 9.Nancy has donuts.She gives one donut to Sana,and then Nancy has more donuts than Sana.At beginning,how many donuts does Sana have?2310 A.10 B.11 C.12 D.13 E.14【答案】B【解析】23−1=2222−10=1212−1=11 10.Joann’s birthday in was May th,which was Sunday.Elizabeth’s birthday in was June st.What day of the week is Elizabeth’s birthday on?202010202021 A.Thursday B.Saturday C.Sunday D.Tuesday【答案】C【解析】It passed days in total.Since,it was Sunday.31−10+21=4242÷7=6 11.A sugar solution is made by mixing ounces of sugar and ounces of water.Find the percent concentration of the solution.721 A.%20 B.%25 C.%30 D.%33.3【答案】B【解析】7÷(7+21)=25\textbackslash%.12.Ellis’s Eel Emporium contains a large tank holding three different types of eel:electric eels,moray eels and freshwater eels.A notice on the tank reads as follows:All the eels are electric eels except for All the eels are moray eels except for All the eels are freshwater eels except for How many eels are in the tank?121416 A.42 B.33 C.24 D.21 E.20【答案】D【解析】Let the number of electric eels be,the number of moray eels be and the number of freshwater eels be.The information on the notice tells us that,and.When you add these three equations,you obtain and hence.Therefore the number of eels in the tank is.xyzy+z=12x+z=14x+y=162x+2y+2z=42x+y+z=2121 13.Tom and Ben played a quiz game.points for a correct answer.Tom got questions right,Ben got questions right.How many more points than Ben did Tom get?(adapted from Math kangaroo,Level,Question#)25820211−214 A.4 B.6 C.8 D.10 E.12【答案】B【解析】August got points,and Ben got points.5×2=108×2=1616−10=6 14.Farmer Baar has 36 sheep,some pink and the rest white.There are twice as many pink sheep as white sheep.How many of the sheep are pink?A.10 B.12 C.20 D.24 E.30【答案】D【解析】36÷(1+2)=12,12×2=24 15.John is 33 years old.His three sons are 5,6 and 10 years old.In how many years will the three sons together be as old as their father?A.4 B.6 C.8 D.10 E.12【答案】B【解析】Let x be the number of years needed for the ages of the three sons sum up to be equal to their dad’s age.Their dad’s age is then 33+x,while the sum of the sons’age is(5+x)x(6+x)+(10+x)=21+3x.We have the following equation:21+3x=33+x 2x=12 x=6 16.In Grade,Amy’s height was cm.When she was Grade,the doctor said that her height was cm taller than last year.What was her height in Grade?(adapted from Math kangaroo Problems,Level,Question#)3136415420191−23 A.cm15 B.cm137 C.cm151 D.cm161 E.cm167【答案】C【解析】136+15=151 cm 17.Blii and Elsa went to see a movie together and sat in the same row.Ela was in the sixth row counting from the front of the room and Elsa was seated in the fourteenth counting from the end.How many rows in their room?(Adapted from 2001 Math Kangaroo Problem,Level 3-4,Question#13)A.8 B.9 C.19 D.20 E.21【答案】C【解析】6+14−1=19 18.Several people buy a boardgame together.If each person pays dollars,more dollars are needed for the payment.If each person pays dollars,dollars are remaining.How much is the boardgame in dollars?60607010 A.600 B.480 C.690 D.550 E.720【答案】B【解析】(60+10)÷(70−60)=760×7+60=480 19.Farmer Dunphy has metres of fencing.He wants to make a closed rectangular pen.He uses a long wall for one of the sides.Each side of the pen is a whole number in metres.What is the largest area that the pen can be?100 A.125m2 B.625m2 C.1000m2 D.1250m2 E.2500m2【答案】D【解析】,when,the largest area is m2.a+2b=100a=2b=5050×(50÷2)=1250 20.How many fingers are there on a dozen pairs of gloves if each glove has fingers?5 A.24 B.30 C.60 D.120【答案】D【解析】There are fingers on a pair of gloves.dozen pairs have.2×5=10A12×10=120 21.Kevin got of the problems correct on a problem test,on a problem test,and on a problem test.What percent of all the problems did Kevin answer correctly?(2010 AMC8 Problem,Question#9)80\textbackslash%25−90\textbackslash%40−70\textbackslash%10−A.64 B.75 C.80 D.84 E.86【答案】D【解析】Ryan answered problems correct on the first test,on the second,and on the third.This amounts to a total of problems correct.The,total number of problems is.Therefore,the percendage is.(0.8)(25)=20(0.9)(40)=36(0.7)(10)=720+36+7=6325+40+10=756375→(D)84 22.A teacher distributes scorecards to students.If everyone gets cards,there will be a shortage of cards.If everyone gets cards,all these cards will just be divided.Then,how many students are there in total?3122 A.4 B.6 C.10 D.12【答案】D【解析】If fewer card is given to students,the situation would transfer from’a shortage of cards’to’all cards are just divided’.So,there are in total students.2−1=11212 23.SASMO 2015 P2 Q5 Today,Wednesday,8th of April 2015,is the day of the SASMO competition and your friend says tha the Singapore Math Kangaroo Contest was 14 days ago.On which day was the SMKC?A.23rd of March,Monday B.24th of March,Tuesday C.25th of March,Wednesday D.26th of March,Thursday E.27th of March,Friday【答案】C【解析】Draw table.24.Suppose of equals of.What percentage of is?(adapted from 2020 AMC 8,Question 15)20\textbackslash%x30\textbackslash%yyx A.5 B.35 C.75 D.150 E.300【答案】D【解析】Since,multiplying the given condition by 5 shows that is percent of.20\textbackslash%=15x30·5=(𝐂)150y 25.A shop purchased some tennis rackets at＄each,and then sold them at＄each.How much did the shopkeeper earn for rackets?10015010 A.＄200 B.＄250 C.＄300 D.＄500【答案】D【解析】(150−100)×10=500.26.Jack bought a batch of goods that he hoped to earn a profit after selling them.On the first day,he sold of his goods at a profit of.On the second day,he sold all remaining goods for a discount.If the total profit is of the planned profit,what was the discount rate?50\textbackslash%60\textbackslash%50\textbackslash%76\textbackslash%A.20\textbackslash%B.21\textbackslash%C.22\textbackslash%D.24\textbackslash%【答案】A【解析】Let the cost for the batch of goods be dollars.Jack finally earned:.On the first day he earned:.Profit for the second day:.Profit rate for the second day:.Percentage discount:.mm×50\textbackslash%×92\textbackslash%=0.38mm×60\textbackslash%×50\textbackslash%=0.30m0.38m−0.30m=0.08m0.08m(m−0.6m)=20\textbackslash%1−(1+20\textbackslash%)(1+50\textbackslash%)=20\textbackslash%27.Paul has books,and Jenny has more books than Paul.How many books do Paul and Jenny have together?136 A.20 B.15 C.22 D.23 E.32【答案】E【解析】Jenny has books.So,there are books in total.13+6=1913+19=32 28.In the land of Seuss,a plate of green eggs costs twice as much as a plate of ham.If a plate of ham costs￠,how much would pay for plates of green eggs and plates of ham?5123 A.￠40 B.￠35 C.￠30 D.￠25【答案】B【解析】Since a plate of green eggs costs twice as much as a plate of ham,a plate of the eggs costs￠.The cost of plates of eggs and plates of ham is￠￠￠￠￠.10232×10+3×5=20+15=35 29.The sum of positive whole numbers is times their difference.When the larger is divided by the smaller,the quotient is．23 A.2 B.3 C.4 D.5【答案】A【解析】The sum must be a multiple of 3.There are many examples,e.g.,2&1,4&2,10&5,etc.The quotient is always 2.30.At the 2018 Tompkins County Fair a vendor is offering a"fair special"on shoes.If you buy one pair of shoes at the regular price of 8034text%text regular price did he save?(adapted from 2013 AMC 8,Question#12)\textbackslash,yougetasecondpairatadiscount,andathirdpairathalftheregularprice.Jamestookadvantageofthe"fairspecial"tobuythreepairs.Whatpercentageofthe240 A.28 B.30 C.36 D.38 E.40【答案】A【解析】First,the amount of money one will pay for three hats without the discount 24080+0.66×80+(1)/(2)×80=text Finding the percentage yields To find the percent saved,we have=\textbackslash.Then,findtheamountofmoneyusingthediscount:172.8172.8240=72\textbackslash%100\textbackslash%−72\textbackslash%=28\textbackslash%31.I had dozen socks in my drawer,but I lost pairs.How many socks do I now have in my drawer?32 A.32 B.34 C.36 D.40【答案】A【解析】I had dozen socks in my drawer,which is socks.When I lost pairs,I lost socks,so I had socks left.3362432 32.Mike and Jack compete in the long jump.Mike jumps twice as far as Jack once.Mike jumps three times.How many times can jack jump the distance equal to Mike？(adapted from Math kangaroo Problems,Level,Question#)20081−26 A.2 B.6 C.3 D.4 E.5【答案】B【解析】We can imagine the distance of Jack’s long jump as,and the distance of Mike’s long jump as.The distance that Mike jumps three times is=.Jack needs to jump times.122×366÷1=6 33.NBA playoffs are held annually.The nd NBA playoffs were held in.When Cindy was years old,the th NBA playoffs were held.How old is Cindy in?6220087662022 A.14 B.15 C.16 D.17 E.18【答案】D【解析】66−62+2008=20127+(2022−2012)=17 34.Rina bought a handbag for＄60 at a discount of 20\textbackslash%.Ana paid＄67.5 for the same handbag.What was the discount rate given to Ana?A.10\textbackslash%B.12\textbackslash%C.15\textbackslash%D.18\textbackslash%【答案】A【解析】Original price:.Discount for Ana:.60÷(1−20\textbackslash%)=75(75−67.5)÷75=10\textbackslash%35.SASMO 2014 P2 Q5 What number between 37 and 47 is exactly divisible by both 2 and 3?A.38 B.39 C.42 D.44 E.45【答案】C【解析】6 x 7=42 36.If each fork costs＄,each spoon costs＄,and each knife costs＄,what is the total cost of forks,spoons,and knives?678345 A.＄40 B.＄46 C.＄80 D.＄86【答案】D【解析】forks cost＄＄.spoons cost＄＄.knives cost＄＄.They cost a total of＄＄＄＄.36×3=1847×4=2858×5=4018+28+40=86 37.A given month has days,and it has four Mondays and four Thursdays.What day of the week is the of this month?3120th A..$$Wednesday B.Thursday C.Friday D.Sunday【答案】A【解析】It implies that there are four Mondays,four Tuesdays,four Wednesdays,and four Thursdays.Similarly,there are five Fridays,five Saturdays,and five Sundays.The first day of the month therefore must be a Friday..The day of this month is a Wednesday,which is the day after Friday,inclusive.20÷7=2R620th6th 38.Grandpa suggested dividing all the peanuts between the family members in the following way:one person would get kilos,two people would get kilos each,four people would get kilos each,one person would get kilos,and one person would not get any peanuts.Grandma suggested dividing the peanuts equally among all of the family members.How many people would get more peanuts in grandma’s suggestion than grandpa’s?5426 A.3 B.4 C.5 D.6 E.7【答案】C【解析】Grandma’s suggestion:Thus,there are people get more peanuts.(1×5+2×4+4×2+1×6+1×0)÷(1+2+4+1+1)=27÷9=34+1=5 39.Anna is years old and the age of her mother is times that of Anna.How old will Anna’s mother be when Anna’s mother is twice as old as Anna?(Math kangaroo Problem,Level)1045−6 A.40 B.50 C.60 D.70 E.80【答案】C【解析】The age difference between them is,which stays the same forever.Then,when Anna’s mother is twice as old as Anna,Anna should be years old,then her mom should be.(4−1)×10=303030×2=60 40.If watermelons can serve people,I need watermelons for people.21560 A.4 B.6 C.8 D.12【答案】C【解析】If melons can serve people,I need melons for people.2154×2=84×15=60 41.On Kellin’s th birthday,Allen was four times her age.On Kellin’s th birthday,how old was Allen?1324 A.39 B.44 C.52 D.63 E.74【答案】D【解析】On Kellin’s th birthday,Allen was four times her age,that is.It is then eleven years until Kellin’s th birthday,so Allen’s age at that time was.13522452+11=63 42.A glass contains of water.The water takes up of the volume of the glass.What is the volume of the glass,in milliliters?240ml23 A.60 B.100 C.120 D.270 E.360【答案】E【解析】240÷23=360.43.At the pumpkin festival,Mike brought a pounds pumpkin.Mary’s pumpkin weighed pounds more than Mike’s.How many pounds is Mary’s pumpkin？(adapted from Math kangaroo Problems,Level,Question#)10520091−26 A.28 B.16 C.18 D.20 E.15【答案】E【解析】Mary’s pumpkin weighs pounds more than Mike’s,so it’s pounds.510+5=15 44.Water makes up of the weight of Kubus the Camel when he is thirsty.After he drinks,Kubus weighs kg and water makes up of his weight.What is the weight of Kubus the Camel when he is thirsty?(Math Kangaroo Problem,Level,Question#)84\textbackslash%80085\textbackslash%20019−1016 A.kg672 B.kg680 C.kg715 D.kg720 E.kg750【答案】E【解析】The ratio between the thirsty Kubus and the water he drank:.So,the weight of the thirsty Kubus is:kg.(100−85):(85−84)=15:1800×1515+1=750 45.Arthur decided to lose weight.On the first month,he lost kg.He decided that each month he would be losing twice as much kilograms as the month before.How many kilograms did Arthur lose in total in the first three monthes?2 A.2 B.6 C.8 D.12 E.14【答案】E【解析】2+4+8=14 46.How many tens must be added to to make?}tens215985 A.770 B.77 C.120 D.1200【答案】B【解析】985−215=770770÷10=77 47.Determine whether 2008 is a common year or a leap year.A.a common year B.a leap year【答案】B【解析】2008÷4=502,so 2008 is a leap year.48.A sugar solution contains grams of pure sugar.How many grams of solution are there?15\textbackslash%18 A.grams90 B.grams100 C.grams120 D.grams150【答案】C【解析】18÷15\textbackslash%=120 grams.49.If March is Monday,what day of the week is st March?19th1 A.Sunday B.Monday C.Wednesday D.Thursday E.Saturday【答案】D【解析】There are 19 days between March and st March.Apart from th March itself,there are days,18 days=2 week and 4 days.Therefore,st March is Thursday.19th119181 50.Elsa started to raise some chicken in her farm in January.The number of chicken triples every month,while she goes to the market to sell chicken every month.On April when she came back from the market,she found she had no chicken left.How many chicken did she raise in January?81 A.30 B.35 C.40 D.45 E.50【答案】C【解析】81÷3=27(81+27)÷3=36(36+81)÷3=39(39+81)÷3=40 51.A pencil is one dollar,and a pencil box is two dollars more expensive than a pencil.Jimmy has seven dollars and bought a pencil box.How many pencils can Jimmy buy？(adapted from Math kangaroo Problems,Level,Question#)20091−26 A.8 B.6 C.1 D.2 E.4【答案】E【解析】A pencil box costs two dollars more than a pencil,so it’s dollars..So He can buy pencils.1+2=37−3=44÷1=4 52.The February of a given year has five Fridays.What day of the week was January th of that year?31 A.Friday B.Saturday C.Wednesday D.Thursday【答案】D【解析】There are seven days in a week.In order to have five Fridays,a month has at least days.Since February has at most days,the st and th days of this February must be Friday,which means that January is Thursday.4×7+1=292912931 53.George takes 4 minutes to go from 1st floor to 3rd floor.He just realised that he forgot his water bottle on the 5th floor.He is now on the 2nd floor.How long would it take him to get his watter bottle?A.4 minutes B.5 minutes C.6 minutes D.8 minutes E.None of the above.【答案】C【解析】2 gaps between 1st to 3rd floor.hence,4/2=2 minutes per gap.Moving from 2nd to 5th floor,3 gaps->3 gaps x 2 minutes per gap=6 minutes.54.Billy has three times as many llamas as lambs.Milly has twice as many lambs as llamas.They have animals in total.How many of the animals are llamas?17 A.5 B.6 C.7 D.8 E.9【答案】E【解析】Let Billy have lambs and llamas.Let Milly have llamas and lambs.Therefore,as they have animals in total,.The only positive integer solution of this equation is,.So the number of llamas is.b3bm2m174b+3m=17b=2m=33b+m=3×2+3=6+3=9 55.If March is Monday,what day of the week is th March?15th26 A.Sunday B.Monday C.Wednesday D.Friday E.Saturday【答案】D【解析】There are 11 days between March and th March.11 days=1 week and 4 days.Therefore,th March is Friday.15th2626 56.Sarah is tall.Benny is taller than Sarah.What is the total height of the children?Round off your answer to decimal place.1.14m0.23m21 A.1.4m B.2.1m C.2.5m D.2.6m【答案】C【解析】Benny’s height Total heights of the children(rounded to d.p.)=1.14+0.23=1.37m2=1.14+1.37=2.51=2.5m1 57.There are students in Pat’s math class.If there are twice as many girls as boys in the class,how many boys are in the class?30 A.5 B.8 C.10 D.20【答案】C【解析】There are students in Pat’s math class.With twice as many girls as boys,the class has girls and boys.302010 58.Lily’s family used tons of water in the first two months,and an average of tons of water on the remaining three tests.The average tons of water for the five months was.2131 A.120 B.22 C.23 D.27 E.25【答案】D【解析】Total tons of water:Average tons of water:21×2+31×3=135135÷5=27 59.Mr.Smith wants to cut a wood into pieces.It takes him minutes to cut a piece.How many minutes will he use to cut?52 A.3 B.4 C.8 D.10 E.12【答案】C【解析】Mr.Smith needs to cut times,which means he needs to use minutes to cut.5−1=44×2=8 60.Paul had eight\textbackslash$5-notes at first.He exchanged all his money for\textbackslash$2-notes only.How many notes did he have in the end?A.16 B.20 C.40 D.80【答案】B【解析】He has 5×8=text Number of 2=text=20=\textbackslash40\textbackslash−notes40÷\textbackslash 61.Farmer Dunphy has metres of fencing.He wants to make a closed rectangular pen.He uses a long wall for one of the sides.Each side of the pen is a whole number in metres.What is the largest area that the pen can be?16 A.25m2 B.27m2 C.30m2 D.28m2 E.32m2【答案】E【解析】,when,the largest area is m2.a+2b=16a=2b=88×(8÷2)=32 62.In how many places do we need to break a wooden stick in order to get pieces?(1999 Math Kangaroo Problem,Level 3-4,Question#3)5 A.3 B.4 C.5 D.6 E.It depends on how long the stick is.【答案】B【解析】5−1=4 63.Tom starts a savings account with＄at a bank.The interest rate is per year.How much interest will he earn in his savings account at the end of the second year?4,0002\textbackslash%A.＄160 B.＄161.6 C.＄4,160 D.＄4,161.6【答案】B【解析】4000×(1+2\textbackslash%)×(1+2\textbackslash%)−4000=161.6.64.If there are pencils in each box,how many pencils are in boxes?880 A.10 B.88 C.640 D.808【答案】C【解析】There are pencils in boxes.80×8=64080 65.At which of these times is the angle between the minute hand and the hour hand of a clock equal to?150∘A.9pm B.8pm C.6pm D.5pm E.4pm【答案】D【解析】At all the times given,the minute hand is pointing to.When the minute hand is pointing to and the angle between the hands is,the hour hand has turned of a complete turn.Therefore the hour hand will point at and the time will be.(There are other times when the angle between the hands is but,of these,only at does the minute hand point to and is not one of the times given.)1212150∘150360=51255pm150∘7pm127pm 66.Lisa is buying potatoes at a grocery store.She can either spend dollars on a bag or dollars on a bag.Whic is the cheaper one?1025−lb1535−lb A.The bag25−lb B.The bag35−lb【答案】A【解析】So,the answer is.1025\textasciitilde\textbackslash$/lb=0.4\textasciitilde\textbackslash$/lb1535\textasciitilde\textbackslash$/lb=0.43\textasciitilde\textbackslash$/lb1025<1535A 67.Ali is arranging the books on his bookshelves.He puts half his books on the bottom shelf and two-thirds of what remains on the second shelf.Finally he splits the rest of his books over the other two shelves so that the third shelf contains four more books than the top shelf.There are three books on the top shelf.How many books are on the bottom shelf？A.60 B.50 C.40 D.30 E.20【答案】D【解析】Since Ali places half his books on the bottom shelf and of the remainder on the second shelf,he places of his books on the second shelf,leaving of his books for the top two shelves.There are three books on the top shelf and four more,so seven books,on the third shelf.Therefore these books represent of the total number of books on the bookshelves.Hence there are books on the bookshelves and half of these,or books,on the bottom shelf.2323×12=13(1−12−13)=1610166030 68.Given that August 15th of a given year is a Friday,What day is June 10th of the same year?A.Monday B.Tuesday C.Friday D.Sunday【答案】B【解析】30−10+31+15=66÷7=9r3$$Tuesday 69.The selling price of a television is＄4800 and its profit percentage is 20\textbackslash%.If the cost of the television is not changed,how much should it be sold for if the profit percentage has to be 75\textbackslash%?A.dollars6000 B.dollars6500 C.dollars7000 D.dollars8000【答案】C【解析】dollars,dollars.4800(1+20\textbackslash%)=40004000×(1+75\textbackslash%)=7000 70.The upper shelf of a bookshelf has books.The lower shelf has books.How many books should be taken from the upper shelf to the lower shelf so that both shelves will have the same number of books?14339 A.52 B.104 C.91 D.46【答案】A【解析】,=.143−39=104104÷252 71.If Pip was 18 years old 5 years ago,how old will he be 7 years from now?A.22 B.24 C.16 D.30 E.32【答案】D【解析】18+5+7=30 72.My dad,Burly Ird,says he has to moan at me two school mornings in every three to get me out of bed.In a twelve-week term,with five schooldays each week,on how many mornings will he moan at me?A.30 B.35 C.36 D.40 E.42【答案】D【解析】The number of moaning mornings is 23×12×5=40.73.In one year,there were 5 Sundays in February.What day of the week was 3rd Feb?A.Saturday B.Monday C.Tuesday D.Wednesday【答案】C【解析】Normally,there are 28 days in February,which has 4 Sundays at most.Therefore,it could be the leap year with 29 days in February.If there are 5 Sundays,the first day in Februray should be Sunday,so Feb 3rd is Tuesday.74.The cost of a computer is dollars and the profit percentage is for each computer.Find the price of the computer.350012\textbackslash%A.dollars3850 B.dollars3920 C.dollars4200 D.dollars4550【答案】B【解析】The price of the computer is:dollars.3500×(1+12\textbackslash%)=3920 75.Given that March th,was Friday,what day was April th,?262021202021\textasciitilde A.Monday B.Tuesday C.Thursday D.Wednesday E.Friday【答案】B【解析】Counting from March th,,after days it was March st,.After days it was April th,.In total,there were days.,which means April th,was Tuesday.26202131−26=5312021202020215+20=2525÷7=3R4202021 76.Tom,Joanna and Jacky each come up with a number.The sum of the three numbers is.Tom’s number is twice Joanna’s number,and Joanna’s number is three times Jacky’s number.What are these three numbers?360 A.36 B.108 C.216 D.360【答案】C【解析】Jacky’s number is”,so Joanna’s number is”,and Tom’s number is”.Jacky’s number:.Joanna’s number:.Tom’s number:.136360÷(6+3+1)=3636×3=10836×6=216 77.(AMC Problem,Question#)Niki usually leaves her cell phone on.If her cell phone is on but she is not actually using it,the battery will last for hours.If she is using it constantly,the battery will last for only hours.Since the last recharge,her phone has been on hours,and during that time she has used it for minutes.If she doesn’t use it any more but leaves the phone on,how many more hours will the battery last?2004812243960 A.7 B.8 C.11 D.14 E.15【答案】B【解析】When not being used,the cell phone uses up of its battery per hour.When being used,the cell phone uses up of its battery per hour.Since Niki’s phone has been on for hours,of those simply on and being used to talk,of its battery has been used up.To drain the remaining the phone can last for more hours without being used.12413988(124)+1(13)=231313124=(B)8 78.Mike bought five ice creams.He had three brothers and he gave each brother an ice cream.How many ice creams was left?(adapted from Math kangaroo Problems,Level,Question#)20111−23 A.1 B.3 C.4 D.2 E.0【答案】D【解析】Each brother gets one ice cream,and three brothers need three ice cream,so Mike has ice cream left.5−3=2 79.Elmp visits the Sesame Street Park every Wednesday.If the 1st of January 2017 was Sunday and February has 28 days,what was the last date in March 2017 in which Elmo visited Sesame Street Park?A.28th March B.29th March C.30th March D.31st March E.None of the above.【答案】B【解析】Draw the calendar out.80.A construction team is going to build a road of miles.The plan is that it finishes%of the road in the first month,%of the road in the second month and%of the road in the third month.How many miles can be built after two months?50304030 A.15 B.20 C.30 D.35【答案】D【解析】%+%=%,%=After two months,miles of road can be built.30407050×703535 81.Kate bought apple pies and Lucy bought cupcakes.They each paid the same amount of money and together they paid dollars.How many dollars does cupcake cost?24161 A.2 B.4 C.6 D.10 E.12【答案】A【解析】cupcakes cost dollars,so one cupcake cost dollars.416÷2=88÷4=2 82.Esther made paper stars and she made times as many paper stars as Amy.How many paper stars did Amy make?183 A.6 B.8 C.9 D.12【答案】A【解析】omitted 83.In a class of pupils,participated in basketball,participated in football,participated in softball and participated in squash.Find the minimum percentage of pupils who participated in all the four sports events.80\textbackslash%85\textbackslash%74\textbackslash%68\textbackslash%A.7\textbackslash%B.10\textbackslash%C.12\textbackslash%D.15\textbackslash%E.None of the above【答案】A【解析】Least percentage of pupils who participated in both basketball and football,Least percentage of pupils who participated in basketball,football and softball,Least percentage of pupils who participated in basketball,football,softball and squash.=80\textbackslash%+85\textbackslash%−100\textbackslash%=65\textbackslash%=65\textbackslash%+74\textbackslash%−100\textbackslash%=39\textbackslash%=39\textbackslash%+68\textbackslash%−100\textbackslash%=7\textbackslash%84.Simon has two identical aquariums.There are quarts of water in one,and quarts of water in the other.How many quarts of water does Simon need to pour from the second aquarium into the first in order to have the same amount of water in both?2642 A.6 B.16 C.10 D.8【答案】D【解析】Difference:Move:Half of42−26=1616=8 85.In years,Li will be times as old as he is now.How old will he be in years?20310 A.10 B.20 C.30 D.50【答案】B【解析】In years,Li will be times his age now,so must be twice his age now.Thus,Li is now and will be in years.20320102010 86.When Paul is years old,his brother Peter is years old.How old is Paul when Peter is years old?Paul is}years old.4710 A.6 B.7 C.8【答案】B【解析】We can find their age difference is.It will never change.So when Peter is years old,Paul is years old.7−4=31010−3=7 87.If Paul gives candies to Billy,they will have the same number of candies.At beginning,Paul has candies.How many candies does Billy have,originally?617 A.5 B.6 C.7 D.8 E.9【答案】A【解析】Their difference:Billy:6+6=1217−12=5 88.Su Li has the same number of ten-cent and fifty-cent coins.The total value is＄6.How many coins does she have in all?A.10 B.20 C.36 D.60 E.None of the above【答案】B【解析】Thus,,in total we have10u+50u=6001u=102u=20 89.Andy is years old and his mother is years old now.In how many years’time will the sum of their ages be?185490 A.9 B.14 C.18 D.28【答案】A【解析】18+54=7290−72=1818÷2=9 90.Together,Mom Kangaroo and her son Jumper weigh kilograms.Mom Kangaroo alone weighs kilograms.How much does Jumper weigh?(Math kangaroo Problems,Level,Question#)605220191−23 A.2 kilograms B.4 kilograms C.8 kilograms D.30 kilograms E.46 kilograms【答案】C【解析】Jumper’s weight is Mom Kangaroo and Jumper’s weight minus the mom’s weight.91.There are three books,Chinese,Math,and English.Sissy wants to put them in bookcase.How many ways are there for three books to put?A.6 B.5 C.4 D.3【答案】A【解析】List out all the possible ways in order.CAECEAACEAECECAEAC 92.Alex had 9 on lunch.How much did Alex spend in the shop?76.Hespentsomeofitinashop.ThenhegavehalfofwhathehadlefttoCharlie.CharliespentaquarterofwhatAlexgavehimonlunch.Charliespent A.$4 B.$12 C.$14 D.$36 E.$40【答案】A【解析】Charlie’s 1/4 is 9,so Charlie gets 4×9=36 dollars,and Alex is left with 36+36=72 dollars,so he spends 76-72=4 dollars 93.Min Ho deposited＄20000 into a bank at the beginning of the year.The annual interest for depositing money into the bank was 5\textbackslash%.How much did Min Ho have in the bank at the end of the year if he did not take out any money from the bank?．A.\textbackslash$1000 B.\textbackslash$19000 C.\textbackslash$21000 D.\textbackslash$31000【答案】C【解析】He has 20000×1.05=\textbackslash21000$at the end of the year.94.The pages of a book are numbered 1,2,3.In total,it takes 852 digits to number all the pages of the book.What is the number of the last page?⋯A.215 B.314 C.320 D.329 E.422【答案】C【解析】omitted jmc 2007#24 95.Eddie and Frank can complete a job together in days.Eddie can do it alone in days.Frank can do it alone indays.1520 A.30 B.40 C.45 D.60【答案】D【解析】,.115−120=1601÷160=60 96.There are pupils in Pip’s school,with more girls than boys.How many girls are at Pip’s school?60030 A.270 B.300 C.315 D.330 E.345【答案】C【解析】Let there be girls in Pip’s school.Then there are boys at the school.So.Therefore,that is.g(g−30)g+g−30=6002g=630g=315 97.A ship was attacked by pirates.One by one the pirates climb a rope to get on the ship.The pirate captain was the th pirate to climb in line,and there were as many pirates in front of him as behind him.How many pirates climbed the rope?(2015 Math Kangaroo Problem,Level 1-2,Question#18)8\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde A.7 B.8 C.12 D.15 E.16【答案】D【解析】The pirate captain was the th pirate and there were as many pirates in front of him as behind him,which means there were pirates in front of him and there were also pirates behind him.The total number of pirates is.8777+7+1=15 98.Half a loaf of bread costs pence more than one quarter of a loaf of bread.How many pence does a whole loaf of bread cost?6 A.6 B.12 C.18 D.24 E.30【答案】D【解析】One quarter of a loaf of bread is.”Half a loaf of bread is.”One quarter of a loaf of bread:.A whole loaf of bread:.126÷(2−1)=66×4=24 99.After Sally takes 20 shots,she has made of her shots.After she takes 5 more shots,she raises her percentage to.How many of the last 5 shots did she make?(2004 AMC 8,Question#6)40\textbackslash%52\textbackslash%A.1 B.2 C.3 D.4 E.5【答案】E【解析】Sally made shots originally.Letting be the number of shots she made,we have.Solving for gives us0.4*20=8x8+x25=0.52xx=5 100.My first day of vacation is May.My last day of vacation is May of the same year.How many days of vacation do I have?1020 A.9 B.10 C.11 D.12【答案】C【解析】NA 101.In a jar of red,green,and blue marbles,all but are red marbles,all but are green,and all but are blue.How many marbles are in the jar?(AMC problem,Question#)6842012819 A.6 B.8 C.9 D.10 E.12【答案】C【解析】Suppose there are red marbles,green marbles,and blue marbles.Thus,we can get,①②③:,.xyz{x+y=4①\textbackslash\textbackslashy+z=6②\textbackslash\x+z=8③++2x+2y+2z=18x+y+z=9 102.After Anna spends of her money and loses of the remainder,she then has 10$left.She started with．1312\textbackslash A.30\textbackslash B.45\textbackslash C.50\textbackslash D.60\textbackslash【答案】A【解析】After Anna spends of her money,she has left.If she loses of this,she has left.Since10(3)/(3)=3×text1323121313=\textbackslash,\textbackslash$10=30 103.Given March 25th of a certain year is Monday,what day of the week would May 1st fall on this year?A.Sunday B.Monday C.Tuesday D.Wednesday【答案】D【解析】The cycle includes seven days,Monday,Tuesday,Wednesday,Thursday,Friday,Saturday and Sunday.There are in total days from March to May.Since，13^(rd)day in the cycle,it is a Wednesday.7+30+1=3825138÷7=5R3$$Mayisthe 104.In an arts and crafts class,the students cut out some triangles,quadrilaterals and pentagons.All the shapes combined have sides.Among them,there are pentagons and the number of quadrilaterals is more than that of triangles.How many quadrilaterals are there?394282 A.90 B.95 C.100 D.105【答案】A【解析】Let represent the number of quadrilaterals,thus the number of triangles can be represented as.So we have.implying that.Therefore there are quadrilaterals.x(x−82)2×5+4x+3(x−82)=394x=9090 105.Sam wants to use two kinds of sugar water with concentrations of and to make a sugar water of g with a concentration of.He correctly calculated the required ratio of the two solutions,but reversed the two bottles of sugar water when preparing them.The actual concentration of the wrongly mixed sugar water is}.5\textbackslash%20\textbackslash%30015\textbackslash%\textbackslash%A.8 B.10 C.12.5 D.15 E.None of the above【答案】B【解析】NA 106.If February contains Friday the 13th,what day of the week is February 1st?．A.Sunday B.Monday C.Wednesday D.Thursday E.Saturday【答案】A【解析】We can count backward by days or by weeks.Count a few weeks back to find that February is a Friday.Then count a few days back to find that February is a Sunday.61 107.Eddie spends minutes to climb from the first floor to the third floor at a constant speed.At this speed,how many minutes does Eddie need to climb from the first floor to the sixth floor?12 A.24 B.30 C.36 D.42 E.48【答案】B【解析】12÷(3−1)=66×(6−1)=30 108.The number of months in a year minus the number of days in a week equals．A.5 B.7 C.9 D.19【答案】A【解析】The number of months in a year minus the number of days in a week is 12−7=5.109.At the 2018 Tompkins County Fair a vendor is offering a"fair special"on hats.If you buy one hat at the regular price of 3040text%text regular price did he save?(adapted from 2013 AMC 8,Question#12)\textbackslash,yougetasecondhatatadiscount,andathirdpairathalftheregularprice.Jamestookadvantageofthe"fairspecial"tobuythreehats.Whatpercentageofthe90 A.15 B.20 C.25 D.30 E.40【答案】D【解析】First,the amount of money one will pay for three hats without the discount 9030+0.6×30+(1)/(2)×30=text Finding the percentage yields To find the percent saved,we have=\textbackslash.Then,findtheamountofmoneyusingthediscount:636390=70\textbackslash%100\textbackslash%−70\textbackslash%=30\textbackslash%110.Find the average of these numbers:7,9,5,3,6 A.3 B.4 C.5 D.6【答案】D【解析】D 111.There were some cupcakes in a bakery.First,Jade ate half of the cupcakes.Then,Neil ate half of the remaining cupcakes.Finally,Terry ate cupcakes and there were cupcakes left.At beginning,how many cupcakes were there in the bakery?62 A.24 B.32 C.48 D.12【答案】B【解析】6+2=88+8=1616+16=32 112.In a zoo,there are three monkeys.The monkeys are all younger than years old.None of them has the same age,and all their ages are whole numbers.The product of their ages is.What is the sum of their ages?58 A.4 B.6 C.7 D.8 E.9【答案】C【解析】The whole numbers smaller than are:(age cannot be)The product of three numbers is.Their sum:51,2,3,4081×2×4=81+2+4=7 113.After every steps that Pip takes forward,he takes steps backwards.Each step is.Pip starts at one end of a hall.Pip will first reach the other end after}steps.321m100m A.100 B.488 C.490 D.500【答案】B【解析】3+2=5,3-2=1 The pattern:Pip move forward 1m in 5 steps100−3=9797×5+3=488 114.Susan is years old.Her sister is one year younger and her brother is one year older.What is the sum of the ages of the three siblings?6 A.10 B.15 C.18 D.21 E.30【答案】C【解析】Susan’s sister is years old and her brother is years old.The sum of the ages of the three siblings is.6−1=56+1=75+6+7=18 115.Peter has grams of a salt solution.How many grams of salt should he add to make it a solution?2020\textbackslash%25\textbackslash%A.grams1 B.grams43 C.grams4 D.grams5【答案】B【解析】Method:Suppose ounces of salt should be added to the solution:.Method:.1x20×20\textbackslash%+x20+x=25\textbackslash%\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitildex=43220×(1−20\textbackslash%)÷(1−25\textbackslash%)−20=43 116.Bridget bakes loaves of bread for her bakery.She sells half of them in the morning for＄each.In the afternoon she sells two thirds of what she has left,and because they are not fresh,she charges only half price.In the late afternoon she sells the remaining loaves at a dollar each.Each loaf costs＄for her to make.In dollars,what is her profit for the day?(AMC A Problem,Question#)482.500.752014103 A.24 B.36 C.44 D.48 E.52【答案】E【解析】She first sells one-half of her loaves,or loaves.Each loaf sells for＄,so her total earnings in the morning is equal to＄＄.This leaves loaves left,and Bridget will sell of them for a price of＄＄.Thus,her total earnings for the afternoon is＄＄.Finally,Bridget will sell the remaining loaves for a dollar each.This is a total of＄＄.The total amount of money she makes is equal to＄.However,since Bridget spends＄making each loaf of bread,the total cost to make the bread is equal to＄＄.Her total profit is the amount of money she spent subtracted from the amount of money she made,which is.48482=242.5024×2.50=602423×24=162.502=1.2516×1.25=2024−16=81×8=860+20+8=880.750.75×48=3688−36=52⇒(E)52 117.At the"Think Flea Market",a vendor is offering a"fair special"on sandals.If you buy one pair of sandals at the regular price of 5040 text%text regular price did he save?(adapted from 2013 AMC 8,Question#12)\textbackslash,yougetasecondpairatadiscount,andathirdpairathalftheregularprice.Owentookadvantageofthe"fairspecial"tobuythreepairsofsandals.Whatpercentageofthe150 A.25 B.30 C.33 D.40 E.45【答案】B【解析】First,find the amount of money one will pay for three sandals without the discount.We have 50×3=text Then,find the amount of money using the discount:105(105)/(150)=70 text%100 text%-70 text%=(B)30\textbackslashsandals15050+0.6×50+12×50=\textbackslash.FindingthepercentageyieldsTofindthepercentsaved,wehave 118.Tom,Jim and Peter earned£together for painting a wall.The ratio of Tom’s reward to Jim’s reward is.The ratio of Jim’s reward to Peter’s reward is.How much money did Tom earn?6203:46:5 A.£60 B.£180 C.£80 D.£240 E.£200【答案】B【解析】,,their rewards were in the ratio of.,.3:4=9:126:5=12:109:12:10620÷(9+12+10)=2020×9=180 119.My mom’s birthday is on Sunday,and my dad’s birthday is days after it.What day of the week will my dad’s birthday be?55 A.Sunday B.Monday C.Tuesday D.Thursday E.Saturday【答案】E【解析】55÷7=7R6.It is Saturday.120.John bought some cupcakes,and each of them cost dollars.He gave the salesperson dollars and got dollars as change.How many cupcakes did John buy?(Adapted from 2005 Math Kangaroo Problem,Level 3-4,Question#3)4204 A.6 B.8 C.10 D.5 E.4【答案】E【解析】(20−4)÷4=4 121.There are two bookshelves,A and B.Shelf A has books,and shelf B has books.We need to take books from shelf A to shelf B,so that books in shelf B is three times more than self A.1100300 A.750 B.800 C.850 D.900【答案】A【解析】The sum is unchanged,which is 1400，1400÷(3+1)=350，1100−350=750．122.A mixture of 45 liters of paint is red tint,yellow tint and water.Five liters of yellow tint are added to the original mixture.What is the percent of yellow tint in the new mixture?(adapted from 2007 AMC 8,Question#17)20\textbackslash%30\textbackslash%50\textbackslash%A.33 B.35 C.37 D.39 E.40【答案】C【解析】Since of the original 45 liters of paint was yellow,and 5 liters of yellow paint were added to make the new mixture,there are liters of yellow tint in the new mixture.Since only 5 liters of paint were added to the original 45,there are a total of 50 liters of paint in the new mixture.This gives of yellow tint in the new mixture,which is(C)37.30\textbackslash%13.5+5=18.537\textbackslash%123.Twice my house number,plus,is.What’s my house number?418 A.5 B.7 C.14 D.40【答案】B【解析】Twice,plus is,so is my house number74187 124.Alex is years older than her two sisters who are twins.The sum of the ages of all three girls is years old.How old is Alex?(Math Kangaroo Problem,Level-,Question#)8322007569 A.12 B.18 C.16 D.20 E.14【答案】C【解析】The age of each sister is years old.Thus,Alex is years old.(32−8)÷3=88+8=16 125.Jacob and Zain take pencils from a box of pencils without replacing them.On Monday Jacob takes of the number of pencils that Zain takes.On Tuesday Jacob takes of the number of pencils that Zain takes.On Wednesday morning the box is empty.How many pencils does Jacob take?212312 A.8 B.7 C.6 D.5 E.4【答案】A【解析】Let the number of pencils Zain takes on Monday and Tuesday be and respectively.Therefore.Hence,when we multiply the equation through by to eliminate the fractions and simplify,we obtain.Since and are both positive integers and since the units digit of is,the units digit of is and hence.Therefore and hence the number of pencils Zain takes is.Therefore the number of pencils Jacob takes is.xyx+23x+y+12y=21610x+9y=126xy10x09y6y=4x=99+4=1321−13=8 126.The fruit store sold a total of boxes of apples in the first three days of last week,and an average of boxes of apples per day in the last four days.How many boxes of apples did this fruit store sell on average each day last week?3318 A.13 B.14 C.15 D.16【答案】C【解析】33+18×4=105105÷7=15 127.The length of Amy’s string is cm.The length of David’s string is cm.What is the total length of their strings?1224 A.cm16 B.cm26 C.cm36 D.cm46【答案】C【解析】12+24=36 128.If a construction company can construct a meter highway in days,how many days does it take to construct a meter highway at the same rate?1000−52600−A.10 B.11 C.12 D.13 E.14【答案】D【解析】It can construct meters per day.To construct meters:days.1000÷5=20026002600÷200=13 129.A school bought volleyballs and basketballs in total for＄.Each basketball costs＄.Each volleyball costs＄.How many basketballs did the school buy?123403025 A.4 B.5 C.6 D.7 E.8【答案】E【解析】If all were basketballs,＄＄the total cost would be＄.＄＄＄There is a difference of＄.＄＄＄＄＄The school bought basketballs.12×30=360360360−340=202030−25=520÷5=412−4=88 130.Calculate(1)6+19=(2)15-8=A.26,7 B.25,8 C.26,8 D.25,7【答案】D【解析】Partition 6 into 1 and 5.19+1=20,20+5=25 Partition 8 into 5 and 3.15-5=10,10-3=7 131.Nate eats pizza slices every day.How many pizza slices will nate eat after a week?12 A.81 B.82 C.83 D.84【答案】D【解析】7×12=84 132.There is a tournament at the pool,First,children signed up and then another children signed up,Six teams with an equal number of members each are needed for the tournament,At least how many more children need to sign up so that,the six teams can be formed.(2017 Math Kangaroo Problem,Level 3-4,Question#13)1319 A.1 B.2 C.3 D.4 E.5【答案】D【解析】The total number of children is,To form six teams with the same number of children in each team,we divide by,,The remaining children will need more children to form the sixth team.13+19=3232632÷6=5R224 133.There are roughly three million people who live in Wales.Nearly six hundred thousand of them speak Welsh.Approximately what percentage of people living in Wales speak Welsh?A.10\textbackslash%B.20\textbackslash%C.30\textbackslash%D.40\textbackslash%E.50\textbackslash%【答案】B【解析】The fraction of people living in Wales who speak Welsh is 6000003000000.This can be simplified to 15,and so the percentage is 20\textbackslash%.134.At dinner,Mom tells Alice to take knifes and forks out of the cupboard and put it on each plate.It is known that there are six plates,four forks,and six knives.How many forks or knives does Alice need to get out of the cupboard?(adapted from Math kangaroo Problems,Level,Question#)20111−26 A.a fork B.a knife C.two forks D.two knives E.None of the above【答案】C【解析】Each plate needs a knife and a fork.There are six plates here,so 1pairs of knives and forks are required,that is,six knives and six forks.But now there are only four forks.forks are required.6×=66−4=2 135.Linda was born on May th.Her brother was born days earlier than her.When her brother was born?(adapted from Math kangaroo Problems,Level,Question#)6920081−24 A.April th27 B.May th15 C.April th28 D.April th26 E.May th16【答案】A【解析】Nine days before May th is April th627 136.There are balls in a box:white balls,red balls and black balls.The number of white balls is times greater than the number of red balls.How many black balls are there in the box?(Math Kangaroo Problem,Level,Question#)15719983−416 A.1 B.3 C.5 D.7 E.9【答案】D【解析】The numbers of white balls and red balls in total must be a multiple of,so from to,only itself can match the condition.Thus,there are black balls in the box.7+1=8115815−8=7 137.If a business owner has a 60,000 in his next best business opportunity,he has earne}100,000accountingprofitandcouldhavemadeexactly A.$160,000 in economic profits.B.$100,000 in economic profits.C.$40,000 in economic profits.D.neither an economic profit or loss.E.none of the above.【答案】C【解析】Accounting profit=revenue minus explicit costs.Economic profit=revenue minus both explicit and implicit costs.Accounting profit is always greater than economic profit as there’s always an opportunity cost.100,000 accounting profit minus the implicit cost of60,000=$40,000 in economic profit.138.Two motor-cyclists John and Kevin were apart and travelling towards each other at a constant speed.They started at the same time,meeting after hours.If Kevin started hours later than John,they would be apart hours after John started.At what speed was John travelling in?800km811270km8km/h A.50 B.5123 C.5212 D.5313 E.None of the above【答案】D【解析】Kevin’s speed Let John’s speed be..=70112=1403km/hxkm/h(x+1403)×8=800⇒x=100−1403=1603=5313km/h 139.February 8th,2016 is Monday.What day is March 30th,2016?A.Monday B.Tuesday C.Wednesday D.Thursday【答案】C【解析】,,it’s Wednesday29−8+30=5151÷7=7\textbackslashR\textasciitilde2 140.The largest possible sum of unequal even numbers,none greater than,is．4100 A.380 B.388 C.390 D.394【答案】B【解析】The largest possible sum is 100+98+96+94=388.141.There were some pieces of candy in a bowl.Sally took half of the pieces of candy.Then Tom took half of the pieces left in the bowl.After that,Clara took half of the remaining pieces.In the end,there were pieces of candy left in the bowl.How many pieces of candy were in the bowl at the beginning?6 A.12 B.18 C.20 D.24 E.48【答案】E【解析】6+6=1212+12=2424+24=48 142.Peter has ounces of a salt solution.How many ounces of salt should he add to make it a solution?2020\textbackslash%25\textbackslash%A.ounces1 B.ounces43 C.ounces4 D.ounces5【答案】B【解析】Method:Suppose ounces of salt should be added to the solution:.Method:.1x20×20\textbackslash%+x20+x=25\textbackslash%\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitildex=43220×(1−20\textbackslash%)÷(1−25\textbackslash%)−20=43 143.There were students in a class.Each student shook hands only once with the other students in the class.How many handshakes were there in total?87 A.28 B.36 C.49 D.56【答案】A【解析】7+6+5+4+3+2+1=28 144.If out of lightbulbs is defective and there are lightbulbs,how many of them are not defective?162016 A.5 B.336 C.1680 D.2016【答案】C【解析】out of of the lightbulbs are not defective.Thus lightbulbs are not defective.5620162016×56=1680 145.In a very popular Chinese restaurant,all seats were filled and there were still customers in line outside the door.After some time,customers finish eating and leave the restaurant,and then more customers join the waiting line.How many people are still in line outside the door?81115 A.0 B.12 C.15 D.18 E.23【答案】B【解析】The line at the door started with people and more came in,for a total of people.After leaving customers,seats were empty,so the number of people left in line was.81523111123−11=12 146.Siti has bookmarks.If she were to give bookmarks to each of her classmates,she would need more bookmarks.How many classmates does Siti have?198618 A.12 B.24 C.30 D.36【答案】D【解析】198+18=216216÷6=36 147.If I start with,and begin to count by,my number will be．23\textquotesingles50th A.149 B.150 C.151 D.152【答案】A【解析】2+(50−1)×3=149.148.Factory can assemble televisions per hour and Factory can assemble televisions per hour.With these constant rates,if assembles televisions in a period,how many televisions can assemble within the same period?A20B30A300B A.300 B.400 C.450 D.600 E.900【答案】C【解析】Time:hours.So,Factory can assemble televisions.300÷20=15B15×30=450 149.Mike deposited＄10000 in the bank.He earned an interest of＄2100 at the end of the second year.What is the interest rate per year of this bank?A.21\textbackslash%B.11\textbackslash%C.10\textbackslash%D.9\textbackslash%【答案】C【解析】Suppose the interest rate is:m10000×(1+m)×(1+m)&=&10000+2100\textbackslash\textbackslashm&=&0.1 150.Given that May of a given year is a Wednesday,what day is May of the same year?430 A.Saturday B.Wednesday C.Thursday D.Tuesday E.Monday【答案】E【解析】days later,it will be May th.,which means May th is Monday.30−4=263026÷7=3R530 151.There are two factories producing the same kind of car parts.There are workers in factory,and every worker produces parts on average.Each worker produces parts on average in factory.Each worker can produce parts on average in two factories together.How many workers are there in factory?36A81101B89B A.38 B.34 C.24 D.22 E.18【答案】C【解析】36×(89−81)÷(101−89)=24 152.Alex and Bob love to fold cranes.For a bag of cranes,Alex will need hours to complete while Bob will need hours.One morning,Alex and Bob started to fold cranes at the same time.After minutes,Alex rested for minutes before continuing to fold cranes while Bob did not rest at all.When they finished a bag of cranes together,Alex folded more cranes than Bob.Find the value of.N233010N24N A.60 B.90 C.120 D.150 E.180 F.None of the above【答案】E【解析】E 153.Chole has crackers and she is distributing the crackers to her friends.How many crackers will each of them get?648 A.4 B.6 C.8 D.10【答案】C【解析】64÷8=8 154.Marko has pieces of candy and Tomo has pieces of candy.How many pieces of candy does Tomo need to give to Marko so that each boy has the same number of pieces of candy?917 A.2 B.3 C.4 D.5 E.6【答案】C【解析】Difference:Move:Half of17−9=88=4 155.There are trees on one side of a road.Workers plan to set one rubbish bin bwtween every two adjacent trees.How many rubbish bins do they need to prepare?10 A.8 B.9 C.10 D.11 E.12【答案】B【解析】10−1=9 156.Mary and Jimmy are eating ice cream of the same size.Jimmy eats ice cream twice as fast as Mary.Mary finishes in four minutes.How many minutes Jimmy need?(adapted from Math kangaroo Problems,Level,Question#)20081−26 A.2 B.6 C.3 D.4 E.5【答案】A【解析】Jimmy’s speed is twice as fast as Mary’s,and the ice cream they eat is the same size,so Jimmy’s time is only half as long as Mary’s,that is,minutes.4÷2=2 157.If of snow falls each hour,how much falls in minutes?60cm100 A.90cm B.1m C.110cm D.120cm【答案】B【解析】60cm/hr=1cm/min=100cm/100mins=1m/100mins.158.There are numbers with an average of.After eliminating a number,the average of the remaining numbers is.What is the eliminated number?97278 A.6 B.64 C.24 D.48 E.60【答案】C【解析】(78−72)×8=48,72−48=24.159.James made a running plan for this week.He ran km on average for the three days,and ran an average of km for the next two dyas,and ran km in total for the remaining two days to complete his plan.How many kilometers are there in James’running plan?4618 A.28 B.34 C.38 D.42 E.60【答案】D【解析】4×3+6×2+18=42 km.160.THere are 3 families in my neighbourhood with three children each;two of the families have twins.All twins are boys.At most how many girls are in these families?A.2 B.3 C.4 D.5 E.6【答案】D【解析】There are 3 families with 3 children=3 x 3=9.If there are 2 twin boys,2 x 2=4,0-4=5.161.Abigail is saving p each week.How many weeks will she take to save£?5020 A.20 B.25 C.30 D.35 E.40【答案】E【解析】£20÷50p=40.162.Tobby attended a Nasional Maths Olympaid(NMO).Tobby answered all questions.For each correct answer,Tobby will get marks.However,for each wrong answer,Tobby will deduct mark.If Tobby scored marks in total,how many questions did Tobby answer correctly?5041110 A.42 B.32 C.18 D.8【答案】B【解析】Assume all questions were answered correctly,Total score Difference in total score Change in score No.of incorrect answer Correct answers=50×4=200=200−110=90=4+1=5=90÷5=18=50−18=32 163.Patrick gets on a 10-problem test,on a 20-problem test and on a 30-problem test.If the three tests are combined into one 60 problem test,which percent is closest to her overall score?(adapted from 2006 AMC 8,Question#12)50\textbackslash%30\textbackslash%30\textbackslash%A.33 B.44 C.55 D.66 E.99【答案】A【解析】50\textbackslash%·10=530\textbackslash%·20=630\textbackslash%·30=9 Adding them up gets 5+6+9=20.The overall percentage correct would be 2060=13=0.3≈(𝐀)33.164.The state income tax where Kristin lives is levied at the rate of of the first＄of annual income plus of any amount above＄.Kristin noticed that the state income tax she paid amounted to of her annual income.What was her annual income?p\textbackslash%28000(p+2)\textbackslash%28000(p+0.25)\textbackslash%A.＄28000 B.＄32000 C.＄35000 D.＄42000 E.＄56000【答案】B【解析】method：the income amount be denoted by.We know that We can now try to solve for:so the answer is.method：,be Kristin’s annual income and the income tax total,respectively.Notice that We are also given that Thus,Solve for to obtain.1LetAA(p+.25)100=28000p100+(p+2)(A−28000)100A(p+.25)A=28000p+Ap+2A−28000p−56000.25A=2A−56000A=32000B2LetATT=p\textbackslash%·28000+(p+2)\textbackslash%·(A−28000)\textasciitilde\textasciitilde\textasciitilde\textasciitilde=[p\textbackslash%·28000+p\textbackslash%·(A−28000)]+2\textbackslash%·(A−28000)\textasciitilde\textasciitilde\textasciitilde\textasciitilde=p\textbackslash%·A+2\textbackslash%·(A−28000)T=(p+0.25)\textbackslash%·A=p\textbackslash%·A+0.25\textbackslash%·Ap\textbackslash%·A+2\textbackslash%·(A−28000)=p\textbackslash%·A+0.25\textbackslash%·A2\textbackslash%·(A−28000)=0.25\textbackslash%·AAA=32000B 165.A salt solution is made by mixing grams of pure salt and grams of water.Find the percent concentration of the solution.832 A.10\textbackslash%B.15\textbackslash%C.20\textbackslash%D.25\textbackslash%【答案】C【解析】8÷(8+32)=20\textbackslash%.166.There are standing in a straight line.The first student is at the start of the line,and the last student is at the end of the line.The distance between each student is meters.How long is the line?(Ignore the thickness of the trees.)82 A.meters8 B.meters11 C.meters14 D.meters15 E.meters16【答案】C【解析】There are intervals between the first student and the last student.Thus,the line is meters long.77×2=14 167.June falls on a Saturday.On what day of the week will August fall?1st201321st2013 A.Monday B.Wednesday C.Friday D.Saturday E.Sunday【答案】B【解析】,R.days after a Saturday is a Wednesday.30−1+31+21=8181÷7=1144 168.SASMO 2015 P2 Q3 The sum of two numbers is 300.One number is 5 times of the other number.What is the difference between the two numbers?A.50 B.60 C.180 D.200 E.None of the above【答案】D【解析】x=1u y=5u 6u=300 1u=50 So,x=50,y=250 Difference 250-50=200 169.Cathy is drawing flowers.The first one is red,the next one blue,the one after it yellow,the fourth one pink,and then again red,blue,yellow,pink,and so on,in the same order.What color will be the th flower?(Adapted from 2003 Math Kangaroo Problem,Level 3-4,Question#4)19 A.Blue$B.Pink$C.Red$D.Black$E.Yellow$【答案】E【解析】,so the th flower is yellow.19÷4=4R319 170.John drinks cups of boba everyday on weekdays and cups of boba everyday on the weekends.Which of the following equations represents how many cups of boba John drinks every week?x2 A.x+2 B.5x+2 C.5x+4 D.5x−4【答案】C【解析】The boba that John drinks during weekdays:The boba that John drinks during weekends:The total boba that John drinks during a week:5x2×2=45x+4 171.Of flamingos,twice as many stood on legs as stood on.All together,on how many legs did all of these flamingos stand?6021 A.80 B.90 C.100 D.110 E.120【答案】C【解析】Of flamingos,stood on legs and stood on.All together,these flamingos stood on legs legs.60402201[(40×2)+20]=100 172.A worm is staying at the bottom of a well with a depth of metres.If it climbs up metres in the daytime and slips down metres at night,which day will it climb up to the ground?1032 A.The th day6 B.The th day7 C.The th day8 D.The th day9【答案】C【解析】omitted 173.Peter has some toy cars,and Paul has more toy cars than Peter.Altogether they have toy cars.How many toy cars does Paul have?428 A.16 B.48 C.20 D.12【答案】A【解析】Paul has toy cars.(28+4)÷2=16 174.The average age of all the teachers in Gotia School is.There are male teachers in Gotia School with an average age of.The average age of female teachers is.How many female teachers are there?3432735 A.5 B.9 C.12 D.18 E.21【答案】E【解析】Total age less than the average:.Thus,there are female teachers.(34−27)×3=2121÷(35−34)=21 175.Cagney can frost a cupcake every seconds and Lacey can frost a cupcake every seconds.Working together,how many cupcakes can they frost in minutes?(AMC Problem,Question#)20305201210A11 A.10 B.15 C.20 D.25 E.30【答案】D【解析】Method1:Cagney can frost one in seconds,and Lacey can frost one in seconds.Working together,they can frost one in seconds.In seconds(minutes),they can frost cupcakes.Method2:In seconds(minutes),Cagney will frost cupcakes,and Lacey will frost cupcakes.Therefore,working together they will frost cupcakes.Method3:Since Cagney frosts cupcakes a minute,and Lacey frosts cupcakes a minute,they together frost cupcakes a minute.Therefore,in minutes,they frost.203020·3020+30=60050=123005(D)25300530020=1530030=1015+10=(D)25323+2=555×5=25⇒(D)176.Bill,Sarah and James each has candies.Bill gives James some candies and James gives Sarah some candies.How many candies are there in total?4 A.0 B.5 C.10 D.12 E.15【答案】D【解析】Giving candies to each other won’t affect the sum of their candies,so there are in total.4+4+4=12 177.Grandma made some cheese dumplings and some blueberry dumplings.Altogether,she made dumplings.If she had made more cheese dumplings,then there would be the same number of blueberry dumplings as cheese dumplings.How many cheese dumplings did grandma make?(2009 Math Kangaroo Problem,Levels 1-2,Question#19)3111 A.10 B.21 C.20 D.15【答案】A【解析】(31−11)÷2=10.178.If an object is thrown straight upward with an initial speed of 8 m/s and takes 3 seconds to strike the ground,from what height was the object thrown?\textasciitilde\textasciitilde\textasciitilde\textasciitilde A.24.2m B.21m C.23m D.2.3m E.69m【答案】B【解析】Key:object is thrown upward.When it reaches the highest point,the velocity is 0.The whole journey is divided into 2 parts:upward-highest point-downward to hit the ground.2 parts have different displacement(and different time).179.Amit,Bede,Cain,Devi,Emily and Frederick sit around a circular table in that order.Amit starts by saying"2015",Bede says"2016",Cain says"2017"and so on round the table.Who will eventually say"5102"?A.Amit$B.Bede$C.Cain$D.Devi$E.Emily$【答案】D【解析】After Amit says"",there are numbers remaining.Thus the counting goes round the table times with a remainder of,so the last to count is Devi.20155102−2015=30873087÷6=5143 180.The length of a rectangle is increased by and the width is decreased by.What percent of the old area is the new area?(adapted from 2009 AMC 8,Question#8)50\textbackslash%20\textbackslash%A.90 B.95 C.100 D.110 E.120【答案】E【解析】1.5×0.8=120\textbackslash%.181.apples and peaches cost.apples and peaches cost.What is the cost of an apple?23$1122$8 A.$1 B.$2 C.$3 D.$4【答案】A【解析】apples peaches＄apples peaches＄peach＄apples(＄)＄apples＄＄＄apple＄＄The cost of an apple is＄.2+\textasciitilde3→112+\textasciitilde2→81→32+2×3→82→8\textasciitilde−6=21→2÷2=11 182.Jenny need to reach her teacher house by for piano class.From her house to teacher’s house,she need to walk for minutes.She was late for minutes.What time did she leave her house?2.15p.m2010 A.2.05a.m.B.2.05p.m.C.1.55a.m.D.1.55p.m.E.2.25p.m.【答案】B【解析】She reached at,thus,minutes before that is2.25p.m.202.05p.m.183.I am twice the age of each of my sons,Barry and Larry.Our three ages have a total of 76.How old is Barry?A.912 B.18 C.19 D.36 E.38【答案】C【解析】The three ages have a total of four times Barry’s age.So Barry is.76÷4=19 184.Mike has ounces of salt solution.Given that there are ounces of pure salt in the solution,how much water is there?4712 A.ounces25 B.ounces35 C.ounces45 D.ounces59【答案】B【解析】47−−12=35 ounces.185.Orange peel is a type of orange color mixing red and yellow paint with a ratio of.In the shop,red paint is selling at dollars per ounce and yellow paint is selling at dollars per ounce.If Richard wants to make ounces of orange peel,how much money does she need?1:25412 A.dollars48 B.dollars52 C.dollars56 D.dollars60【答案】B【解析】12÷(1+2)=44×(1×5+2×4)=4×13=52 186.At the"Think Flea Market",a vendor is offering a"fair special"on plushies.If you buy one plushie at the regular price of 5040 text%text regular price will he save?(adapted from 2013 AMC 8,Question#12)\textbackslash,yougetasecondoneatadiscount,andathirdoneathalftheregularprice.Owentakesadvantageofthe"fairspecial"tobuythreeplushies.Whatpercentageofthe150 A.25 B.30 C.33 D.40 E.45【答案】B【解析】First,find the amount of money one will pay for three sandals without the discount.We have 50×3=text Then,find the amount of money using the discount:105(105)/(150)=70 text%100 text%-70 text%=(B)30\textbackslashsandals15050+0.6×50+12×50=\textbackslash.FindingthepercentageyieldsTofindthepercentsaved,wehave 187.In London 2012,the USA won the most medals:46 Gold,29 Silver and 29 Bronze.China was second with 38 Gold,27 Silver and 23 Bronze.How many more medals did the USA win compared to China?A.6 B.14 C.16 D.24 E.26【答案】C【解析】USA won-104 medals in total’China won 88 medals.Difference=16.188.Speedy Wiggins cycles to school,a journey that takes minutes at mph.How far does he travel to school?3012 A.miles3 B.miles4 C.miles6 D.miles10 E.miles20【答案】C【解析】Cycling at mph,Speedy would go miles in an hour.So in minutes he cycles miles miles.12123012÷2=6 189.Geraint always cycles to work,leaving at am every morning.When he averages,he arrives minutes late.However,when he averages,he arrives minutes early.What speed should he average to arrive on time?815km/h\textbackslash;1030km/h\textbackslash;10 A.20km/h\textbackslash;B.21km/h\textbackslash;C.22.5km/h\textbackslash;D.24km/h\textbackslash;E.25km/h\textbackslash;【答案】A【解析】Let be the distance Geraint cycles and let hours be the time his journey should take if he is to be on time.Since,the information in the question tells us that and that.When we subtract the second equation from the first,we obtain and so.Hence,from the second equation,and so.Therefore,to arrive on time,Geraint needs to travel in hour,which is an average speed of.xkmtdistancespeed=timex15=t+16x30=t−16x30=26x=101030=t−16t=13+16=1210km1220km/h\textbackslash;190.Susie Starfish and her five sisters went to the cinema with Ollie Octopus and his four brothers.They bought a box of popcorn for every arm they had.How many boxes of popcorn did they buy?A.13 B.57 C.62 D.65 E.70【答案】E【解析】There are starfish and octopuses.So the number of boxes.65=6×5+5×8=70 191.A hour clock loses minutes each day.The clock will first return to the correct time in．12−10 A.days36 B.days72 C.days120 D.days144 E.days60【答案】B【解析】Clock shows the correct time after a hr loss.With a min.loss daily,it takes days to lose hr&days to lose hr.12−10−617212 192.After a discount of 30\textbackslash%,the price of a bed is＄210.Besides,senior citizens are given a further discount of＄15.What is the percentage discount given to senior citizens for the bed?A.30\textbackslash%B.32\textbackslash%C.35\textbackslash%D.36\textbackslash%【答案】C【解析】Original price:.Selling price after discount:.Discount rate:.210(1−30\textbackslash%)=300210−15=1951−(195300)=1−65\textbackslash%=35\textbackslash%193.Alex had some trading cards.After giving trading cards to Ben,Alex received another trading cards from David.If Alex has trading cards now,how many trading cards does he have at first?3642241 A.235 B.230 C.225 D.220【答案】A【解析】241−42+36=235 194.How many digits have to be written in order to write down every number from to?1110 A.110 B.109 C.221 D.222 E.330【答案】D【解析】From to there are digits.From to there are digits.From to there are digits.In total,there are digits191×9=910992×90=1801001103×11=339+180+33=222 195.Daniel raises some ducks and dogs.All the ducks and dogs have legs and pairs of wings in total.If all the ducks and dogs each lifts one leg off the ground,they lift}legs in total.185 A.18 B.13 C.9 D.7 E.5【答案】D【解析】pairs of wings means there are ducks,so there are legs for dogs,which is.Thus,there are animals and they will lift legs.5518−5×2=88÷4=22+5=77 196.Lewis drives from London to Brighton at an average speed of 60mph.On the way back,he gets stuck in traffic and his average speed is only 40mph.What is his average speed for the whole journey?A.55mph B.50mph C.48mph D.45mph E.Impossible to determine【答案】C【解析】Let the distance from London to Brighton be miles.Since time distance speed,the times Lewis spent on the two parts of his journey are hours and hours.Hence the total time in hours that he travelled is.Therefore his average speed for the whole journey is.d=÷d60d40d60+d40=2d+3d120=5d120=d242d÷(d24)mph=48mph 197.A sugar solution contains grams of pure sugar.How many ounces of solution are there?15\textbackslash%18 A.grams90 B.grams100 C.grams120 D.grams150【答案】C【解析】18÷15\textbackslash%=120 grams.198.Judy needed to reach the th floor of a building.It took her seconds to walk from the st floor to the th floor.How many seconds will it take to go from the rd to the th floor at the same speed?104015310 A.60 B.70 C.80 D.90 E.100【答案】B【解析】40÷(5−1)=10(10−3)×10=70 199.Bill,Sarah and James each has cookies at beginning.Bill gives James some cookies and James gives Sarah cookies.How many cookies do they have in total now?42 A.0 B.5 C.10 D.12 E.15【答案】D【解析】Giving cookies to each other won’t affect the sum of their cookies,so there are in total.4+4+4=12 200.In a class of students,are wearing jeans.What is the ratio of students wearing jeans to students not wearing jeans?186 A.1:2 B.1:3 C.2:3 D.2:1【答案】A【解析】If students are wearing jeans,then are not.The ratio of students wearing jeans to students not wearing jeans is.618−6=126:12=1:2 201.On average,each student has balls.Each of the girls has balls on average.There are boys,and their average number of balls is}.14152425 A.6 B.7 C.8 D.9 E.10【答案】C【解析】14×(15+25)=560560−15×24=200200÷25=8 202.All the animals stand in rows in the magic forest.There is the same number of animals in each row.There are rows on the left of monkey and rows on the right of it.In its row,there are animals in front of it and animals behind it.How many animals are there in the forest?3262 A.36 B.40 C.45 D.54 E.63【答案】D【解析】(3+2+1)×(6+2+1)=54 203.Billy has twice as many basketballs as soccer balls.Milly has four times as many soccer balls as basketballs.They have a total of 18 balls.How many of them are basketballs?A.5 B.6 C.7 D.8 E.9【答案】A【解析】Let Billy have soccer balls and basketballs.Let Milly have basketballs and soccer balls.Therefore,as they have balls in total,.The only positive integer solution of this equation is,.So the number of basketballs is.b2bm4m173b+5m=18b=1m=32b+m=2×1+3=5 204.Kate sold some dresses and Tasha sold more dresses than Kate.If Tasha sold thrice as many dresses as Kate,how many dresses did Kate sell?30 A.10 B.15 C.30 D.45【答案】B【解析】30÷2=15 205.The hands of a circular clock form aangle at P.M.6:15 A.82.5∘B.90∘C.97.5∘D.270∘【答案】C【解析】At,hr.hand has moved from,so.6:15(1/4)×30∘6∠=90∘+30∘/4=97.5∘206.White and White Jr.have apples in total,and White has more appled than junior,so White Jr has}apples．5010 A.15 B.20 C.40 D.60【答案】B【解析】(50−10)÷2=20 207.Which of these months has 31 days?．A.February B.April C.August D.November【答案】C【解析】omitted 208.There are students in your class.The ratio of boys to girls is.How many boys and girls are there?502:3 A.and3020 B.and2030 C.and1520 D.and2015【答案】B【解析】According to the ratio 2:3,we could know the total is 5.Then the number of boys is 50×25=20.The number of girls is 50×35=30.209.Tom has toys in total,and Tim has more toys than Tom.The number of Amanda’s toys is equal to the sum of that of Tom and Tim.How many toys does Amanda have.202 A.39 B.42 C.44 D.47 E.None of the above【答案】B【解析】We know that Tim has toys.The sum of Tom’s and Tim’s toys is.20+2=2220+22=42 210.The length of a rectangle is increased by and the width is decreased by.What percent of the old area is the new area?(adapted from 2009 AMC 8,Question#8)30\textbackslash%25\textbackslash%A.90.5 B.96.5 C.97.5 D.98.5 E.110.5【答案】C【解析】1.3×0.75=97.5\textbackslash%.211.What is the greatest number of days that can occur after the first of one month and before the first of the next month?A.27 B.28 C.29 D.30【答案】D【解析】A month has at most days,Hence,the greatest number of days in that month,after the first,is.Then,the next day is another.3131−1=301st 212.Water from the first faucet fills the swimming pool in hours.Water from each of the two other faucets fills the same swimming pool times faster.In how many hours will the swimming pool be filled if all three faucets are opened?184 A.1 B.2 C.3 D.4 E.5【答案】B【解析】The efficiency of the first faucet is and that of the other two is.Thus it takes hours to fill the pool.118291÷(118+29×2)=2 213.SASMO 2015 P2 Q4 Susan prepared a plate of cookies for her friends Ashley,Sam,Max and Olivia.Susan tried the first cookie before serving them to her friends.Ashley took 2 cookies and gave 1 to Sam.Max then took 3 cookies,and gave 1 to Olivia and 1 to Susan.If they each ate the cookies they ended up with,who ate the most cookies?A.Susan B.Ashley C.Sam D.Max E.Olivia【答案】A【解析】Susan:+1+1 Ashley:+1 Sam:+1 Max:+1 Olivia:+1 214.The distance between Town A and Town B is.Eric drives from Town A to Town B at a speed of while Chien drives from Town B to Town A at a speed of.How many hours will it take for them to meet each other?620km75km/h80km/h A.4 B.6 C.24 D.124【答案】A【解析】As they are driving toward each other,the total speed is miles per hour.Then the time needed is hours.75+80=155620÷155=4 215.Elmp vists the Sesame Street Park every Wednesday.If the 1st of January 2017 was Sunday and February has 28 days,what was the last date in March 2017 in which Elmo visited Sesame Street Park?A.28th March B.29th March C.30th March D.31st March E.None of the above.【答案】B【解析】Draw the calendar out.216.Ashley had a basket of apples.Her family took half of the apples after dinner.Next morning,her family took half of the remaining apples.There were apples left in the basket.How many apples were in the basket at first?2 A.4 B.6 C.8 D.11 E.16【答案】C【解析】2+2=44+4=8 217.A series of colored lanterns are arranged in the pattern``red,red,green,yellow,yellow,red,red,green,yellow,yellow’’What color is the lantern?⋯52th A.red B.green C.yellow【答案】A【解析】Since,the colored lantern is red.52÷(3+2)=10r252th 218.Jin loves carrots!Yesterday she ate of her carrots,and today she ate of the remaining carrots.She then discovered that she had carrots left.Yesterday she must have started with carrots.122312 A.36 B.48 C.60 D.72【答案】D【解析】If carrots are left after Jin eats of today’s carrots,then carrots are of the carrots she started with today.So Jin began today with carrots.Since Jin ate yesterday,she started with carrots.1223121336122×36 219.This year,March th falls on a Thursday.What day of the week will it be in days?1930 A.Wednesday B.Thursday C.Friday D.Saturday E.Sunday【答案】D【解析】30÷7=4R2,two days after Thursday,which is Saturday.220.A alcohol solution contains g of water.How many g of solution are there?70\textbackslash%120 A.g200 B.g300 C.g400 D.g500【答案】C【解析】120÷(1−70\textbackslash%)=400 g.221.It’s summer time!A beverage shop mixes bottles of apple and bottles of watermelon juice to make the new blended juice.The costs of a bottle of apple and a bottle of watermelon juice are and dollars,respectively.If the size of the bottle does not change,what is the cost of each bottle of the blended juice?1020811 A.7 B.8 C.9 D.10 E.11【答案】D【解析】Total cost:.There are bottles,so each bottle of the blended juice should be dollars.10×8+11×20=30010+20=30300÷30=10 222.Irene mixes kilograms of dogfood that contains rice with kilograms of dogfood that contains rice.Find the percent concentration of the rice in the new mixture.10050\textbackslash%40080\textbackslash%A.70\textbackslash%B.72\textbackslash%C.75\textbackslash%D.74\textbackslash%【答案】D【解析】100×50\textbackslash%+400×80\textbackslash%100+400=74\textbackslash%.223.Chris and Debbie want to buy the same book,but they do not take enough money.Chris needs dollars and cents more to buy that book.Debbie needs dollars and cents more to buy that book.The sum of their own money is equal to the price of the book.How much is the book?230380 A.dollars and cents230 B.dollars and cents460 C.dollars and cents760 D.dollars and cents380 E.dollars and cents610【答案】E【解析】dollars and cents+dollars and=dollars and cents230380610 224.The average cost of a long-distance call in the USA in 1985 was 56 cents per minute,and the average cost of a long-distance call in the USA in 2018 was 2 cents per minute.Find the approximate percent decrease in the cost per minute of a long-distance call.(2007 AMC 8,Question#6)A.90 B.95 C.96 D.97 E.98【答案】C【解析】The percent decrease is(the amount of decrease)/(original amount)the amount of decrease is so the percent decrease is which is about56−2=54545696\textbackslash%225.There are inlets(namely and)in a pool.If only inlet is open,it takes minutes to fill up the empty pool.If only inlet is open,it takes minutes to fill up the empty pool.Now,inlets and will be open in turns,according to such an order,open inlet for minute,for minutes,for minutes,for minute,for minute,for minutes So on and so forth.How long,in the nearest minutes,does it take to fill up the empty pool?2ABA36B48ABA1B2A2B1A1B2⋯A.36 B.39 C.41 D.44 E.48 F.None of the above【答案】C【解析】C 226.Joe lives on the rd floor.He needs to spend minutes to move from the th floor to the th floor.How many minutes does he need to climb from the st floor to the rd floor?3124513 A.12 B.24 C.36 D.48 E.60【答案】B【解析】12×(3−1)=24 227.Three people,,and have a total of.Given that the ratio of s total to s total is,and has more than,how much does have?ABC$200A′B′4:3A$20CC A.24 B.36 C.48 D.60 E.72【答案】D【解析】Assume that borrows.Therefore,,for a total sum of increments,or.One increment is dollars.Therefore,has a total of dollars.C$20A:B:C=4:3:411$220220÷11=20C4×20−20=60 228.If May is Monday,what day of the week is st May?29th1 A.Sunday B.Monday C.Wednesday D.Tuesday E.Saturday【答案】B【解析】There are 29 days between May and st May.Apart from th May itself,there are 28 days=4 week.Therefore,st March is Monday.29th1291 229.Linda paid dollars for potatoes.How many dollars did Linda pay for the same kind of potatoes if she bought more of them?(adapted from Math kangaroo Problems,Level,Question#)84620081−213 A.18 B.20 C.24 D.22【答案】B【解析】Linda paid＄for potatoes,,so we can know potatoes cost dollars.In total Linda should pay dollars for potatoes.848÷4=2122×10=2010 230.There are people in Harry’s family with an average height of cm.The heights of Harry,Harry’s mom,Harry’s sister,and Harry’s brother are cm,cm,cm,and cm,respectively.What is the height of Harry’s dad?5168170160162175 A.163 B.165 C.171 D.173 E.178【答案】D【解析】..(170−168)−(168−160)−(168−162)+(175−168)=−5168+5=173 231.Vera invited guests to her birthday party.She had pizzas,and each of them was cut into slices.Each person at the party ate one slice of pizza.How many slices of pizza were left over?(2015 Math Kangaroo Problem,Level 1-2,Question#14)1328 A.5 B.4 C.3 D.2 E.1【答案】D【解析】There were slices.slices of pizza were ate,so there were slices left.8×2=1613+1=1416−14=2 232.If this is March,what month will it be months from today?1993 A.January B.February C.March D.April【答案】D【解析】Since 12×166+1=1992+1=1993,the month will be April.233.In it was estimated that there were lions in Africa.Over years this figure has decreased by.What is the current estimate for the number of lions in Africa?19752500004090\textbackslash%A.25000 B.100000 C.160000 D.225000 E.275000【答案】A【解析】A decrease means of of the lions remain.90\textbackslash%10\textbackslash%250000=250000÷10=25000 234.Annie usually leaves her cell phone on.If her cell phone is on but she is not actually using it,the battery will last for hours.If she is using it constantly,the battery will last for only hours.Since the last recharge,her phone has been on hours,and during that time she has used it for minutes.If she only keeps using the phone hours more and then leaves the phone on,how many more hours will the battery last after she leaves the phone on?(Adapted from AMC Problem,Question#)36102012032004812 A.0 B.1 C.3 D.4 E.5【答案】A【解析】When not being used,the cell phone uses up of its battery per hour.When being used,the cell phone uses up of its battery per hour.Since Annie’s phone has been on for hours,of those simply on and being used,of its battery has been used up.To drain the remaining,the phone can last for more hours without being used.1361102018218×(136)+2×(110)=710310(310−3×110)÷136=0 235.A cow gives liters of milk each day.If the milkman sells%of the milk,how many liters of milk is left with him?2480 A.4 B.4.8 C.19.2 D.20【答案】B【解析】%=,,liters of milk is left with him.24×8019.224−19.2=4.84.8 236.Patrick got into a lift.He went down six floors,up seven floors and then down eight floors.He was finally on the third floor.Which floor did Patrick get into the lift?A.3rd B.4th C.10th D.11th【答案】C【解析】3+8−7+6=10 237.Together,Bob,Colin and Dave weigh.Bob weighs more than Colin and more than Dave.How much does Bob weigh?195kg9kg6kg A.60kg B.66kg C.69kg D.70kg【答案】D【解析】Nil 238.Helen said to Mary,"If you give me apples,I will have exactly as many apples as you."How many more apples does Mary have than Helen?4 A.3 B.6 C.8 D.12 E.15【答案】C【解析】Difference:4+4=8 239.To make a pudding,you need ounces of flour and ounces of milk.You have ounces of flour and want to make as many puddings as possible.How much milk do you need?21010 A.ounces20 B.ounces30 C.ounces40 D.ounces50 E.ounces60【答案】D【解析】The ratio of flour to milk is or.With ounces of flour,you could make as many as puddings.At the same time,you need more ounces of milk.The ratio of flour to milk is,or.2:101:51055010:501:5 240.NBA playoffs are held annually.The nd NBA playoffs were held in.When Judy was years old,the th NBA playoffs were held.When was Judy born?6220081058 A.1991 B.1992 C.1994 D.1996 E.1998【答案】C【解析】62−58=42008−4−10=1994 241.Frank stands in line and has people behind him,If there are a total of people in line,how many people are there in front of Frank?76110 A.33 B.34 C.35 D.36【答案】A【解析】If there are a total of people in line,subtract those behind Frank and Frank himself:,the number in front of Frank.110110−76−1=33 242.A teacher distributes scorecards to students,if everyone gets cards,there will be a shortage of cards.If everyone gets cards,all these cards will just be divided.Then,how many students are there in total?3122 A.4 B.6 C.10 D.12【答案】D【解析】If less card is given to students,the situation would transfer from’a shortage of cards’to’all cards are just divided’.Therefore.the shortage of cards is equal to the number of cards that everyone gets less card.So,there are in total students.2−1=11212112÷1=12 243.Which date is days after November?1006th A.February14 B.February15 C.February16 D.February17【答案】A【解析】It’s days from Nov.to Feb.;days later is days.92(30+31+31)668100 244.Karl Lecter has been collecting,and coins in a jar.All but of his coins are coins,all but are coins,and all but are coins.How much money does he have?1p2p5p101p102p105p A.8p B.10p C.25p D.40p E.80p【答案】D【解析】All but of the coins are coins,which tells us that the number of and coins adds up to.Similarly,the total of the and coins is and the total of the and coins is.He therefore has of each coin,giving a total of.101p2p5p101p5p101p2p105(5×1)+(5×2)+(5×5)=40p 245.When I add together the number of sides of a quadrilateral,a trapezoid,and a parallelogram,I get a total of．A.12 B.13 C.14 D.15【答案】A【解析】Quadrilaterals,trapezoids,and parallelograms each have sides each,so the total number of sides is.44+4+4=12 246.A ship was attacked by pirates.One by one the pirates climb a rope to get on the ship.The pirate captain was the th pirate to climb in line,and there were as many pirates in front of him as behind him.How many pirates climbed the rope?(2015 Math Kangaroo Problem,Level 1-2,Question#18)8\textasciitilde A.7 B.8 C.12 D.15 E.16【答案】D【解析】The pirate captain was the th pirate and there were as many pirates in front of him as behind him,which means there were pirates in front of him and there were also pirates behind him.The total number of pirates is.8777+7+1=15 247.If January falls on a Friday,which day of the week will January fall on?282000282001 A.Thursday B.Friday C.Saturday D.Sunday E.Monday【答案】D【解析】is a leap year and the period includes Feb,so there are days.R Friday days Sunday200029366366÷7=522+2arrow 248.There are benches in the park,which have the same length.They are placed on one side of the road every meters from end to end.Given that the length of the road is meters,how long is the bench?9774 A.m1 B.m2 C.m3 D.m4【答案】B【解析】The intervals are meters in total.So,the sum of length of all the benches is meters and each of them is meters.9−1=87×8=5674−56=1818÷9=2 249.Nancy did an experiment.She inserted a paper straw vertically into the bottom of a bottle of black ink.Then,she found that the length of the black part of the paper straw was exactly cm.She turned the straw upside down and inserted the other end vertically into the bottom of the bottle.She found that the length of the part not colored of the straw was exactly half of that of all the black parts.The paper straw was}cm.12 A.12 B.24 C.28 D.30 E.36【答案】E【解析】The black parts of the straw was cm,so the part not colored was cm.Thus,the length of the straw was cm.12+12=2424÷2=1224+12=36 250.,and start from the same place at the same time and chase a cyclist in front of them along the same road.The three cars catch up with him in,and minutes respectively.Given that car’s speed is kilometers per hour,car’s speed is kilometers per hour.Find car’s speed.ABC61012A24B20C A.21 B.19 C.18 D.16 E.15【答案】B【解析】B 251.A salt solution contains g of water.How many g of solution are there?25\textbackslash%75 A.g100 B.g25.5 C.g25 D.g102【答案】A【解析】75÷(1−25\textbackslash%)=100 g.252.At the red light,seven buses of the same length stop in a line.Given that the length of each bus is meters,and the distance between each two adjacent buses is meters,how long is the line?52 A.m35 B.m49 C.m47 D.m54【答案】C【解析】Among the buses,there are intervals.So the answer is meters.77−1=67×5+2×6=47 253.sakura trees were planted along one side of the road.The trees were planted at intervals.After drivers complained the road was too pink,pineapple trees were planted on the other side of the road at intervals.How many pineapple trees were planted,if there were sakura and pineapple trees at both ends of the road?374m6m A.24 B.25 C.144 D.18【答案】B【解析】Number of sakura intervals=Length of road=Number of pineapple intervals=Number of pineapple trees=37−1=3636×4=144m144m÷6m=2424+1=25 254.Agnijo has half as many apps as Sam who has a third as many apps as Naomi.Altogether,they have apps.How many apps does Sam have?180 A.20 B.30 C.40 D.60 E.90【答案】C【解析】Let Agnijo have apps.Now Sam has,and Naomi.Therefore,and so.Hence Sam has apps.n2n6nn+2n+6n=9n=180n=180÷9=202×20=40 255.In the amusement park,Jessie is playing with darts.For each time she hits the bullseye,she can win two toys.At the beginning she has toys and at the end she has toys.How many times did she hit the bullseye?(Adapted from 2006 Math Kangaroo Problem,Level 3-4,Question#5)323 A.6 B.8 C.10 D.5 E.4【答案】C【解析】(23−3)÷2=10 256.October 10th,2021 is Sunday.What day is October th of the same year?}26 A.Sunday B.Monday C.Tuesday D.Wednesday【答案】C【解析】,,it’s Tuesday.26−10=1616÷7=2\textbackslashR\textasciitilde2 257.is}more than.380254 A.126 B.124 C.534 D.634【答案】A【解析】380−254=126 258.There are flags on one side of a road.The distance between neighboring flags is meters.Grace walked from the first flag to the last flag.How many meters did she walk?(Adapted from 2007 Math Kangaroo Problem,Level 3-4,Question#5)115 A.45 B.50 C.55 D.65 E.75【答案】B【解析】(11−1)×5=50 259.Colin was preparing for the PE test.On the first day,he ran km.He decided that each day he would be running m more than the day before.How many meters did he run in total in the first days?11005 A.5600 B.5700 C.5800 D.6000 E.6100【答案】D【解析】1000+1100+1200+1300+1400=6000 260.Wendy had stickers.First,she gave Aiden three stickers.Then,she gave Terry stickers.Now,each of the three people had the same number of stickers.At the beginning,how many stickers did they have in total?307 A.120 B.90 C.85 D.60 E.55【答案】D【解析】Now,Wendy had stickers.Then,all of them had stickers,which was equal to the total number of stickers they had at beginning.30−3−7=2020×3=60 261.Bram bought beans for＄.At this price,beans cost．603.00100 A.＄3.50 B.＄4.00 C.＄5.00 D.＄5.50【答案】C【解析】If beans cost＄,then bean costs￠and beans cost＄.603.00151005 262.Historians say that William the Conqueror was born in 1028.How many years ago was that?A.790 B.810 C.910 D.990 E.1010【答案】D【解析】The number of years from William’s birth is.2018−1028=990 263.A 20%increase in the price of milk leads to a 10%decrease in the quantity of cereal purchased.The cross-price elasticity of demand between milk and cereal is A.-0.5 and the two goods are substitutes.B.-0.5 and the two goods are complements.C.0.5 and the two goods are complements.D.-2 and the two goods are substitutes.E.2 and the two goods are complements.【答案】B【解析】This is an application of the cross-price elasticity equation:%change in QDx/%change in Py.-0.10/0.2=-0.5.A negative number means the goods are complements.264.If one bag of chips costs 75￠,then three of these bags cost．A.$0.25 B.$1.50 C.$2.25 D.$3.00【答案】C【解析】One bag costs 75￠.Three such bags cost 3×$0.75=$2.25.265.After Sally takes shots,she has made of her shots.After she takes more shots,she raises her percentage to.How many of the last shots did she make?(adapted from 2004 AMC 8,Question#6)2040\textbackslash%552\textbackslash%5 A.1 B.2 C.3 D.4 E.5【答案】E【解析】Sally made shots originally.Letting be the number of shots she made,we have.Solving for gives us0.4*20=8x8+x25=0.52xx=5 266.If August falls on Monday,which day of the week will September fall on?Below is Chris’answer.Number of days from 1 Aug to 12 Sept:31+12=43 43 7=6 R 1 Hence,12 September is a Tuesday.Is Chris’s answer correct?If not,what is the correct answer?．112÷A.Sunday B.Monday C.Tuesday D.Wednesday【答案】B【解析】Number of days from August to September weeks Therefore,September will fall on Monday.112=31+12−1=4242÷7=612 267.The owner of a bicycle store had a sale on bicycles(two-wheelers)and tricycles(three-wheelers).Each cycle had two pedals.When he counted the total number of pedals of the cycles,he got 50.When he counted the total number of wheels of the cycles,he got 64.How many tricycles were offered in the sale?A.8 B.10 C.12 D.14 E.16【答案】D【解析】let be the number of bicycles,be the number of tricycles50÷2=25xy2x+3y=64x+y=25 268.If cans of Sweet Stuff Soda all together contain teaspoons of sugar,then there are a total of teaspoons of sugar in cans.69615 A.192 B.208 C.240 D.288【答案】C【解析】If cans contain teaspoons of sugar,can contains teaspoons of sugar.Thus cans contain teaspoons of sugar.696196÷6=161516×15=240 269.Given that January st,was Monday,on what day did January st,fall?1201812019 A.Tuesday B.Monday C.Sunday D.Wednesday【答案】A【解析】was a common year which had days.Thus,January st,fell on one day after Monday,which was Tuesday.201836512019 270.Three zebras take part in a contest.The winner is the zebra with the most number of stripes.QingLe has stripes,ChenXi has more than QingLe.QingLe has fewer stripes than YueYing.How many stripes does the winner have?1535 A.16 B.18 C.20 D.21 E.23【答案】C【解析】NA 271.In the yard there is an equal number of pigs,ducks and chickens.Together,they have legs.How many ducks are there in the yard?144 A.18 B.21 C.35 D.42 E.43【答案】A【解析】Suppose there are ducks in the yard.Since there is an equal number of pigs,ducks and chickens,,.x2x+4x+2x=144x=18 272.Paul was going to buy servings of ice cream,but he was cents short.So,he bought servings and had cents left.What was the price of one serving of ice cream?480330 A.cents70 B.cents80 C.cents90 D.dollar1 E.dollar cents110【答案】E【解析】cents dollar and cents.(80+30)÷(4−3)=110=110 273.A salt solution is made by mixing g of salt and g of water.Find the percent concentration of the mixture.100400 A.15\textbackslash%B.20\textbackslash%C.25\textbackslash%D.30\textbackslash%【答案】B【解析】.100÷(100+400)×100\textbackslash%=20\textbackslash%274.When kilograms of sugar water is mixed with some sugar water,it gives a mixture with a sugar concentration of.How much sugar water is needed?}430\textbackslash%10\textbackslash%26\textbackslash%10\textbackslash%kg A.1 B.2 C.3 D.4 E.5【答案】A【解析】Use the cross method to see that the ratio of solution to solution is.Therefore,of solution is needed.30\textbackslash%10\textbackslash%\textbackslash\textbackslash↘↙\textbackslash\textbackslash26\textbackslash%\textbackslash\textbackslash↙↘\textbackslash\textbackslash16\textbackslash%4\textbackslash%\textbackslash\textbackslash30\textbackslash%10\textbackslash%4:11kg10\textbackslash%275.Cindy has bookmarks.If she were to give bookmarks to each of her classmates,she would need more bookmarks.How many classmates does Cindy have?50610 A.4 B.6 C.10 D.12【答案】C【解析】50+10=6060÷6=10 276.A mixture of 30 liters of paint is red tint,yellow tint and water.Five liters of yellow tint are added to the original mixture.What is the percent of yellow tint in the new mixture?(2007 AMC 8,Question#17)25\textbackslash%30\textbackslash%45\textbackslash%A.25 B.35 C.40 D.45 E.50【答案】C【解析】Since of the original 30 liters of paint was yellow,and 5 liters of yellow paint were added to make the new mixture,there are liters of yellow tint in the new mixture.Since only 5 liters of paint were added to the original 30,there are a total of 35 liters of paint in the new mixture.This gives of yellow tint in the new mixture,which is(C)40.30\textbackslash%9+5=1440\textbackslash%277.Josh lives on the th floor.He needs to climb steps to move from the nd floor to the th floor.How many steps does he need to climb from the st floor to the th floor?6242416 A.72 B.60 C.48 D.36 E.32【答案】B【解析】24÷2×(6−1)=60 278.The page numbers of a book are from to.Tim adds up the page numbers.In his calculation,he misses a page number and the sum of remaining pages is.What is the missing page number}.162621940 A.12 B.13 C.14 D.15【答案】B【解析】(1+62)×62÷2=19531953−1940=13.279.Suppose of equals of.What percentage of is?(adapted from 2020 AMC 8,Question 15)50\textbackslash%x30\textbackslash%yyx A.40 B.60 C.80 D.120 E.200【答案】B【解析】50\textbackslash%·x=30\textbackslash%·yx=0.6·y 280.Grandma made some cheese dumplings and some blueberry dumplings.Altogether,she made dumplings.If she had made more cheese dumplings,then there would be the same number of blueberry dumplings as cheese dumplings.How many cheese dumplings did grandma make?(Math Kangaroo Problem,Levels,Question#)311120091−219 A.10 B.21 C.20 D.15【答案】A【解析】(31−11)÷2=10.281.After the game,Owen is thirsty again.This time he gets a mixture of 3 liters of juice,which contain of apple juice,of mango juice,and of water.liters of mango is added to the original mixture.What is the percent of mango in the new mixture?(Adapted from 2007 AMC 8,Question#17)25\textbackslash%30\textbackslash%45\textbackslash%0.5 A.2.5 B.3.5 C.4 D.4.5 E.5【答案】C【解析】Since of the original 30 liters of paint was yellow,and 5 liters of yellow paint were added to make the new mixture,there are liters of yellow tint in the new mixture.Since only 5 liters of paint were added to the original 30,there are a total of 35 liters of paint in the new mixture.This gives of yellow tint in the new mixture,which is(C)40.30\textbackslash%9+5=1440\textbackslash%282.Grandma made some cheese dumplings and some blueberry dumplings.Altogether,she made dumplings.If she had made more cheese dumplings,then there would be the same number of blueberry dumplings as cheese dumplings.How many cheese dumplings did grandma make?3111 A.10 B.21 C.20 D.15【答案】A【解析】(31−11)÷2=10.283.Joann’s birthday in was May th,which was Sunday.Elizabeth’s birthday in was June st.On what day did Elizabeth’s birthday fall?202010202021 A.Thursday B.Saturday C.Sunday D.Tuesday【答案】C【解析】It passed days in total.Since,it was Sunday.31−10+21=4242÷7=6 284.Three zebras take part in a contest.The winner is the zebra with the most number of stripes.Runa has stripes,Zara has more than Runa.Runa has fewer stripes than Biba.How many stripes does the winner have?1535 A.16 B.18 C.20 D.21 E.23【答案】C【解析】NA 285.Sara is years old and Mike is.How old will Sara be when Mike is years old?5920 A.16 B.20 C.24 D.28 E.30【答案】A【解析】Their difference in age:When Mike is,Sara is9−5=42020−4=16 286.The boundary of a lake is long.Trees are planted at regular intervals of round the lake.How many trees are planted round the lake?600m6m A.99 B.100 C.101【答案】B【解析】In the case of circular tracks,number of intervals number of trees,,trees are planted round the lake.=600÷6=100100 287.A machine started printing posters at on Monday at the rate of posters per hour.After every hours of printing,it was paused for an hour.How many posters were printed by.the next day?9.00a.m.1000611.00a.m A.20000 B.22000 C.23000 D.26000【答案】C【解析】NA 288.A shop purchased a kind of Lego at＄each.It then sold them at＄each.How much did the shopkeeper earn for Legos?1251685 A.＄190 B.＄200 C.＄210 D.＄215【答案】D【解析】(168−125)×5=215.289.Jenny paid dollars for books.How many dollars should she pay in total for the same kind of books if she bought more of them?1535 A.34 B.37 C.40 D.42 E.44【答案】C【解析】,so dollars for each book,15=3×553+5=88×5=40 290.There are baby chickens on a farm.The number of hens on the farm is of the baby chickens,and the number of roosters is of the number of hens.How many roosters are there on the farm?360089116 A.180 B.200 C.100 D.225【答案】B【解析】Hens baby chickens,Roosters hens,We can write the formula as:.=×89=×1163600×89×116=3200×116=200 291.Students in the third grade lined up and formed a square array to perform a dance.Each side of the outermost layer had students.How many students in total are there on the outermost layer?37 A.148 B.152 C.144 D.140 E.156【答案】C【解析】,or students.36×4=14437×4−4=144 292.The mushrooms picked by white rabbits in days will be eaten by gray rabbits in days.In how many days will gray rabbits eat up mushrooms picked by white rabbits in days?23341556 A.1 B.2 C.3 D.4 E.6【答案】D【解析】The mushrooms picked by white rabbits in days will be eaten by gray rabbits in days,so the mushrooms picked by white rabbits in days will be eaten by gray rabbits in days.Thus,the mushrooms picked by white rabbits in days will be eaten by gray rabbits in days.2334111256154 293.Jimmy’s father brought Jimmy three pet dogs,and Jimmy could only keep one.How many dogs did Jimmy’s father want to take away?(adapted from Math kangaroo Problems,Level,Question#)20111−23 A.1 B.3 C.4 D.2 E.0【答案】D【解析】3−1=2 294.In a garage,the ratio of red cars to black cars is 8:5,and the ratio of black cars to white cars is 3:4.The minimum number of cars in the garage is．A.20 B.59 C.74 D.91【答案】B【解析】The ratio of red cars to black cars is;the ratio of black cars to white cars is.The minimum number of cars is.8:5=24:153:4=15:2024+15+20=59 295.In the Avengers League,there are superheroes.Six of the superheroes from the galaxy guard left.How many heroes are left?(adapted from Math kangaroo Problems,Level,Question#)2520071−26 A.19 B.23 C.24 D.25 E.20【答案】A【解析】There are superheroes in total.After subtracting,there are left.25625−6=19 296.In a verbal test,the average score of students is.The lowest score is.At most how many student(s)can get points?40255100 A.11 B.10 C.9 D.8 E.7【答案】D【解析】Total points:.To have as many points as possible,we should consider there are only two groups of students:everyone gets points in a group and everyone gets in the other group.,so there must be less than people getting points.If there are nine s:,which is impossible.If there are eight s:.Thus,the answer is.40×25=1000100510010×100=1000101001009×100+31×5=1055>10001008×100+32×5=960<10008 297.If I write all letters of the English alphabet in alphabetical order times in a row,then the th letter I write will be．2662806 A.A B.E C.V D.Z【答案】D【解析】Since 806÷26=31,the 806th letter Iwrite will be the last letter of the 31st time I write the full alphabet;it will be a Z.298.Amy mixes g of a sugar solution and g of a sugar solution together.After}of water evaporates,the percent concentration of solution is.1020\textbackslash%4025\textbackslash%40\textbackslash%A.g15 B.g18 C.g20 D.g25【答案】C【解析】g.g.10×20\textbackslash%+40×25\textbackslash%=12(10+40)−12÷40\textbackslash%=20 299.A snail is climbing up from the bottom of a-meter-deep well.It climbs up meters during the daytime,and slides down meter every night.How many days will it take to get out of the well?1531 A.5 B.6 C.7 D.8 E.9【答案】C【解析】It climbs up meters actually everyday.It takes days in total,and in the last day,it climbs up meters.3−1=212÷2+1=73 300.Annie had twice as many paper clips as Beth,After Beth had used paper clips,Annie had times as many as Beth.How many paper clips did Annie have?154 A.15 B.45 C.60 D.75【答案】C【解析】Let the number of Annie’s and Beth’s be 2n and n.2n=4(n-15),so n=30,2n=30 301.It takes workers hours to paint a bridge.Working at the same rate,how many hours would workers require to do the job?14460108 A.45 B.65 C.80 D.96【答案】C【解析】It takes workers hours to paint a bridge.That’s worker-hours.For workers,the job takes hours.14460144×60=86401088640÷108=80 302.A gift store buys some gifts at＄125 each.It wants to earn＄25 for each gift after a discount of 25\textbackslash%.What is the selling price before the discount for each shirt?A.dollars160 B.dollars180 C.dollars190 D.dollars200【答案】D【解析】(125+25)÷(1−25\textbackslash%)=200 dollars.303.Daniel is learning that five pennies spread out on his desk are the same number of coins as five pennies in a pile.According to Piaget,how old is Daniel likely to be?A.1 year B.2 years C.4 years D.8 years E.13 years【答案】D【解析】Daniel is learning conservation of number,a skill that Piaget believed children learn in the concrete operational stage 304.Amy mixes g of a salt solution and g of a salt solution together.How many g of water should she add to the mixture to make it a solution?3030\textbackslash%2020\textbackslash%10\textbackslash%A.70 B.72 C.75 D.80【答案】D【解析】g.g.30×30\textbackslash%+20×20\textbackslash%=9+4=1313÷10\textbackslash%−(30+20)=80 305.Arrange balls to form a square.One ball is placed at each corner of the square.How many balls are there on each side of the square?}28 A.5 B.6 C.7 D.8 E.9【答案】D【解析】Put ball in each corner(balls in total).Remaining balls:So,each side has ball at each corner and balls in the middle,giving a total of balls.1428−4=2424÷4=6168 306.The average pocket money of the whole class is dollars.Each of the girls in the class has dollars on average.There are boys in the class,and their average pocket money is}dollars.912492.518 A.36 B.28 C.69 D.85 E.89【答案】E【解析】More than average:.Each boy should have dollars less than the average,so each of them has dollars.(92.5−91)×24=3636÷18=291−2=89 307.of the passengers on the bus were adults and the rest were children.There were children.How many adults were there?3724 A.42 B.30 C.18 D.15 E.10【答案】C【解析】1−37=4724÷47=4242−24=18.308.When Teddy was years old,his father’s age was times his age.When his father is years old,how old will Teddy be?5742 A.6 B.9 C.11 D.12【答案】D【解析】,His father was years old when Teddy was years old.Age difference years old or,His father was years old when Teddy was years old.years later years old Teddy will be years old when his father is years old.7×5=35355=35−5=3042−30=12\textasciitilde\textasciitilde7×5=3535542−35=75+7=12\textasciitilde1242 309.The average height of all the teachers in Grape School is.There are male teachers in Grape School with an average height of.The average height of female teachers is.How many female teachers are there?1685180162 A.5 B.9 C.10 D.18 E.21【答案】C【解析】Total height less than the average:.Thus,there are female teachers.(180−168)×5=6060÷(168−162)=10 310.There are only lilies and roses in Bud’s garden.One third of the flowers are roses.There are 12 roses in total.How many flowers are there in Buds’s garden?A.12 B.16 C.20 D.24 E.36【答案】E【解析】12÷13=36.311.A shop purchased some tennis rackets at＄each.It then sold them at＄each.How much did the shopkeeper earn for rackets?15017510 A.＄150 B.＄200 C.＄250 D.＄300【答案】C【解析】(175−150)×10=250.312.Little Pig is standing in a line.There are animals in the line and her position is the th counting from front to back.How many animals are behind her?164 A.10 B.11 C.12 D.13 E.14【答案】C【解析】Ms.Pig is included in the"",so there are animals behind her.416−4=12 313.There are people in Linda’s family with an average weight of kg.The weights of Linda,Linda’s mom,Linda’s sister,and Linda’s brother are kg,kg,kg,and kg,respectively.What is the weight of Harry’s dad?55645555060 A.65 B.66 C.68 D.70 E.75【答案】D【解析】56×5−45−55−50−60=70 kg 314.Della decides to buy some stationaries for her students.The price of two schoolbags is equal to the price of six notebooks,and the price of six pencilcases is equal to nine notebooks.Given that one schoolbag can be exchanged for four pens,how many pens can be exchanged for one pencilcase?A.6 B.5 C.4 D.3 E.2【答案】E【解析】schoolbag notebooks pens,and pencilcases notebooks,Then,pencilcases notebooks pens.So,pencilcase pens.1=3=46=92=3=41=2 315.Suppose of equals of.What percentage of is?(adapted from 2020 AMC 8,Question 15)20\textbackslash%x40\textbackslash%yyx A.35 B.50 C.75 D.150 E.200【答案】E【解析】20\textbackslash%·x=40\textbackslash%·yx=2·y 316.If of a certain number is,the certain number is．1000\textbackslash%100 A.1 B.10 C.100 D.1000【答案】B【解析】If is,then of that,,is of the number.1000\textbackslash%100(110)th10100\textbackslash%317.Jin loves carrots!Yesterday she ate of her carrots,and today she ate of the number of carrots she ate yesterday.She ate 14 carrots today.Yesterday she had started with carrots.7927 A.18 B.4 C.49 D.60 E.63【答案】E【解析】14÷27÷79=63 318.A total of chickens and rabbits are caged together.If there are legs in total,how many chickens are there in the cage?2056 A.20 B.16 C.15 D.12 E.10【答案】D【解析】Suppose the number of chickens is,so the number of rabbits is.,.x(20−x)2x+(20−x)×4=56x=12 319.Ellie and Gloria have to interview a total of people.Ellie can interview people every week.If Gloria and Ellie work together,they can finish all the work in weeks.How many weeks will it take to finish interviewing everyone by Gloria herself?400604 A.8 B.10 C.12 D.14 E.16【答案】B【解析】Working together:people every week Gloria:people every week weeks400÷4=100100−60=40400÷40=10\textasciitilde 320.balloons are distributed to Ariel and seven other children.Each of them can get at least one balloon,and no two of them get the same number of balloons.For Ariel,what is the largest possible number of balloons she can get?50 A.22 B.18 C.16 D.14 E.10【答案】A【解析】The largest number of balloons Ariel can get is:,that is,balloons at most.50−−(1+2+3+4+5+6+7)=2222 321.students came into the classroom in turn.The number of students that came in before Mike was more than the number of students who came in after him.Which place did Mike come in?(Adapted from 2015 Math Kangaroo Problem,Level 3-4,Question#13)295 A.11 B.12 C.16 D.17 E.18【答案】E【解析】The sum of the number of students that came in before Tom and the number of students that came in after him is 29−1=28.The number of students that came in before Mike was(28+6)÷2=17,so Mike was the eighteenth.322.A sugar solution contains ounces of pure sugar.How many ounces of solution are there?15\textbackslash%18 A.ounces90 B.ounces100 C.ounces120 D.ounces150【答案】C【解析】18÷15\textbackslash%=120 ounces.323.The sum of two numbers is 71.The difference of the two numbers is 9.Find the bigger number.A.31 B.40 C.62 D.80【答案】B【解析】71+9=80 80 2=40÷324.For a quarter(￠),Pat can play a video game for minutes.How many quarters does Pat need to play for an hour?255 A.10 B.12 C.20 D.55【答案】B【解析】For a quarter(￠),Pat can play a video game for minutes.The number of-minute intervals in hour is.2555160÷5=12 325.The teacher has sweets.She wants to give eight students the same number of sweets.How many more sweets should she prepare?(adapted from Math kangaroo Problems,Level,Question#)1420201−216 A.0 B.1 C.2 D.3 E.4【答案】C【解析】,In this equation,means everyone can get sweet.There are sweets left,the teacher also needs sweets.14=8+68168−6=2 326.Given that May of a certain year is a Monday,what day of the week will July fall on in the same year?168 A.Monday B.Tuesday C.Wednesday D.Thursday E.Friday F.Saturday G.Sunday【答案】E【解析】May:June:July:R31−16+1=1630816+30+8=5454÷7=75 327.of the beads in a box are blue.of the blue beads are small.lf there are small blue beads,how many beads are there altogether in the box?1413700 A.1200 B.2100 C.2450 D.4900 E.8400【答案】E【解析】of the total beads are small blue beads.14×13=112700×12=8400 328.Nick bought apples from the supermarket.%of them were red and%of them were green.How many red apples did he buy?204060 A.8 B.10 C.12 D.14【答案】A【解析】%=.20×408 329.Famer had ducks.He had three times as many ducks as Farmer.Farmer had more ducks than Farmer.How many ducks did Farmer have?A1233BB199CC A.212 B.411 C.610 D.3898【答案】A【解析】Farmer B’s duck:Farmer C’s duck:1233÷3=411411−199=212 330.Given that June,was Thursday,what day was June,?142012142014 A.Monday B.Tuesday C.Friday D.Saturday E.Sunday【答案】D【解析】It would pass days,which means June,was two days after Thursday.It was Saturday.365+365=730142014 331.There are some apples and pears in a basket,each of them are green or yellow.There are three more apples than the total number of green fruit.There are yellow pears.How many yellow apples are there in the basket?86 A.4 B.5 C.6 D.7 E.8【答案】B【解析】NA 332.Starting with some gold coins and some empty treasure chests,I tried to put gold coins in each treasure chest,but that left treasure chests empty.So instead I put gold coins in each treasure chest,but then I had gold coins left over.How many gold coins did I have?．9263 A.9 B.27 C.45 D.63 E.81【答案】C【解析】Suppose is the number of treasure chests.Thus the number of gold coins can be represented as or.So,,.There are gold coins.x9(x−2)6x+39(x−2)=6x+3x=79×(7−2)=45 333.On a map represents.The distance between town A and town B is.A car leaves town A and travels towards town B at km per hour.How long does it take the car to travel to town B?4cm50km14cm35 A.4hours B.5hours C.10hours D.14hours E.18hours【答案】B【解析】If represents,represents.So,their actual distance apart is.hours.4\textasciitildecm50\textasciitildekm2\textasciitildecm25\textasciitildekm14÷2×25=175\textasciitildekm175÷35=5 334.Students guess that Norb’s age is,,,,,,,,,and.Norb says,"At least half of you guessed too low,two of you are off by one,and my age is a prime number."How old is Norb?(AMC problem,Question#)242830323638414447492011821 A.29 B.31 C.37 D.43 E.48【答案】C【解析】If at least half the guesses are too low,then Norb’s age must be greater than.If two of the guesses are off by one,then his age is in between two guesses whose difference is.It could be,,or,but because his age is greater than,it can only be or.Lastly,Norb’s age is a prime number so the answer must be.36231374836374837 335.Joan needs pounds of metal with silver.If Joan combines one metal with silver,and another with silver,how much of each metal does Joan need respectively?25027\textbackslash%23\textbackslash%43\textbackslash%A.200;50 B.150;100 C.100;150 D.50;200【答案】A【解析】,silver:,silver:.43\textbackslash%−27\textbackslash%27\textbackslash%−23\textbackslash%=164=4123\textbackslash%250×44+1=20043\textbackslash%250×44+1=50 336.If I start with,and begin to count in s,my number will be}.2350th A.148 B.149 C.150 D.151 E.152【答案】B【解析】2+(50−1)×3=149.337.Emma is years old.Anna is years old.Peter is older than Emma but younger than Anna.How old is Peter?912 A.13 B.8 C.10 D.7 E.5【答案】C【解析】NA 338.Some kangaroos are lining at bakery.Tom is the third kangaroo from the back,and the fifth from the front.How many kangaroos are there lining up in total?A.8 B.7 C.6 D.5【答案】B【解析】3+5−1=7 339.Henderson has sweets more than Flora.After teacher Johnny gave each of them more sweets,they have a total of sweets.How many sweets does Flora has at first?9743 A.16 B.10 C.9 D.17 E.19【答案】B【解析】43−14−9=2020÷2=10 340.If today is a Tuesday,then days ago was a.15 A.Saturday B.Sunday C.Monday D.Wednesday【答案】C【解析】Today is Tues.days ago was Tues.days ago was Mon.1415 341.In a jar of red,green,and blue marbles,all but are red marbles,all but are green,and all but are blue.How many marbles are in the jar?．161814 A.16 B.18 C.20 D.24 E.36【答案】D【解析】Suppose there are red marbles,green marbles and blue marbles.Thus,we can get,①②③:,.xyz{x+y=14①\textbackslash\textbackslashy+z=16②\textbackslash\x+z=18③++2x+2y+2z=48x+y+z=24 342.Sanjay let me finish his box of mints.He had eaten of them.If mints were left for me,how many mints were there in the box at the start?5836 A.96 B.58 C.68 D.36 E.56【答案】A【解析】36÷(1−58)=96 343.Calculate:11×7+17×13+113×19+⋯+11207×1213 A.12121213 B.3031213 C.2021213 D.12126065 E.None of the above【答案】C【解析】C 344.There are students in Think Primary School.Three-tenths of the students are in year and three-fifths of the year students are girls.How many year girls are there in Think Primary School?300555 A.36 B.48 C.54 D.60 E.90【答案】C【解析】300×310×35=54 345.The five-digit number is a multiple of.What digit does A represent?411A29 A.0 B.1 C.2 D.3 E.None of the above【答案】B【解析】From the Divisibility Rule of,the sum of the digit of 411A2 must be divisible by.Hence A=.994+1+1+4+2=8+A1 346.Iron Man’s flying speed is km/h,which is times the speed of a regular airplane.What is the speed of the airplane?12,25025 A.km/h490 B.km/h500 C.km/h4900 D.km/h5000 E.km/h245【答案】A【解析】The speed of the airplane is 12250÷25=490km/h.347.I am threading blue and purple beads onto a necklace in the ratio.I use beads in total.How many more purple beads than blue do I use?2:598 A.7 B.35 C.42 D.14 E.49【答案】C【解析】The ratio means that in beads are blue and in purple.Since,there are blue and purple beads,hence more purple than blue.2:5275798÷7=14287070−28=42 348.If Pip was 10 years old 5 years ago,how old will he be 7 years from now?A.12 B.14 C.16 D.22 E.18【答案】D【解析】10+5+7=22 349.Harry planted some trees around a m by m square garden.If there are trees planted at each of the corners,and the distance between every trees is m,at least how many trees did Harry plant?2020425 A.16 B.18 C.20 D.22【答案】A【解析】intervals on each side trees on each side20÷5=44+1=54×5−4=16 350.There is a basket of peaches.Three students take turns to take peaches.Sana takes less than the half of peaches.Joann takes more than half of the remaining peaches.Now,there are peaches in the basket.How many peaches are there in the basket at beginning?225 A.20 B.22 C.24 D.28 E.18【答案】C【解析】5+2=77+7=1414−2=1212+12=24 351.Mother’s Day in was May th,which was Sunday.Father’s Day in was June st.On what day did Father’s Day fall?202010202021 A.Thursday B.Saturday C.Sunday D.Tuesday【答案】C【解析】It passed days in total.Since,which means the Father’s Day fell on Sunday as well.31−10+21=4242÷7=6 352.Andy has candies.Bob has twice as many candies as Andy.Chloe has times as many candies as Andy.How many candies do they have altogether?64 A.24 B.35 C.42 D.48【答案】C【解析】omitted 353.James wants to make cakes.Each day he makes one cake.He made the first cake on Tuesday.What day of the week will it be when he makes the last cake?(Adapted from 2011 Math Kangaroo Problem,Level 3-4,Question#2)5 A.Wednesday B.Thursday C.Friday D.Saturday E.Sunday【答案】D【解析】Count day by day directly.354.Half a loaf of bread costs pence more than one-fourth of a loaf of bread.How many pence does a whole loaf of bread cost?(Math Kangaroo Problem,Level,Question#)619983−414 A.6 B.12 C.18 D.24 E.30【答案】D【解析】One-fourth of a loaf of bread is"unit".Half a loaf of bread is"units".One-fourth of a loaf of bread:.A whole loaf of bread:.126÷(2−1)=66×4=24 355.Many years ago,of May was a Friday.Which day of the week was of May in that year?1st23rd A.Thursday B.Friday C.Saturday D.Sunday E.Monday【答案】C【解析】First Friday:of May Second Friday:of May Third Friday:of May Fourth Friday:of May of May was a Saturday in that year.1st8th15th22nd23rd 356.There are stools and chairs in the room.Each stool has legs,and each chair has legs.Altogether there are legs.How many chairs are there in the room?3417 A.5 B.4 C.3 D.2 E.1【答案】D【解析】If there are five stools,the chairs have legs,which is not applicable.If there are four stools,the chairs have legs,which is also not applicable.If there are three stools,the chairs have legs,which implies that there are chairs and is applicable according to the question.17−3×5=217−3×4=517−3×3=88÷4=2 357.The cost of my algebra book is of that of my geometry book.The cost of my geometry book is that of my calculus book.If my calculus book costs＄,how much do all books cost together?200\textbackslash%43213 A.＄28 B.＄56 C.＄84 D.＄105【答案】D【解析】The cost of the calculus book is＄.The cost of my geometry book is＄＄.My algebra book costs＄＄.All books cost＄＄＄＄in total.2121×(43)=2828×2=56321+28+56=105 358.There are chocolates in Swee Tuth’s box,each of flavours.She likes only of the flavours.If she picks a chocolate at random,what is the probability of her getting one she doesn’t like?18296 A.29 B.13 C.49 D.12 E.23【答案】B【解析】Out of chocolates there are of the flavours that she likes.So the probability of Swee Tuth getting one she doesn’t like is.186×2=12618=13 359.Maddie is years older than Lola,and Lola is years younger than Ellie.How much older is Ellie than Maddie?26 A.years2 B.years3 C.years4 D.years5 E.years6【答案】C【解析】Ellie is years older than Lola,and Maddie is years older than Lola.Therefore Ellie is years older than Maddie.624 360.Some students are going to an amusement park.If each student carries bottles of water in his or her backpack,there will be students carrying nothing;if one of the students carries bottles of water and the rest students carry bottles each,all the bottles of water can be carried to the park.There are}bottles of water in total that need to be carried.9228 A.80 B.90 C.92 D.102【答案】B【解析】Solve the problem as a problem of surplus and shortage.If each student carries bottles,there will be a shortage of bottles;if each student carries bottles,there will be a shortage of bottles.Therefore,there are students and bottles of water.99×2=1888−2=6(18−6)÷(9−8)=1212×9−18=90 361.In a certain calendar year,there are more Mondays than Fridays,and more Sundays than Wednesdays.Which day of the week is March in that year?1st A.Monday B.Tuesday C.Wednesday D.Thursday E.Friday F.Saturday G.Sunday【答案】D【解析】Nil 362.A worm is staying at the bottom of a well with a depth of metres.If it climbs up metres in the daytime and slips down metres at night,which day will it climb up to the ground?1341 A.The th day4 B.The th day5 C.The th day6 D.The th day7【答案】A【解析】It climbs up metres in the day time and slips down metre at night,so it climbs up metres in a whole day.For the first days,it climbs metres.During the day time of the forth day,it climbs metres and reaches the ground.Then it needs four days to climb up to the ground.413394 363.A jacket was on sale.The original price was＄180,and Peter bought it at＄135.What was the discount rate?A.135\textbackslash%B.180\textbackslash%C.75\textbackslash%D.25\textbackslash%【答案】D【解析】1−135÷180=25\textbackslash%.364.Justin said to his mom,"If I had planted three times as many flowers as I planted,I would have planted more flowers than I have planted now."How many flowers did Justin plant?48 A.12 B.23 C.24 D.22【答案】C【解析】48÷(3−1)=24 365.Ella and George are lining up for dinner.Ella is sitting in the fifth from the front of the line,and George is sitting at the sixth from the end of the line.George and Ella are standing together.How many people are there in total?(adapted from 2001 Math Kangaroo Problem,Level 3-4,Question#13)A.12 B.11 C.10 D.9 E.8【答案】C【解析】5+6−1=10 366.There are children lining up outside a theme park.John is the th person counting from the front of the line and Mary is the th person counting from the back of the line.How many children are standing in line between John and Mary?20142 A.1 B.2 C.3 D.4 E.5【答案】D【解析】Mary is the th person in the line,so there are children are between them.20−2+1=1919−14−1=4 367.A mixture of liters of paint is red tint,yellow tint and water.liters of yellow tint are added to the original mixture.What is the percent of yellow tint in the new mixture?(adapted from 2007 AMC 8,Question#17)8020\textbackslash%30\textbackslash%50\textbackslash%20 A.33 B.36 C.39 D.42 E.44【答案】E【解析】The original mixture contains liters of yellow tint.liters of yellow tint is added to the mixture,the new mixture now has liters of yellow tint.New percent of yellow=80×30\textbackslash%=242024+20=444480+20=44\textbackslash%368.Calculate:13+23+33+⋯+173+183 A.4447881 B.23409 C.12654 D.29241 E.None of the above【答案】D【解析】D 369.A sugar solution contains g of pure sugar.How many g of solution are there?30\textbackslash%12 A.g30 B.g40 C.g50 D.g60【答案】B【解析】12÷30\textbackslash%=40 g.370.more than is}.943 A.42 B.52 C.62 D.50【答案】B【解析】43+9=52 371.My mom’s birthday is on Sunday,and my dad’s birthday is days later.On what day of the week will my dad’s birthday be?．55 A.Sunday B.Monday C.Tuesday D.Thursday E.Saturday【答案】E【解析】After day,it is Monday;after days,it is Tuesday;after days,it is Wednesday After days,it is still Monday,and the period is days.(weeks)(days).The birthday is Saturday.123⋯8755÷7=7R6 372.Sammy’s mom is years older than his dad.Right now,his dad is years old.How old was his mother years ago?62710 A.32 B.21 C.15 D.23 E.22【答案】D【解析】Now,his dad is years old,his mom is years older than his dad,so his mom is years old.years ago,his mom was years old.276331033−10=23 373.Given that October th,was Wednesday,on what day will October th,fall?102018102022 A.Monday B.Tuesday C.Wednesday D.Thursday【答案】A【解析】During this period,is a leap years.Therefore,October,is days after Wednesday,which is Monday.20201020221+2+1+1=5 374.The average cost of a long-distance call in the USA in 1985 was 56 cents per minute,and the average cost of a long-distance call in the USA in 2018 was 2 cents per minute.Find the approximate percent decrease in the cost per minute of a long-distance call.(adapted from 2007 AMC 8,Question#6)A.90 B.95 C.96 D.97 E.98【答案】C【解析】The percent decrease is(the amount of decrease)/(original amount)the amount of decrease is so the percent decrease is which is about56−2=54545696\textbackslash%375.At which of these times is the angle between the minute hand and the hour hand of a clock equal to 150∘?A.9pm B.8pm C.6pm D.5pm E.4pm【答案】D【解析】At all the times given,the minute hand is pointing to.When the minute hand is pointing to and the angle between the hands is,the hour hand has turned of a complete turn.Therefore the hour hand will point at and the time will be.(There are other times when the angle between the hands is but,of these,only at does the minute hand point to and is not one of the times given.)1212150∘150360=51255pm150∘7pm127pm 376.In hours Rob drove.He drove at an average rate of.4120kmm/min A.30 B.105 C.120 D.500【答案】D【解析】NA 377.SASMO 2015 P2 Q10 John is 5 years old this year.His sister is 2 years old.What is the sum of their age after 3 years?A.18 B.16 C.14 D.12 E.10【答案】A【解析】5+3=87+3=1010+8=18 378.Jack was able to sell%of his vegetables before noon.If he had 200 pounds of vegetables in the morning,how many pounds of vegetables was he able to sell by noon?30 A.30 B.50 C.60 D.140【答案】C【解析】%=,He was able to sell pounds of vegetables by noon.200×306060 379.I am going to travel at a rate of per hour.How many minutes will my trip take?200km60km A.60 B.200 C.260 D.320【答案】B【解析】I am going to travel at per hour.Since per hour is the same as per minute,my trip will take minutes.200km60km60km1km200 380.Last year,at the school where Gill teaches Mathematics,out of the pupils were girls.This year,the number of pupils in the school has increased to.The proportion of girls is the same as it was last year.How many girls are there at the school this year?315600640 A.339 B.338 C.337 D.336 E.335【答案】D【解析】Last year,the fraction of girls at the school was.This year,there are more pupils at the school,but the proportion of girls has remained the same.So there are more girls at the school this year,making a total of.315600=63120=21404021315+21=336 381.Chloe is buying candies at a grocery store.She can either spend dollars on a ounce bag or dollars on a ounce bag.Which is a better buy?8151220 A.ounce bag15 B.ounce bag20【答案】A【解析】8dollars15ounces12dollars20ounces 382.Jin loves carrots!Yesterday she ate of her carrots,and today she ate of the number of she ate yesterday.She ate 10 carrots today.Yesterday she have started with carrots.1427 A.36 B.48 C.60 D.72 E.140【答案】E【解析】10÷27÷14=140 383.Tom scored a basket at the end of the third quarter of a basketball game between the Lakers and the Warriors.At that point,what fraction of the whole game remained to be played?A.14 B.13 C.12 D.34 E.23【答案】A【解析】Basketball games consist of four quarters.Tom’s scoring at the end of the third quarter implies that there is one quarter left,which is equivalent to 1/4 of the entire game.384.Five positive integers(not necessarily all different)are written on five cards.Boris calculates the sum of the numbers on every pair of cards.He obtains only three different totals:57,70 and 83.What is the largest integer on any card?A.35 B.42 C.48 D.53 E.82【答案】C【解析】Let the five integers be a,b,c,d and e with a≤b≤c≤d≤e.The smallest total is 57,which is an odd number so b≠a.Similarly,the largest total is 83,which is also an odd number so d≠e.Hence we now have a<b≤c≤d<e and a+b=57 and d+e=83.Only one possible total remains and so b=c=d with c+d=70.This gives c=d(=b)=35 and therefore e,the largest integer,is 83−35=48(whilst a=22).385.The average cost of a long-distance call in the USA in 1985 was 44 cents per minute,and the average cost of a long-distance call in the USA in 2005 was 11 cents per minute.Find the approximate percent decrease in the cost per minute of a long-distance call.(adapted from 2007 AMC 8,Question#6)A.25 B.50 C.75 D.100 E.125【答案】C【解析】The percent decrease is(the amount of decrease)/(original amount)the amount of decrease is so the percent decrease is which is about44−11=333344(𝐜)75\textbackslash%386.James lives on the second floor,and Paul lives in the same building but has to walk up five times as many stairs as James.There are no stairs to the entrance of the building.On which floor does Paul live?(Adapted from 2000 Math Kangaroo Problem,Level 3-4,Question#4)A.On the floor2nd B.On the floor3rd C.On the floor4th D.On the floor5th E.On the floor6th【答案】E【解析】5+1=6 387.Greta was tall years ago,when she was taller than her brother.They both have grown,but now Greta is shorter than her brother.If her brother grew in those two years,Greta is now tall.110cm210cm10cm40cmcm A.120 B.130 C.140 D.150【答案】B【解析】Greta was tall years ago,when she was taller than her brother.Her brother was then.Now Greta is shorter than her brother.If her brother grew,he is now.Greta is now tall.110cm210cm100cm10cm40cm140cm130cm 388.The average weight of students in Class is kilograms.The average weight of students in Class is kilograms.The total weight of students in Class is kilograms.What is the average weight of the students in the classes?4A3711B415C1613 A.kilograms36 B.kilograms38 C.kilograms40 D.kilograms43【答案】B【解析】kilograms in total.kg.4×37+11×41+161=760760÷(4+11+5)=38 389.Cici and Kiki took the same quiz.They agreed on the following rules:a person got points for a correct answer and lost points otherwise(getting a wrong answer or skipping a question).They each answered questions and together got points.If Cici got more points than Kiki,how many questions did Kiki answer correctly?105109515 A.6 B.7 C.8 D.9【答案】A【解析】Kiki got points.If she answered all the questions correctly,she would have gotten points.Hence,she skipped or got wrong answers and she answered questions correctly.(95−15)÷2=40100(100−40)÷(10+5)=410−4=6 390.Amy and Bella bought some cookies in the ratio of.Bella gave cookies to Amy.Then the ratio of the number of cookies Amy had to that of Bella was.How many cookies did they have at first?3:491:1 A.54 B.63 C.72 D.126【答案】D【解析】Total number of cookies both of them had did not change.Make total the same number of units by finding LCM.Before After cookies at first(and also in the end)in total.→A:B:Total→3:4:7→6:8:14→A:B:Total→1:1:2→7:7:141u=914u=14×9=126 391.Alex,John and Sam went to buy oranges.Alex paid 20text and Sam only paid 5120$oranges altogether.They divided them in proportion to the amount of money each of them had paid.How many oranges did John get?\textbackslash,Johnpaid15\textbackslash.Theybought A.15 B.30 C.45 D.60 E.None of the above【答案】C【解析】A:J:S 20:15:5=40 120/40=3 oranges per person 3*15=45 oranges 392.If February is Monday,what day of the week is th February?3th27 A.Sunday B.Monday C.Wednesday D.Thursday E.Saturday【答案】D【解析】We can count backward by days or by weeks.Count a few weeks back to find that nd February is a Monday.Then count a few days back to find that th February is a Wednesday.2224 393.The speed of high-speed train is approximately kilometres per hour,while the walking speed of a person is approximately metres per second.Approximately,how many times is the speed of a high-speed train faster than the walking speed of a person?．3505 A.2 B.20 C.70 D.200 E.700【答案】B【解析】The speed of high-speed train is approximately kilometres per hour,which is approximately metres per second.So its speed is roughly times faster than metres per second.350100205 394.Martha had＄.She bought caramels at￠each.How many chocolate mints at￠each can she buy with the money she has left?1.5012510 A.12 B.11 C.10 D.9【答案】D【解析】Martha had＄.She bought caramels at￠each,spengding￠and leaving her with￠.With￠,she can buy mints at￠each.1.5012560909090÷10=910 395.Balloons are sold in packets of,,and.Marius buys exactly balloons.What is the smallest number of packets he can buy?(2017 Math Kangaroo Problem,Level 3-4,Question#11)5102570 A.3 B.4 C.5 D.6 E.7【答案】B【解析】70=25+25+10+10 396.Three hens and four rabbits are in a cage.How many legs do they have?(adapted from Math kangaroo Problems,Level,Question#)20111−24 A.12 B.15 C.18 D.22 E.24【答案】D【解析】A hen has two legs and a rabbit has four legs,so three hens have six legs and four chickens have sixteen legs.6+16=22 397.A police spots a burglar from m apart.The burglar immdiately runs away at a speed of m/s and the police starts chasing him at m/s at the same time.At this rate,how long will it take the police to catch the burglar?480812 A.seconds24 B.seconds40 C.minutes1 D.minutes2【答案】D【解析】The distance between them is m,and the difference between their speeds is m/s.It takes seconds to catch the burglar,which is minutes48012−8=4480÷4=1202 398.At the 2013 Winnebago County Fair a vendor is offering a"fair special"on sandals.If you buy one pair of sandals at the regular price of 5040 text%text regular price did he save?(2013 AMC 8,Question#12)\textbackslash,yougetasecondpairatadiscount,andathirdpairathalftheregularprice.Javiertookadvantageofthe"fairspecial"tobuythreepairsofsandals.Whatpercentageofthe150 A.25 B.30 C.33 D.40 E.45【答案】B【解析】First,find the amount of money one will pay for three sandals without the discount.We have 50×3=text Then,find the amount of money using the discount:105(105)/(150)=70 text%100 text%-70 text%=(B)30\textbackslashsandals15050+0.6×50+12×50=\textbackslash.FindingthepercentageyieldsTofindthepercentsaved,wehave 399.There was a-meter long corridor in the school.The teacher asked Jack to put a flowerpot on the corridor every three meters.How many flowerpots did Mike put?(adapted from Math kangaroo Problems,Level,Question#)1520081−27 A.4 B.5 C.7 D.6 E.8【答案】D【解析】The corridor is divided into segments.The number of flowerpots is one more than that of the segments,so.15÷3=55+1=6 400.The original price of a pair of shoes was\textbackslash$85.Then,it was sold at a discount of 20\textbackslash%.What was the price of the pair of shoes after the discount?A.$17 B.$52 C.$68 D.$102【答案】C【解析】After discount,price became of original price.85×80text%=text8100\textbackslash%−20\textbackslash%=80\textbackslash%\textbackslash85×0.8=\textbackslash 401.Julia has eaten one-quarter of the pizza.What is the ratio of the number of pizza that remain to the number Julia has eaten?A.1:3 B.3:1 C.1:4 D.4:1 E.4:3【答案】B【解析】Julia has eaten one-quarter of the pizza.So three-quarters of the pizza remain.Therefore the required ratio is.34:14=3:1 402.In a certain quiz show there are the following rules:every participant has points at the beginning and has to answer questions.For each correct answer,the participant earns point,and for each incorrect answer,the participant loses point.Mrs.Smith had points at the end of this quiz show.How many correct answers did she give?(Math Kangaroo Problem,Level,Question#)1010111420113−417 A.7 B.8 C.9 D.6 E.4【答案】A【解析】Full score:.Smith gets questions wrong,and questions correct.10+10×1=20(20−14)÷(1+1)=310−3=7 403.My mom’s birthday is on Sunday,and my dad’s birthday is days after it.On what day of the week will my dad’s birthday be?(Math Kangaroo Problem,Levels,Question#)5519993−49 A.Sunday B.Monday C.Tuesday D.Thursday E.Saturday【答案】E【解析】55÷7=7R6.It is Saturday.404.Penelope paid＄24.58 for pens and pencils.If pens cost 9￠each and pencils cost 4￠each,at most how many pens did Penelope purchase?A.273 B.272 C.271 D.270【答案】D【解析】Continue subtracting￠from￠until the difference is a multiple of.This happens when the difference is￠which is￠.4245892430270×9 405.The selling price of a sofa set is＄and the profit percentage is for each set sold.If the cost of the sofa set is not changed,what is the new profit percentage if raising the profit to＄?550010\textbackslash%1800 A.24\textbackslash%B.25\textbackslash%C.30\textbackslash%D.36\textbackslash%【答案】D【解析】5500÷(1+10\textbackslash%)=5000,1800÷5000=36\textbackslash%.406.A worm is at the bottom of a well with a depth of metres.If it climbs up metres in the day and slips down metre at night,how many days will it take the worm to climb up to the ground?1131 A.8 B.7 C.6 D.5 E.4【答案】D【解析】It climbs up meters in the day time and slips down meter at night,so it climbs up meters in a whole day.For the first days,it climbs meters.During the day time of the fifth day,it climbs meters and reaches the ground.Then it needs five days to climb up to the ground.312483 407.Bowen has ounces of a sugar solution.After}of water evaporates,the percent concentration of the solution is.(Evaporate:the water turns from liquid into vapor and is no longer in the solution anymore.)4025\textbackslash%40\textbackslash%A.ounces15 B.ounces12 C.ounces9 D.ounces6【答案】A【解析】40−40×25\textbackslash%÷40\textbackslash%=40−25=15 ounces.408.Patrick gets on a 10-problem test,on a 20-problem test and on a 30-problem test.If the three tests are combined into one 60 problem test,which percent is closest to her overall score?(adapted from 2006 AMC 8,Question#12)80\textbackslash%60\textbackslash%50\textbackslash%A.50 B.52 C.55 D.58 E.60【答案】D【解析】,,Adding them up gets.The overall percentage correct would be.80\textbackslash%·10=860\textbackslash%·20=1250\textbackslash%·30=158+12+15=353560≈0.58 409.Gawel lives on the 2nd floor,and Pawel lives in the same building but has to walk up twice as many stairs as Gawel.There are no stairs to the entrance of the building.On which floor does Pawel live?A.on the nd floor2 B.on the rd floor3 C.on the th floor4 D.on the th floor5 E.on the th floor6【答案】B【解析】Gawel lives on the second floor,so he only needs to walk up one floor.Pawel has to walk up twice as many stairs as Gawel,so he needs to walk up two floors.So,Pawel lives on the rd floor.3 410.Ben stands in line and has people behind him,If there are a total of people in line,how many people are there in front of Ben?76110 A.33 B.34 C.35 D.36【答案】A【解析】If there are a total of people in line,subtract those behind Ben and Ben himself:,the number in front of Ben.110110−76−1=33 411.A jacket was on sale.The original price was＄180,and Peter bought it at＄135.What was the discount?A.135\textbackslash%B.180\textbackslash%C.75\textbackslash%D.25\textbackslash%【答案】D【解析】1−135÷180=25\textbackslash%.412.The sum of two numbers is.The smaller number is.What is the greater number?800356 A.1156 B.556 C.454 D.444【答案】D【解析】800−356=444 413.There are chickens and rabbits in the case,and the total number of legs is.How many rabbits in this case?2048 A.4 B.6 C.8 D.10 E.12【答案】A【解析】If all were rabbits,the total number of legs would be.The difference is.20×4=80$8080−48=32$324−2=232÷2=1620−16=4 414.A sugar solution is made by mixing ounces of sugar and ounces of water.Find the percent concentration of the solution.1015 A.20\textbackslash%B.25\textbackslash%C.30\textbackslash%D.40\textbackslash%【答案】D【解析】10÷(10+15)=40\textbackslash%.415.Mother baked cookies.She gave cookies to her friend and packed the rest equally into bottles.She put cookies in each bottle.How many bottles did she use?4084 A.7 B.8 C.9 D.10【答案】B【解析】,.Mother used bottles.40−8=3232÷4=88 416.Julian started reading a book with pages.He read pages on each day from Monday to Friday and pages on each day on Saturday and Sunday.He started reading on a Thursday.On which day of the week did he finish reading the book?．348611 A.Friday B.Saturday C.Sunday D.Monday【答案】D【解析】Thursday to Sunday pages week(Monday to Sunday)pages weeks pages After reading another pages in weeks,Julian has another pages left to read.It will now be a Monday and Julian can finish reading the last pages.arrow6×2+11×2=34348−34=3141arrow11×2+6×5=526arrow52×6=3123126(314−−312)=22 417.%of the students at Hamilton Middle School have red hair.There are students at Hamilton Middle School.How many students at Hamilton Middle School have red hair?5800 A.5 B.40 C.400 D.760【答案】B【解析】%=,students at Hamilton Middle School have red hair.800×54040 418.My pay is the same every day I work.I worked every day in,even weekends.In March,I earned＄.I earned for all of.19929301992 A.＄11346 B.＄11315 C.＄10980 D.＄10950【答案】C【解析】In March,there are days.I earned＄,which is＄each day.For all of,I earned＄＄.31930÷31301992366×30=10980 419.Zosia is drawing kangaroos.The first one is blue,the next one green,the one after it red,the fourth one yellow,and then again blue,green,red,yellow,and so on,in the same order.What color will the seventeenth kangaroo be?(2003 Math Kangaroo Problem,Level 3-4,Question#4)A.Blue$B.Green$C.Red$D.Black$E.Yellow$【答案】A【解析】A group of the blue one,the green one,the red one,and the yellow one is repeating.17÷4=4R1,so the seventeenth one is blue.420.William is 15 years old,and his sister is 23 years old.How old will his sister be when William is 23 years old?A.23 B.31 C.38 D.26【答案】B【解析】omitted 421.Luna,Lily,and Lucy are talking about their ages.years ago,Luna was born,and Lily was years old.This year,the sum of ages of these people is.When Luna was born,how old was Lucy?65333 A.7 B.8 C.9 D.10 E.11【答案】D【解析】Six years ago,the sum of ages of Luna,Lily,and Lucy was.Lucy was years old.33−6×3=1515−0−5=10 422.Jack mixed g of salt solution,g of salt solution,and g of salt solution together.What is the percent concentration of salt solution at this time?20010\textbackslash%20015\textbackslash%40020\textbackslash%A.15\textbackslash%B.16\textbackslash%C.16.25\textbackslash%D.17\textbackslash%【答案】C【解析】200×10\textbackslash%+200×15\textbackslash%+400×20\textbackslash%200+200+400×100\textbackslash%=16.25\textbackslash%.423.After Sally takes 20 shots,she has made of her shots.After she takes 10 more shots,she drops her percentage to.How many of the last 5 shots did she make?(adapted from 2004 AMC 8,Question#6)75\textbackslash%60\textbackslash%A.2 B.3 C.4 D.5 E.6【答案】B【解析】Sally made shots originally.Letting be the number of shots she made,we have.Solving for gives us0.75*20=15x15+x30=0.6xx=3 424.Crystal and Angela had a poem recitation game.Each poem in their game earned points.Crystal recited poems and Angela recited poems.How many more points than Crystal did Angela earn?(adapted from Math kangaroo,Level,Question#)271120211−214 A.4 B.6 C.8 D.10 E.12【答案】C【解析】Angela recited poems more than Crystal.There are 42 points11−7=4×=8 425.A test is with a full score of points.Five students in a group wants to reach an average of points.If everyone scores a different whole number,the lowest score among them could be}.10092 A.60 B.61 C.66 D.70 E.71【答案】C【解析】92×5−(100+99+98+97)=66.426.Given that April,was Friday,what day was May,?152011112011 A.Thursday B.Saturday C.Tuesday D.Wednesday【答案】D【解析】Counting from April,,after days it will be April,.After days,it will be May,.In total,there are days.,which means May,was Wednesday.15201130−15=153020111111201115+11=2626÷7=3R5112011 427.The perimeter of a cuboid is 180.What is the largest volume?A.216 B.3375 C.720 D.9600 E.1200【答案】B【解析】180÷12=1515×15×15=3375 428.A train travels from Exeter to Cambridge at a speed of.Given that Cambridge is away from Exeter,How far is the train away from Cambridge after setting off for 5 hours?55km/h420km A.55km B.145km C.275km D.420km【答案】B【解析】420−(55×5)=420−275=145 429.In the teachers’lounge there are tables with chairs by each one,tables with chairs by each,and tables with chairs by each.How many chairs are there in the lounge?(2003 Math Kangaroo Problem,Level 3-4,Question#5)644236 A.40 B.25 C.50 D.36 E.44【答案】C【解析】6×4+4×2+3×6=50 430.Helga is climbing stairs in such a way that she goes up steps at a time.She is standing on the third step now.On which step will she be after she moves up times?23 A.9 B.1 C.6 D.5 E.8【答案】A【解析】Moving up times is steps.Now she is on the third step,after moving up steps,she is on the ninth step.366 431.If today is Tuesday,what day of the week will be 86 days later?A.Wednesday B.Thursday C.Friday D.Saturday【答案】B【解析】．2 days later will be Thursday.86÷7=12⋯⋯2 432.Last month,the price of a couch increased by 60025text%text at the sale.What is the percentage decrease in the cost of the couch as compared to the original price of the couch before the discount?\textbackslash.Duringasalethismonth,thecouchwasofferedatadiscount.Johnboughtthecouchat2250 A.6.66\textbackslash%B.5\textbackslash%C.6.25\textbackslash%D.None of the above.【答案】C【解析】Price before discount 2250=text Original price of the couch before increase 3000-text400=text250=text Percentage decrease 150textbackslas=10075×\textbackslash3000=\textbackslash600=\textbackslashPricedecrease2400−\textbackslash150=\textbackslash2400}×100\textbackslash%=6.25\textbackslash%433.Anna is lining up to get some ice-cream.Counting from the front,she is the th in the line.Counting from the back,she is the th.How many people are there lining up?47 A.9 B.10 C.11 D.12【答案】B【解析】4+7−1=10 434.Jerry starts a savings account with＄at a bank.The interest rate is per year.How much interest will he earn in his savings account at the end of the second year?7,0003\textbackslash%A.＄426 B.＄426.3 C.＄4,263 D.＄4,263.6【答案】B【解析】7000×(1+3\textbackslash%)×(1+3\textbackslash%)−7000=426.3.435.A bookstore purchases some story books at＄22 each.If the bookstore wants to earn＄11 for each book,what is the selling price of each book?A.＄22 B.＄33 C.＄35 D.＄44【答案】B【解析】22+11=33.436.There are four books on my shelf.The almanac and the dictionary together weigh 4310g.The biography and the cookbook together weigh 2325g.If the almanac and the biography together weigh 2795g,what is the weigh of the cookbook and dictionary together?A.2620g B.3270g C.3840g D.4100g【答案】C【解析】The almanac,the dictionary,the biography,and the cookbook together weigh 4310g+2325g=6635g.Since the almanac and the biography together weigh 2795g,the cookbook and the dictionary together weigh 6635g−2795g=3840g.437.There are balloons in the shop.Pip bought of them.The shop left}balloons.7249 A.20 B.32 C.40 D.52 E.60【答案】C【解析】72×(1−49)=32 438.On Monday morning,a snail fell down a well which is meters deep.During the day,it climbs up meters,and during the night it slides down meter.On what day of the week will the snail get out of the well?(Math kangaroo Problem,Level,Question#)102119985−618 A.Tuesday$B.Thursday$C.Saturday$D.Sunday$E.Monday$【答案】A【解析】Except the last day,the snail could climb up m.Thus,it takes the snail days to get out of the well.days from Monday is the next Tuesday.2−1=1(10−2)÷1+1=99 439.When one ounce of water is added to a mixture of acid and water,the new mixture is acid.When one ounce of acid is added to the new mixture,the result is acid.The percentage of acid in the original mixture is(AHSME Problem,Question#)20\textbackslash%3313\textbackslash%197333 A.22\textbackslash%B.24\textbackslash%C.25\textbackslash%D.30\textbackslash%E.3313\textbackslash%【答案】C【解析】Let be the original number of ounces of acid and be the original number of ounces of water.We can write two equations and.Then cross-multiply to get rid of the fractions.,Solve the system to get and.The percentage of acid in the original mixture is.awaa+w+1=15a+1a+w+2=135a=a+w+13a+3=a+w+1a=1w=311+3=25\textbackslash%440.Brandon is engaging sprint race on the track.He is in the fifth place now,and there are players behind him.There are extra groups signing up for sprint race,and the number of players of each group are idential.How many sprint players are there in total?85 A.65 B.70 C.78 D.84 E.96【答案】D【解析】(5+1+8)×(5+1)=84 441.A shop advertises everything is"half price in today’s sale."In addition,a coupon gives a discount on sale prices.Using the coupon,the price today represents what percentage off the original price?(adapted from 2012 AMC 8,Question#8)25\textbackslash%A.40\textbackslash%B.42.5\textbackslash%C.57.5\textbackslash%D.62.5\textbackslash%E.70\textbackslash%【答案】D【解析】75\textbackslash%·50\textbackslash%=37.5\textbackslash%1−37.5\textbackslash%=62.5\textbackslash%442.James can frost a cookie every seconds and Lacey can frost a cookie every seconds.Working together,how many cookies can they frost in minutes?(Adapted from AMC Problem,Question#)121510201210A11 A.50 B.60 C.80 D.90 E.100【答案】D【解析】In seconds(minutes),James will frost cookies,and Lacey will frost cookies.Therefore,working together they will frost cookies.6001060012=5060015=4050+40=(D)90 443.Judy ran for minutes.If her average speed was meters per minute,then how many meters did Judy run?1680 A.800 B.5 C.1280 D.96【答案】C【解析】80×16=1280 444.The length of a rectangle is increased by and the width is decreased by.What percent of the old area is the new area?(2009 AMC 8,Question#8)10\textbackslash%10\textbackslash%A.90 B.99 C.100 D.101 E.110【答案】B【解析】In a rectangle with dimensions,the new rectangle would have dimensions.The ratio of the new area to the old area is10×1011×999/100=(B)99 445.The price ratio of goods to is.If their prices were increased by respectively,the price ratio would be.What are the prices of these two goods?AB7:2\textbackslash$605:2 A.,\textbackslash$315\textbackslash$90 B.,\textbackslash$320\textbackslash$100 C.,\textbackslash$330\textbackslash$120 D.,\textbackslash$350\textbackslash$200【答案】A【解析】The price difference between the two goods did not change.Before is After is Make difference the same number of units in both ratios by finding LCM.Before is After is Therefore,The original prices of these two goods were and.→A:B:Difference7:2:5→A:B:Difference5:2:3\textasciitilde→A:B:Difference21:6:15→A:B:Difference25:10:15\textasciitilde4u=\textbackslash$601u=\textbackslash$60÷4=\textbackslash$15\textasciitildeA=21u=21×15=\textbackslash$315B=6u=6×15=\textbackslash$90 446.Ela and Kasia boarded a super-train.Ela took a seat in the seventeenth car counting from the front of the train,and Kasia was seated in the thirty-fourth car counting from the end.The girls were sitting in the same car.How many cars did the super-train have?(2001 Math Kangaroo Problem,Level 3-4,Question#13)A.48 B.49 C.50 D.51 E.52【答案】C【解析】17+34−1=50 447.James had dollars,and he deposited＄in Bank and＄in Bank.At the end of the year,James received an interest of＄in total.Given that the sum of the annual interest rates of the two banks is,find the interest rates of the two banks,respectively.100007000A3000B46010\textbackslash%A.;.2\textbackslash%8\textbackslash%B.;.3\textbackslash%7\textbackslash%C.;.4\textbackslash%6\textbackslash%D.;.5\textbackslash%5\textbackslash%【答案】C【解析】Let be the interest rate of bank:.xA7000x+3000(10\textbackslash%−x)=460x=4\textbackslash%448.Peter has a rope,and he ties some knots,each using-cm rope.He ties knots in total.After he ties the last knot,the knots divide the rope into pieces equally,and the length of each piece is cm.What is the length of the entire rope?10257 A.cm425 B.cm432 C.cm456 D.cm478 E.cm480【答案】B【解析】25×10+(25+1)×7=432 449.The scale of a map is:of an inch miles.If the distance on the map between two towns is inches,the actual distance between the towns is．34=1012 A.miles90 B.miles120 C.miles150 D.miles160【答案】D【解析】Since,the actual distance between the towns is miles.12÷34=1616×10=160 450.Gawel lives on the second floor,and Pawel lives in the same building but has to walk up twice as many stairs as Gawel.There are no stairs to the entrance of the building.On which floor does Pawel live?(2000 Math Kangaroo Problem,Level 3-4,Question#4)A.on the nd floor2 B.on the rd floor3 C.on the th floor4 D.on the th floor5 E.on the th floor6【答案】B【解析】Gawel lives on the second floor,so he only needs to walk up one floor.Pawel has to walk up twice as many stairs as Gawel,so he needs to walk up two floors.So,Pawel lives on the rd floor.3 451.I ate half an apple pie on Saturday and two thirds of the remainder on Sunday.What fraction of the pie was left for Monday?A.None B.12 C.13 D.23 E.16【答案】E【解析】After I eat one half,half of the apple pie is left.Eating two thirds of this half leaves one third of one half of the pie,which is one sixth,for Monday.452.The length of Amy’s string is.The length of David’s string is.What is the total length of both strings?35cm29cm A.54cm B.49cm C.64cm D.65cm E.66cm【答案】C【解析】35+29=64 453.Cici bought pencils and notebooks in total for.Each pencil cost.Each notebook costs.How many notebooks did Cici buy?126628 A.5 B.6 C.7 D.8 E.10【答案】C【解析】12×2=248−2=666−24=4242÷6=7 454.There are oranges,apricots and peaches in a big basket.How many fruits are there in the basket if the peaches and the apricots together are 18,the oranges and the apricots together are 28 and 30 fruits are not apricots?A.46 B.20 C.40 D.38 E.29【答案】D【解析】If we sum up the number of A and P,the result is 18.But if we sum up A and O,result is 28 instead.Hence,there must be 10 more O than P.Note that there are a total of 30 I and P.Therefore,there are(30+10)/2=20 Oranges.Total=20+18=38.455.Suppose of equals of.What percentage of is?(2020 AMC 8,Question 15)15\textbackslash%x20\textbackslash%yxy A.5 B.35 C.75 D.13313 E.300【答案】C【解析】Since,multiplying the given condition by 5 shows that is percent of.20\textbackslash%=15y15·5=(𝐂)75x 456.Five people took the same test and got an average score of 80.Four of the people scored 80,85,82,and 90,respectively.What is the score of the remaining person?A.80 B.76 C.73 D.63 E.56【答案】D【解析】There are points more than the average,so the last score is.0+5+2+10=1780−17=63 457.It is now.How many minutes does it take for the clock’s hour and minute hands to overlap for the first time?4:00 A.minutes43711 B.minutes101011 C.minutes21911 D.minutes22911 E.minutes42711【答案】C【解析】(30×4)÷(6−0.5)=120÷5.5=24011=21911 minutes.458.Chloe and Zoe are both students in Ms.Demeanor’s math class.Last night they each solved half of the problems in their homework assignment alone and then solved the other half together.Chloe had correct answers to only of the problems she solved alone,but overall of her answers were correct.Zoe had correct answers to of the problems she solved alone.What was Zoe’s overall percentage of correct answers?(2017 AMC 8,Question#14)80\textbackslash%88\textbackslash%90\textbackslash%A.89 B.92 C.93 D.96 E.98【答案】C【解析】Assume the total amount of problems is 100 per half homework assignment,since we are dealing with percentages,and not values.Then,we know that Chloe got 80 problems correct by herself,and got 176 problems correct overall.We also know that Zoe had 90 problems she did correct alone.We can see that the total amount of correct problems Chloe and Zoe did was.Therefore Zoe has problems out of 200 problems correct.This is(C)percent.176−80=9696+90=18693 459.Three boxes under my stairs contain apples or pears or both.Each box contains the same number of pieces of fruit.The first box contains all twelve of the apples and one-ninth of the pears.How many pieces of fruit are there in each box?A.14 B.16 C.18 D.20 E.36【答案】B【解析】(1−19)÷2=49,49−19=13,12÷13=36,36×49=16.460.Duckings are walking in a queue when they are following the mother duck.Joey the duckling is the 6th from the front and 8th from the back(including the mother duck).Some of the ducklings at the back moved away from the queue making Joey the middle duckling in the queue.How many ducklings moved away from the queue?A.2 B.3 C.4 D.5 E.None of the above.【答案】A【解析】total number of duck and ducklings in the queue is 6+(8-1)=13.if 2 ducklings at the back moved away,it would be 13-2=11 in the queue,and the middle ducking would be 6th from the front,which is Joey’s position.461.Every week,Robyn swims while Sam sings.For every of Sam’s songs,Robyn swims lengths.If Robyn swims lengths,how many songs does Sam sing?2954 A.6 B.8 C.10 D.12 E.18【答案】D【解析】Sam sings songs in the time that Robyn swims lengths.The time that she takes for lengths is times longer,so Sam will sing songs.295454÷9=62×6=12 462.If today is a Wednesday,then days ago was a．22 A.Tuesday B.Wednesday C.Thursday D.Friday【答案】A【解析】Today is Wednesday.days ago was Wednesday.days ago was Tuesday.or weeks day.day before Wednesday was a Tuesday.2122\textasciitilde\textasciitilde22÷7=311 463.John drinks cups of boba everyday on weekdays and cups of boba everyday on the weekends.Which of the following equations represents how many cups of boba John drinks every week?x1 A.x+2 B.5x+2 C.5x+1 D.5x−1【答案】B【解析】The boba that John drinks during weekdays:The boba that John drinks during weekends:The total boba that John drinks during a week:5x2×1=25x+2 464.This year Gareth is seven times the age of his son Herbie.In six years’time Gareth will be four times as old as Herbie.What is the difference between Gareth’s and Herbie’s ages this year?A.years16 B.years20 C.years24 D.years36 E.years42【答案】D【解析】Let Herbie’s age this year be years.Then Gareth’s age this year is years.In years’time,their ages will be years and years respectively.We are told that.This gives so that and.So the present ages are and,giving a difference of years.h7h6h+67h+67h+6=4(h+6)7h+6=4h+243h=18h=667×6=4236 465.A piece of pasture can feed cow for days or cows for days.If the grass grows at the same speed every day,how many cows can it feed for days?．173019246 A.38 B.45 C.49 D.52【答案】C【解析】17×30=51019×24=456510−456=5454÷(30−24)=9510−30×9=240240+6×9=294294÷6=49 466.The month of February of a given year has five Fridays.What day of the week is January of that year?31 A.Tuesday B.Thursday C.Friday D.Saturday【答案】B【解析】There are seven days in a week;so,in order to have five Fridays,a month has at least days.Since February has at most days,the and days of this February must both be Fridays,which means that January is a Thursday.4×7+1=29291st29th31 467.Several students are singing in a line.Amy is the fourth one from the left.From the right,Amy is the fourth too.How many students are singing?(adapted from Math kangaroo Problems,Level,Question#)20191−25 A.5 B.6 C.7 D.8 E.9【答案】C【解析】It comes when we count Amy twice.The number of all singing students is4+4=84+4−1=7 468.If six days ago was a Tuesday,then eight days from today is a．A.Monday B.Tuesday C.Wednesday D.Thursday【答案】B【解析】days ago was a Tuesday.Today is Monday.Thus,in days’time,it will be a Tuesday.68 469.In the sequence of letters the word is repeated indefinitely.What is the letter in this sequence?KANGAROOKANGAROOKANG⋯KANGAROO2017th A.K B.N C.G D.R E.O【答案】A【解析】The sequence repeats every letters.Since,the letter in the sequence is the first of the repeating sequence and hence is.KANGAROOKANGAROOKANG⋯82017=8×252+12017thK 470.There are students in your class.The ratio of boys to girls is.How many boys and girls are there?.303:2 A.and3020 B.and2030 C.and1812 D.and1218【答案】C【解析】According to the ratio 3:2,we could know the total is 5.Then the number of boys is 30×35=18.The number of girls is 30×25=12.471.A bag contains raffle tickets in red,white and blue.The ratio of red to white tickets is and the ratio of white to blue tickets is.What is the smallest number of tickets that would have to be picked to make sure having selected at least half of one colour?1005:48:7 A.48 B.49 C.50 D.51 E.52【答案】A【解析】First we must work out the number of tickets of each colour.Let the numbers of red,white and blue tickets be,and b respectively;we have and.Writing as,we can combine the ratios to find.Hence for a total of tickets,there must be red,white and blue tickets.Now the largest number of red tickets one can select without having half of them is,and likewise and for white and blue tickets.So it would be possible to select tickets and still not have half or more of any particular colour of ticket.However,the very next ticket,the,would have to be a red,a white or a blue one,and so one of the colours would now have at least half of its number selected.rwr:w=5:4w:b=8:7r:w10:8r:w:b=10:8:710040322819151319+15+13=4748th 472.Alice’s first day in Caterpillar Club was Tuesday.She wants to throw a party on her day in the club.If Alice attends the club everyday,on which day of the week will the party be?40th A.Friday B.Saturday C.Sunday D.Monday E.None of the above【答案】B【解析】40th day=39th day after first day joining.39 days/7=5 weeks R 4 days.4 days after Tues is Saturday.473.Jenny is years old.She has sisters,Julie and Jas.Julie is year older than Jas.In two year’s time,their total age will be years.How old is Julie now?52118 A.3 B.4 C.5 D.6 E.7【答案】B【解析】NA 474.Julia has eaten one-quarters of the pizza.What is the ratio of the number of pizza that remain to the number Julia has eaten?A.1:3 B.3:1 C.1:4 D.4:1 E.4:3【答案】B【解析】Julia has eaten one-quarters of the pizza.So three-quarter of the pizza remain.Therefore the required ratio is.34:14=3:1 475.Will is selling apples at the farmer’s market.After selling of them,he has left.How many apples did Will have to start with?25150 A.250 B.375 C.90 D.60【答案】A【解析】He has remaining after selling.We can write the equation as:.3525150÷35=250 476.Brandon is engaging sprint race on the track,and he is in the first group.On the track,there are players in front of him,and there are players behind him.There are extra groups signing up for the sprint race,and the number of players of each group are identical.How many sprint players are there in total?585 A.65 B.70 C.78 D.84 E.96【答案】D【解析】There are players in each group.There are players in total.5+8+1=1414×6=84 477.Niko counted a total of birds perching in three trees.Five minutes later,birds had flown away from the first tree,birds had flown away from the second tree and birds had flown away from the third tree.He noticed that there was now the same number of birds in each tree.How many birds were originally perched in the second tree?60684 A.14 B.18 C.20 D.21 E.22【答案】E【解析】Let the number of birds remaining in each tree be x.Therefore x+6+x+8+x+4=60,which has solution x=14.Hence the number of birds originally perched in the second tree is 14+8=22.478.A tank filled with litres of water weighs.The same tank filled with litres of water weighs.What is the weight of the empty tank?200350kg150315kg A.120kg B.150kg C.165kg D.210kg E.None of the above【答案】D【解析】T+200L=350kg①-)T+150L=315kg②______________________(50L=35kg)x3=150L=105kg 315kg-105kg=210kg⋯⋯479.A total of chickens and rabbits are caged together.If there are legs in total,how many chickens and rabbits are in the cage,respectively?42124 A.;2012 B.;2220 C.;2024 D.;1921【答案】B【解析】Suppose all the animals in the cage are chickens:there should be legs.However,legs are missing because we counted rabbits.Hence,there are rabbits and chickens.2×42=84124−84=4040÷2=202042−20=22 480.A string meters long is cut into pieces of equal length.What is the sum of the lengths of any of these pieces?1264 A.2m B.4m C.6m D.8m【答案】D【解析】The string meters long is cut into pieces of length.The sum of the lengths of any of these pieces is.1262m44×2m=8m 481.William plans to take days to drive to New York City from his home.However,since there is heavy traffic,he drives miles less each day and arrives in New York City days later than his plan.What is the distance between William’s home and New York City?16208 A.miles480 B.miles1080 C.miles960 D.miles720 E.miles1200【答案】C【解析】We set up an equation in terms of as the distance and as the speed in miles per day originally.We have Thus,the distance between William’s home and New York City is miles.dxd=16x=24(x−20)16x=24x−480480=8xx=6060×16=960 482.Calculate:1×10+2×9+3×8+⋯+9×2+10×1 A.200 B.140 C.210 D.180 E.None of the above【答案】E【解析】E 483.The sum of Ben’s age and Ben’s grandma’s age is.Ben’s grandma’s age is three times older than Ben’s age.How old is Ben’s grandma?96 A.24 B.48 C.72 D.96【答案】C【解析】The sum of Ben’s age and Ben’s grandma’s age is.Since grandma is three times older than Ben,on the number line,can be divided into portions,and each portion is.Ben is years old,and grandma is three times older.9696496÷(1+3)=242424×3=72 484.Five children divided some cakes equally.What percents of the cakes two of them could get in total?A.5\textbackslash%B.10\textbackslash%C.20\textbackslash%D.40\textbackslash%【答案】D【解析】Five children divided some cake equally.Two of the children totally got of the cake and.2525=0.4=40\textbackslash%485.This year,March falls on a Thursday.What day of the week will it be in days?1930 A.Wednesday B.Thursday C.Friday D.Saturday E.Sunday【答案】D【解析】30÷4=7R2,two days after a Thursday is a Saturday.486.A group of students go apple-picking.On average,each boy picks apples and each girl picks apples.The average number of apples picked by everyone in this groups is.If there are boys,then how many girls are there in the group?30202615 A.15 B.10 C.9 D.20 E.23【答案】B【解析】Every boy picks more than the average,so boys pick more in total,which is equal to the number that girls picked less than the average in total.Every girl picks less than the average,so there are girls.30−26=44×15=6026−20=660÷6=10 487.If June is Sunday,what day of the week is st June?10th1 A.Sunday B.Monday C.Wednesday D.Friday E.Saturday【答案】D【解析】We can count backward by days or by weeks.There are 9 days in between,that means 1 week and 2 days.Then count a few days back to find that st June is a Friday.1 488.The possible grades on an exam are,,,,or.In a class of students,of them got s,them got s,of them got s,and of them got s.How many students got s?54321200110515425\textbackslash%315\textbackslash%21 A.40 B.60 C.80 D.100【答案】B【解析】200×(1−110−15−25\textbackslash%−15\textbackslash%)=60.489.In,both John and Mary have the same amount of pocket money per month.In,John had an increase of and Mary a decrease of in their monthly pocket money.In,John had a decrease of and Mary an increase of in their monthly pocket money.John had a}increase/decrease in his pocket money in compared to.Mary had a}increase/decrease in her pocket money in compared to.Which one of the following statements is correct?2005200610\textbackslash%10\textbackslash%200710\textbackslash%10\textbackslash%\textasciitilde\textbackslash%20072005\textbackslash%20072005\textasciitilde A.Both have the same amount of pocket money now.B.John has more pocket money now.C.Mary has more pocket money now.D.It is impossible to tell who has more pocket money now.【答案】A【解析】Statement is correct.In the amount of pocket money that each has be.In,John has while Mary has.Ax20071.1×0.9x=0.99x0.9×1.1x=0.99x 490.Lena the panda has bamboos.She eats bamboos each day.She ate the bamboo on Tuesday.On which day did she start eating the bamboos?30318th A.Monday B.Tuesday C.Wednesday D.Thursday E.Friday【答案】D【解析】NA 491.A particular cattle is fed,and of special food on Day,and respectively by a farmer.From Day onwards,the amount of food fed to the cattle follows the following rule:(i)if the total amount of food fed to the cattle in the past days is or more,the cattle will be fed less than the day before.(ⅱ)if the total amount of food fed to the cattle in the past days is less than,the cattle will be fed more than the day before.Calculate the minimum number of days for the total amount of food fed to the cattle to exceed.7kg8kg9kg1234324kg2kg324kg1kg2018kg A.280 B.284 C.288 D.292 E.None of the above【答案】E【解析】Amount of food fed to the cattle follows the pattern:Total amount of food fed in the first days..789756789756789756789756⋯⋯6=42kg2018=48×6+1=289 492.Emily was years old last year,and her sister was years old six years ago.What is the age difference between Emily and her sister today?(adapted from 2005 Math Kangaroo Problem,Level 1-2,Question#17)66 A.4 B.5 C.7 D.13 E.14【答案】B【解析】Emily was years old last year,which means Emily is years old this year.Her sister was years old six years ago,which tells us her sister is years old this year,so the age difference is today.676125 493.Sinnce,its ones’digit is a.What is the ones’digit of?72=499250 A.0 B.2 C.4 D.8【答案】C【解析】The ones’digits repeat in groups of four:,,,,,,,,.The ones’digits of,,are,,.24862486⋯2482492%50624 494.Chloe is buying candies at a grocery store.She can either spend dollars on a bag or dollars on a bag.Which is a better buy?815−ounce1220−ounce A.The bag15−ounce B.The bag20−ounce【答案】A【解析】8dollars15ounces12dollars20ounces 495.If February is a month that contains Friday the 13th,what day of the week is February 1?A.Sunday B.Monday C.Wednesday D.Thursday E.Saturday【答案】A【解析】We can count backward by days or by weeks.Count a few weeks back to find that February is a Friday.Then count a few days back to find that February is a Sunday.61 496.Tower is high.The total height of Tower and Tower is.What is the difference between the height of the two towers?}.A64mAB112mm A.14 B.15 C.16 D.17 E.18【答案】C【解析】112−64=4864−48=16 497.Clara,Pablo and Miguel share some money in the ratio.Miguel then gave Pablo and Clara each of his share,leaving Clara with￡more than Miguel.How much money does Pablo now have?3:1:425\textbackslash%6 A.￡2 B.￡3.60 C.￡4 D.￡6 E.￡12【答案】D【解析】The initial ratio of the children’s money is.When Miguel shares half of his portion,the ratio becomee.Given that Clara now has￡more than Miguel,Pablo now has￡.3:1:43+1:1+1:4−2=4:2:2=2:1:166 498.Adam paid£6 for buns.How many dollars did Tom pay for the same kind of buns if he bought?155 A.2 B.3 C.4 D.5【答案】A【解析】There groups of buns in buns:,so buns cost£.351515÷5=356÷3=2 499.SASMO 2014 P2 Q7 There are 14 children playing"The eagle catches the chicks."One of them is the’eagle’while another child is the’mother hen’whose job is to protect the’chicks’.The rest of the children are the’chicks’.After a while,the’eagle’has caught 5’chicks’.How many’chicks’are still around?A.6 B.7 C.8 D.9 E.10【答案】B【解析】14-1(eagle)-1(mother hen)=12(chicks)12-5 7 chicks 500.For every soccer balls Elena bought for the gym,she bought basketballs.If she bought soccer balls,she bought a total ofballs.7435 A.20 B.35 C.45 D.55【答案】D【解析】out of balls that Elena bought are soccer balls.If there are soccer balls,then there is a total of balls.7117×5=3511×5=55 501.Chloe and Zoe are both students in Ms.Demeanor’s math class.Last night they each solved half of the problems in their homework assignment alone and then solved the other half together.Chloe had correct answers to of the problems she solved alone,but overall of her answers were correct.Zoe had correct answers to of the problems she solved alone.What was Zoe’s overall percentage of correct answers?(2017 AMC 8,Question#14)90\textbackslash%60\textbackslash%70\textbackslash%A.45 B.48 C.50 D.60 E.65【答案】C【解析】Assume the total amount of problems is 100 per half homework assignment,since we are dealing with percentages,and not values.Then,we know that Chloe got 90 problems correct by herself,and got 120 problems correct overall.We also know that Zoe had 70 problems she did correct alone.We can see that the total amount of correct problems Chloe and Zoe did was.Therefore Zoe has problems out of problems correct.Thus percent.120−90=3030+70=100200100200=50 502.When Cici was born,Linda was years old.The sum of their ages years later will be.How old will be Linda years later?114373 A.12 B.22 C.24 D.26【答案】C【解析】Suppose that Cici will be years old years later,Linda will be years old.,so.Thus,Linda will be years old years later.x4(x+11)x+(x+11)=37x=1313+11=243 503.My age is years less than times my sister’s age.If I am,the sum of my age and my sister’s age is．3527 A.33 B.36 C.39 D.42【答案】A【解析】My age,,is years less than times my sister’s age,so is times her age.Thus,my sister is.The sum of our ages is.2735305627+6=33 504.Valeria has grams of a sugar solution.How many grams of sugar is in the solution?How many grams of water is in the solution?6520\textbackslash%A.;2065 B.;1352 C.;1365 D.;2052【答案】B【解析】Sugar:ounces;Water:ounces.65×20\textbackslash%=1365−13=52 505.Each watermelon’s full price is dollars.Currently,the watermelons on a discounted price for dollars each.Ms.Lee wants to buy of them.She needs to pay dollars in total.433 A.8 B.9 C.10 D.12 E.14【答案】B【解析】3+3+3=9 506.19 less than 67 is}.A.58 B.68 C.38 D.48【答案】D【解析】67−19=48 507.The ages of Tom’s father,Tom’s mother and Tom are together.Tom’s mother is years older than Tom and years younger than Tom’s father.How old is Tom?86242 A.6 B.12 C.32 D.30 E.36【答案】B【解析】Tom’s mother is years old.Tom is years old.(86+24−2)÷3=3636−24=12 508.How many ways are there to make using some combination of,and notes?$80$5$10$20 A.16 B.25 C.36 D.49 E.None of the above【答案】E【解析】Condition on the number of note you use.gives possibility,gives possibilities,gives possibilities,gives possibilities,gives possibilities.$204133251709 509.Mark and Karl have dollars in total.The money Mark owns is three times the money Karl owns.How many dollars does Mark have?(Adapted from 1999 Math Kangaroo Problem,Level 3-4,Question#6)100 A.20 B.25 C.35 D.75 E.80【答案】D【解析】100÷(3+1)×3=75 510.If today is Monday,which day of the week will it be days later?．22 A.Sunday B.Monday C.Tuesday D.Wednesday【答案】C【解析】Since there are 7 days in a week,the day will repeat again after 7 days.Thus,if today is Monday,it will be Monday again a week later.week R.The day after days is the same as the day after day.day after Monday is Tuesday.Therefore,it will be Tuesday days later.22÷7=31221122 511.In a maths test,the average score of students is.The lowest score is.At most how many student(s)can get points?40255100 A.11 B.10 C.9 D.8 E.7【答案】D【解析】Total points:.To have as many points as possible,we should consider there are only two groups of students:everyone gets points in a group and everyone gets in the other group.,so there must be less than people getting points.If there are nine s:,which is impossible.If there are eight s:.Thus,the answer is.40×25=1000100510010×100=1000101001009×100+31×5=1055>10001008×100+32×5=960<10008 512.The class organized students to do gymnastics side by side，there are two people in each row.Bob and Tick observed that there were rows in front of them and rows in the back.How many people in the class did gymnastics together?(adapted from 2000 Math Kangaroo Problem,Level 3-4,Question#12)and811 A.36 B.38 C.40 D.42 E.44【答案】C【解析】It can be seen from the question that Bob and Tick have rows in front and rows in the back.There are rows in total,and there are two people in each row,so there are people in total.8112040 513.If represents on a map and the actual distance between two towns is,then their distance apart on the map is．6cm50km125km A.8cm B.10cm C.15cm D.18cm E.12cm【答案】C【解析】If represents,represents.So,their distance apart on the map is.6\textasciitildecm50\textasciitildekm3\textasciitildecm25\textasciitildekm125÷25×3=15\textasciitildecm 514.How many days are there in exactly weeks?52 A.364 B.365 C.366 D.367【答案】A【解析】Each week has days,so weeks has days.75252×7=364 515.A"combo"ticket to enter the fair and ride unlimited rides is＄.A``per ride"ticket costs＄to enter and＄per ride.For a"combo’’ticket to cost less than a"per ride"ticket,a person must go on at least rides.3012.505 A.3 B.4 C.6 D.7【答案】B【解析】A fair sells acombo"ticket for＄entry and a per ride"ticket for＄to enter plus＄per ride.Aper ride"ticket costs＄＄＄for rides and＄＄＄for rides.3012.50512.50+15=27.50312.50+20=32.504 516.Niki usually leaves her cell phone on.If her cell phone is on but she is not actually using it,the battery will last for hours.If she is using it constantly,the battery will last for only hours.Since the last recharge,her phone has been on hours,and during that time she has used it for minutes.If she doesn’t use it any more but leaves the phone on,how many more hours will the battery last?243960 A.7 B.8 C.11 D.14【答案】B【解析】When not being used,the cell phone uses up of its battery per hour.When being used,the cell phone uses up of its battery per hour.Since Niki’s phone has been on for hours,of those simply on and being used to talk,of its battery has been used up.To drain the remaining the phone can last for more hours without being used.12413988(124)+1(13)=231313124=(B)8 517.A worm is staying at the bottom of a well with a depth of meters.If it climbs up meters in the day time and slips down meter at night,which day will it climb up to the ground?1131 A.3 B.4 C.5 D.6 E.7【答案】C【解析】It climbs up meters in the day time and slips down meter at night,so it climbs up meters in a whole day.For the first days,it climbs meters.During the day time of the fifth day,it climbs meters and reaches the ground.Then it needs five days to climb up to the ground.312483 518.The sum of the ages of Anita and Peter is years.What is the sum of their ages three years ago?20 A.18 B.17 C.14 D.11【答案】C【解析】20−3×2=14 519.James makes a long noodle.He takes some bites of the noodle,each time eating cm of the noodle from the middle of only one piece.At last,he has pieces of the noodle with the total length of cm.How long was the entire noodle in cm at the beginning?(Adapted from 2022 AMC 8 Problem,Question#11)51224 A.94 B.89 C.80 D.79 E.75【答案】D【解析】There are pieces of noodle left,so he takes bites of the noodle.Thus,the length of the noodle he ate is cm.The total length of the entire noodle was cm.1212−1=1111×5=5555+24=79 520.A mixture of liters of paint is red tint,yellow tint and water.liters of yellow tint are added to the original mixture.What is the percent of yellow tint in the new mixture?(adapted from 2007 AMC 8,Question#17)2516\textbackslash%24\textbackslash%60\textbackslash%15 A.52.5 B.55 C.57.5 D.60【答案】A【解析】The original mixture contains liters of yellow tint.liters of yellow tint is added to the mixture,the new mixture now has liters of yellow tint.New percent of yellow=25×24\textbackslash%=6156+15=212125+15=52.5\textbackslash%521.Edwin has three flowers,one red,one blue and one yellow.They have petals in total.The blue flower has petals less than the red one and petals more than the yellow one.How many petals does the red flower have?5045 A.12 B.13 C.17 D.21 E.22【答案】E【解析】Blue:Red:(50+5−4)÷3=1717+4=21 522.Mike has a bookcase with three layers,and the proportion of books placed on the upper,middle and lower layers is.Given that there are books on the middle level,books should be removed from middle level and added to the lower level so that the number of books on each level can be exactly the same.5:6:4240 A.48 B.40 C.60 D.80【答案】B【解析】Lower level:,The number of books to be added to the lower level:.So,the answer is.240÷6×4=160(240−160)÷2=40B 523.Barb likes to help her father with housework.She dusts every days,sweeps every days,and cooks dinner every days.If she does all chores on one Sunday,she next does all on the same day on a．34533 A.Wednesday B.Thursday C.Friday D.Saturday【答案】B【解析】The least common multiple of,and is.We know that,then the remainder tells us that it will be on Thursday.3456060÷7=8……4 524.This year,October falls on a Sunday.What day of the week will it be after days?(adapted from 2015 Math Kangaroo Problem,Level 3-4,Question#8)2838 A.Wednesday B.Thursday C.Tuesday D.Friday E.Sunday【答案】A【解析】38÷7=5R3,three days after Sunday,which is Wednesday.525.A family made a trip.For half the distance,they drove at per hour;for the other half,they drove at per hour How many hours did this trip take?100km50km25km A.3 B.4 C.5 D.6【答案】A【解析】For the first,they drove at-that took.For the other second,they drove at-that took.The trip took.50km50km/hr1hr50km25km/hr2hrs3hrs 526.James has g of a salt solution,and then g of water evaporates.Find the percent concentration of salt solution at this time.6008\textbackslash%120 A.10\textbackslash%B.12\textbackslash%C.15\textbackslash%D.18\textbackslash%【答案】A【解析】g,g,.600×8\textbackslash%=48600−120=48048÷480×100\textbackslash%=10\textbackslash%527.The rabbit Cici picks mushrooms in the forest.She finds one mushroom every meters,and she finds mushrooms in total.How long does Cici walk from where she finds the first mushroom to where she finds the last one?58 A.13 B.35 C.36 D.40【答案】B【解析】There are spaces..8−1=77×5=35 528.Given March of a certain year is Monday,what day of the week would May fall on that year?．251 A.Tuesday B.Wednesday C.Thursday D.Friday【答案】B【解析】May is days after March.Since,weeks after is still Monday and days after that is a Wednesday.16+30+1=372537÷7=5R252 529.Jane released a homing pigeon at a.m..The pigeon arrived at its destination at a.m..How many miles did the pigeon travel if it flies miles in hours?(adapted from 2007 Math Kangaroo Problem,Level 5-6,Question#18)5:3011:301202 A.120 B.720 C.360 D.300 E.420【答案】C【解析】The flying speed is miles/hr,and the flying time is hours.So,the total distance is miles.120÷2=6011:30−5:30=660×6=360 530.A bag of toffee is dollars,a bag of cotton candy is dollars,and a bag of orange candy is dollars.Now,the candy shop decides to mix bags of toffee,bags of cotton candy,and bags of orange candy for bags of assorted candy.What should be the price of the assorted candy in dollars to keep the total revenue unchanged?8613305020100 A.7.5 B.8 C.9.5 D.10 E.12【答案】B【解析】Total revenue:dollars A bag of assorted candy:dollars30×8+50×6+20×13=800800÷100=8 531.There are some ducks and sheep in a farm.The number of sheep is more than ducks.The number of ducks is half the number of sheep.In total,how many ducks and sheep are there in the farm?10 A.26 B.30 C.33 D.39 E.40【答案】B【解析】10+10+10=30 532.Pat paints twice as fast as Lee.If it took Lee hours to paint a room,how long would it have taken if both had painted the room together?6 A.hours2 B.hours3 C.hours9 D.hours18【答案】A【解析】Lee paints the room once in hours.Pat paints the room twice in hours.Together,they paint the room times in hours.So,it takes them hours to paint it once together.66362 533.Ben and Ken have some books.After Ben sends books to Ken,he has fewer book than Ken.Which of the following is true?41 A.Originally,Ben had more books than Ken.3 B.Originally,Ben had more books than Ken.4 C.Originally,Ben had fewer book than Ken.1 D.Originally,Ben had more books than Ken.9 E.Originally,Ben had more books than Ken.7【答案】E【解析】4+4−1=7 534.John bought pencils and notebooks in total for£.Each pencil cost£.Each notebook costs£.How many notebooks did John buy?104428 A.4 B.5 C.6 D.7 E.8【答案】A【解析】If all were pencils,the total cost would be£.The difference is£.John bought notebooks.10×2=202044−20=24248−2=624÷6=44 535.Lily’s age plus Judy’s age was equal to two years ago.What is the sum of their ages this year?(adapted from 2016 Math Kangaroo Problem,Level 1-2,Question#16)17 A.16 B.17 C.18 D.19 E.21【答案】E【解析】17+2×2=21 536.If I start with,and begin to count by s,my number will be}.23\textquotesingle50th A.148 B.149 C.150 D.151 E.152【答案】B【解析】2+(50−1)×3=149.537.Jucy and Nicole are celebrating their birthdays together.Seven years ago,when Jucy turned years old,she received a newborn cat as a birthday present.Today the sum of the ages of the two people and the cat is years.Jucy is}years younger than Nicole.634 A.1 B.2 C.3 D.4【答案】A【解析】Seven years ago:Jucy:cat:This year:Jucy:cat:Nicole:707+6=130+7=734−13−7=1414−13=1 538.Tom goes to the supermarket to buy egg tarts.There are two kinds of egg tarts.One has tarts in the box and the other has tarts in the box.The unit price of the egg tarts is the same.If Tom wants egg tarts,how many boxes does he need at least?(adapted from 2011 Math Kangaroo Problem,Level 3-4,Question#10)61076 A.5 B.8 C.9 D.11 E.13【答案】B【解析】76=10+10+10+10+10+10+10+6 539.A gift store buys some gifts at＄125 each.It wants to earn＄25 for each gift after a discount of 25\textbackslash%.What is the selling price before the discount for each gift?A.dollars160 B.dollars180 C.dollars190 D.dollars200【答案】D【解析】(125+25)÷(1−25\textbackslash%)=200 dollars.540.It takes Mary minutes to walk uphill m from her home to school,but it takes her only minutes to walk from school to home along the same route.What is her average speed,in m/min,for the round trip?(adapted from 2003 AMC 10 Problem,Question#4)3030010 A.10 B.30 C.20 D.15 E.12【答案】D【解析】Mary walks a total of meters in minutes.Average speed:m/min300+300=60040600÷40=15 541.Twenty-eight students from the fourth grade competed in a math competition.Each student earned a different number of points.The number of students who received more points than Tomek is two times smaller than the number of students who had fewer points than Tomek.In which position did Tomek finish that competition?(Math Kangaroo Problem,Level,Question#)20023−423 A.th6 B.th10 C.th8 D.th9 E.th7【答案】B【解析】Except for Tomek,there are students.The number of students who received more points than Tomek is,so Tomek is in the place.28−1=2727÷(2+1)=99+1=10th 542.January,was a Sunday.January,(a leap year)was a．1198911988 A.Friday B.Saturday C.Sunday D.Monday【答案】A【解析】days weeks days.Jan is weeks days before Jan.This date in is days before Sunday so it is on a Friday.366=522119885221198919882 543.Algebra books cost each,and geometry books cost each.How much do algebra books and geometry books cost in total?$12.50$1465 A.$145.00 B.$146.50 C.$150.00 D.$151.50【答案】A【解析】Six algebra books cost$12.50×6=$75.Five geometry books cost$14×5=$70.All together,they cost a total of$145.544.A test is with a full score of points.Five students in a group wants to reach an average of points.If everyone scores a different whole number,the lowest score among them could be}.10091 A.60 B.61 C.67 D.70 E.71【答案】B【解析】91×5−(100+99+98+97)=61.545.Jack’s sister is years old,which is less than times Jack’s age.Assume Jack is years old,then．2224x A.x=4 B.x=5 C.x=6 D.x=8【答案】C【解析】The equation can represents this situation is,so,,.So,the answer is.4x−2=224x=24x=66 546.Jason and Ross are in line to check tickets.There are people in front of Jason and people behind.Ross happens to be in the middle of the entire line.How many people are there between Ross and Jason?(adapted from 2000 Math Kangaroo Problem,Level 3-4,Question#12)3616 A.18 B.17 C.16 D.15 E.14【答案】D【解析】The total:,Jack’s location:,so there are people between Jack and Rose.36+16+1=53(53−1)÷2=2115 547.Amy mixes grams of a salt solution and grams of a salt solution together.How many grams of water should she add to the mixture to make it a solution?3030\textbackslash%2020\textbackslash%10\textbackslash%A.70 B.72 C.75 D.80【答案】D【解析】ounces.ounces.30×30\textbackslash%+20×20\textbackslash%=9+4=1313÷10\textbackslash%−(30+20)=80 548.dogs are cqually divided into groups,how many dogs are there in each group.123 A.3 B.4 C.6 D.2 E.12【答案】B【解析】12÷3=4 549.My pet frog jumps per jump.If it wants to jump from one end of a field to another,the least number of jumps it will take is．3m100m A.33 B.34 C.70 D.97【答案】B【解析】Since with remainder,it takes my frog jumps to jump.It needs more jump,for jumps in all,to go at least.100÷3=3313399m134100m 550.In,the Math Kangaroo competition is taking place in some schools for the th time.Alice took part in the th Math Kangaroo when she was years old.In what year was Alice born?(Adapted from 2008 Math kangaroo Problem,Level 3-4,Question#9)201019109 A.1996 B.1994 C.1992 D.1990 E.1988【答案】C【解析】The th Math Kangaroo was taking place in,which means that Alice was years old in,so she was born in.102001920011992 551.Half a loaf of bread costs pence more than one-fourth of a loaf of bread.How many pence does a whole loaf of bread cost?6 A.6 B.12 C.18 D.24 E.30【答案】D【解析】One-fourth of a loaf of bread is.”Half a loaf of bread is.”One-fourth of a loaf of bread:.A whole loaf of bread:.126÷(2−1)=66×4=24 552.Ben has pairs of shoes,of which shoes are red,shoes are bule,and the rest are green.How many pairs of shoes are green?942 A.3 B.6 C.4 D.5 E.7【答案】B【解析】9−2−1=6 553.Antonette gets on a 10-problem test,on a 20-problem test and on a 30-problem test.If the three tests are combined into one 60 problem test,which percent is closest to her overall score?(2006 AMC 8,Question#12)70\textbackslash%80\textbackslash%90\textbackslash%A.40 B.77 C.80 D.83 E.87【答案】D【解析】70\textbackslash%·10=780\textbackslash%·20=1690\textbackslash%·30=27 Adding them up gets 7+16+27=50.The overall percentage correct would be 5060=56=5·16.6=83.3≈(𝐃)83.554.Rick and Roy each stands at different ends of a straight road that is m long.They run toward each other.Rick’s speed is and Roy’s speed is.They will meet in seconds.202121m/s22m/s A.35 B.4 C.47 D.50【答案】C【解析】2021÷(21+22)=47.555.You have green cards and the ratio of your red cards to green cards is.How many cards do you have?123:2 A.18 B.20 C.24 D.30【答案】D【解析】is the product of and.Then multiple by is the number of red cards.The total number of cards is.12623630 556.Chloe and Zoe are both students in Ms.Demeanor’s math class.Last night they each solved half of the problems in their homework assignment alone and then solved the other half together.Chloe had correct answers to of the problems she solved alone,but overall of her answers were correct.Zoe had correct answers to of the problems she solved alone.What was Zoe’s overall percentage of correct answers?(2017 AMC 8,Question#14)80\textbackslash%90\textbackslash%75\textbackslash%A.87.5 B.90 C.92.5 D.95.5 E.100【答案】A【解析】Assume the total amount of problems is 100 per half homework assignment,since we are dealing with percentages,and not values.Then,we know that Chloe got 80 problems correct by herself,and got 180 problems correct overall.We also know that Zoe had 75 problems she did correct alone.We can see that the total amount of correct problems Chloe and Zoe did was.Therefore Zoe has problems out of problems correct.Thus percent.180−80=100100+75=175200175200=87.5 557.Mr.owns a home worth＄.He sells it to Mr.at a profit based on the worth of the house.Mr.sells the house back to Mr.at a loss.Then:(AHSME Problem,Question#)A10000B10\textbackslash%BA10\textbackslash%19515 A.comes out evenA B.makes＄on the dealA1100 C.makes＄on the dealA1000 D.loses＄on the dealA900 E.loses＄on the dealA1000【答案】B【解析】Mr.sells his home for dollars dollars dollars to Mr..Then,Mr.sells it at a price of dollars dollars dollars,thus.A(1+10\textbackslash%)×10000=1.1×10000=11000BB(1−10\textbackslash%)×11000=0.9×11000=990011000−9900=(B)\textasciitildeA\textasciitildemakes\textasciitilde1100\textasciitildeon\textasciitildethe\textasciitildedeal 558.A alcohol solution contains grams of water.How many grams of solution are there?60\textbackslash%120 A.200 B.250 C.300 D.400【答案】C【解析】120÷(1−60\textbackslash%)=300 ounces.559.A,B,C,D and E sit around a circular table in that order.A starts by saying"100",B says"101",C says"102"and so on round the table.Who will eventually say"2023"?A.A$B.B$C.Cain$D.Devi$E.Emily$【答案】D【解析】After Amit says"",there are numbers remaining.Thus the counting goes round the table times with a remainder of,so the last to count is Devi.20155102−2015=30873087÷6=5143 560.Brown wants to put some board between his books.He has books in total.If he wants to put one board between every two adjacent books,how many boards does he need to prepare?10 A.9 B.10 C.11 D.12 E.13【答案】A【解析】10−1=9 561.In a class of students,are wearing jeans.What is the ratio of students wearing jeans to students not wearing jeans?186 A.1:2 B.1:3 C.2:3 D.2:1【答案】A【解析】If students are wearing jeans,then are not.The ratio of students wearing jeans to students not wearing jeans is.618−6=126:12=1:2 562.How many two-digit numbers are divisible by but not by?36 A.14 B.15 C.17 D.30 E.None of the above【答案】B【解析】There are-multiples of less than.of them are one-digit numbers:,and.Hence there are-digit multiples of.Similarly,there are-digit multiples of.Hence,the answer is 30-15=15.Answer：(B)994−3=3331003369302396+6−1=16−1=1526 563.Water from the first faucet fills the swimming pool in minutes.Water from each of the two other faucets fills the same swimming pool times faster.In how many minutes will the swimming pool be filled if all three faucets are opened?703 A.210 B.40 C.30 D.20 E.10【答案】E【解析】The efficiency of the first faucet is and that of the other two is.Thus,it takes minutes to fill the pool.1703701÷(170+370×2)=10 564.Chloe and Zoe are both students in Ms.Demeanor’s math class.Last night they each solved half of the problems in their homework assignment alone and then solved the other half together.Chloe had correct answers to of the problems she solved alone,but overall of her answers were correct.Zoe had correct answers to of the problems she solved alone.What was Zoe’s overall percentage of correct answers?(adapted from 2017 AMC 8,Question#14)80\textbackslash%90\textbackslash%75\textbackslash%A.87.5 B.90 C.92.5 D.95.5 E.100【答案】A【解析】Assume the total amount of problems is 100 per half homework assignment,since we are dealing with percentages,and not values.Then,we know that Chloe got 80 problems correct by herself,and got 180 problems correct overall.We also know that Zoe had 75 problems she did correct alone.We can see that the total amount of correct problems Chloe and Zoe did was.Therefore Zoe has problems out of problems correct.Thus percent.180−80=100100+75=175200175200=87.5 565.There is an empty tank which needs bottles of water to fill with.The workers pour bottles of water during the day,but uses bottle of water during the night.In how many days can the tank be filled with water?2951 A.5 B.6 C.7 D.8 E.9【答案】C【解析】Every day:bottles.But for the last day,the tank can be filled with water without using during the night.5−1=429÷4=7R1 566.The selling price of a sofa set is＄and the profit percentage is for each set sold.If the cost of the sofa set is not changed,what is the profit percentage if the profit is＄?650030\textbackslash%1200 A.20\textbackslash%B.24\textbackslash%C.25\textbackslash%D.30\textbackslash%【答案】B【解析】6500÷(1+30\textbackslash%)=5000,1200÷5000=24\textbackslash%.567.Owen sees an archery right after he entered the carnival.After Owen takes 20 shots,he has made of his shots.After he takes 5 more shots,he raises his percentage to.How many of the last 5 shots did she make?(adapted from 2004 AMC 8,Question#6)55\textbackslash%56\textbackslash%A.1 B.2 C.3 D.4 E.5【答案】C【解析】Owen made shots originally.Letting be the number of shots she made,we have.Solving for gives us(C)30.55*20=11x11+x25=0.56xx=568.I read page of a book on Nov,pages on Nov,pages on Nov,and so on.I followed this pattern for the whole month.Altogether,how many pages did I read in November?112233 A.30 B.31 C.465 D.496【答案】C【解析】There are in total days in Nov.301+2+3+4+⋯+30=(1+30)×30÷2=465 569.Chloe and Zoe are both students in Ms.Demeanor’s math class.Last night they each solved half of the problems in their homework assignment alone and then solved the other half together.Chloe had correct answers to of the problems she solved alone,but overall of her answers were correct.Zoe had correct answers to of the problems she solved alone.What was Zoe’s overall percentage of correct answers?(adapted from 2017 AMC 8,Question#14)90\textbackslash%84\textbackslash%80\textbackslash%A.79 B.82 C.84 D.86 E.88【答案】A【解析】Assume the total amount of problems is per half homework assignment,since we are dealing with percentages,and not values.Then,we know that Chloe got problems correct by herself,and got problems correct overall.We also know that Zoe had problems she did correct alone.We can see that the total amount of correct problems Chloe and Zoe did was.Therefore Zoe has problems out of problems correct.This is(C)percent.1009016880168−90=7880+78=15820079 570.If April is Friday,what day of the week is st April?15th1 A.Sunday B.Monday C.Wednesday D.Friday E.Saturday【答案】D【解析】There are 14 days between st April and April.14 days=2 week Therefore,st April is Friday.115th1 571.Grandma made some cheese dumplings and some blueberry dumplings.Altogether,she made dumplings.If she had made more cheese dumplings,then there would be the same number of blueberry dumplings as cheese dumplings.How many cheese dumplings did grandma make?（Math Kangaroo Problem,Levels,Question#）311120091−219 A.10 B.21 C.20 D.15【答案】A【解析】(31−11)÷2=10.572.A worm is staying at the bottom of a well with a depth of metres.If it climbs up metres in the day time and slips down metre at night,which day will it climb up to the ground?1341 A.The th day4 B.The th day5 C.The th day6 D.The th day7【答案】A【解析】It climbs up metres in the day time and slips down metre at night,so it climbs up metres in a whole day.For the first days,it climbs metres.During the day time of the forth day,it climbs metres and reaches the ground.Then it needs four days to climb up to the ground.413394 573.The volume of a cuboid is 216.What is the least sum of the length of all its edges?A.216 B.32 C.72 D.96 E.120【答案】C【解析】Given the product of three numbers,the smaller the difference,the smaller the sum.,so the answer is6×6×6=2166×12=72.574.The state income tax where Kristin lives is levied at the rate of of the first＄of annual income plus of any amount above＄.Kristin noticed that the state income tax she paid amounted to of her annual income.What was her annual income?(AMC Problem,Question#)p\textbackslash%28000(p+2)\textbackslash%28000(p+0.25)\textbackslash%2001123 A.＄28000 B.＄32000 C.＄35000 D.＄42000 E.＄56000【答案】B【解析】Method：the income amount be denoted by.We know that We can now try to solve for:so the answer is.Method:Let,be Kristin’s annual income and the income tax total,respectively.Notice that We are also given that Thus,Solve for to obtain.1LetAA(p+.25)100=28000p100+(p+2)(A−28000)100A(p+.25)A=28000p+Ap+2A−28000p−560000.25A=2A−56000A=32000B2ATT=p\textbackslash%·28000+(p+2)\textbackslash%·(A−28000)\textasciitilde\textasciitilde\textasciitilde\textasciitilde=[p\textbackslash%·28000+p\textbackslash%·(A−28000)]+2\textbackslash%·(A−28000)\textasciitilde\textasciitilde\textasciitilde\textasciitilde=p\textbackslash%·A+2\textbackslash%·(A−28000)T=(p+0.25)\textbackslash%·A=p\textbackslash%·A+0.25\textbackslash%·Ap\textbackslash%·A+2\textbackslash%·(A−28000)=p\textbackslash%·A+0.25\textbackslash%·A2\textbackslash%·(A−28000)=0.25\textbackslash%·AAA=32000B 575.Kate sold dresses and Tasha sold thrice as many dresses as Kate.How many dresses did Tasha sell?10 A.30 B.26 C.20 D.42【答案】A【解析】=3×1030 576.My cat snoozes for minutes in each hour.For how many hours a day does my cat snooze?50 A.5 B.10 C.15 D.20 E.50【答案】D【解析】Sleeping for minutes every hour through the day is of every hour and thus of the day.Of hours,is hours.505656245620 577.In a candy shop,the shopkeeper allows the exchange of sweet wrappers for new sweet.Peter has sweets at first.What is the largest possible number of sweets that Peter could have eaten?3181 A.119 B.120 C.121 D.122 E.Non of the above【答案】C【解析】With sweets wrappers.Peter can exchange for more sweets With the additional sweets wrappers,Peter can exchange for more sweets.with the additional sweets wrappes.Peter can exchange for more sweets.with the additional sweets wrappers.Peter can exchange for more sweet.Therefore,the largest possible number of sweets Peter could have eaten is.81813=2727273=9993=3333=181+27+9+3+1=121 578.There are roses in a garden,and the number of daisies is more than times that of roses.How many flowers are there in the garden altogether?1556 A.95 B.110 C.120 D.135【答案】B【解析】15×6=9090+5=9595+15=110 579.The sum of the ages of four children Anil,Benu,Chas and Dave is.Dave is years older than Chas,and years older than Benu.Anil is years younger than Chas.How old is Anil?．20533 A.1 B.4 C.5 D.6 E.9【答案】A【解析】Two of the pieces of information relate to Chas,so we can try to relate the ages of the others to his age.Given Dave is years older than Chas,but years older than Benu,we can tell that Benu is years older than Chas.Given also that Anilis years younger than Chas,we can say that the sum of the ages of the four children is more than four times Chas’age.So four times Chas’age plus four is twenty,and so Chas must be four.So Anil is just year old.5323(−3+2+5=4)1 580.Allen has a collection of fossils.Of these,%are fossilized snail shells.How many fossilized snail shells does Allen have?24035 A.205 B.156 C.84 D.35【答案】C【解析】%=,Allen has fossilized snail shells.240×358484 581.Daniel had Lego pieces,he used pieces to make a mini statue.How many pieces of Lego does Daniel have now?5142 A.42 B.19 C.9 D.0【答案】C【解析】51−42=9 582.Grandma made some cheese dumplings and some blueberry dumplings.Altogether,she made dumplings.If she had made more cheese dumplings,then there would be the same number of blueberry dumplings as cheese dumplings.How many cheese dumplings did grandma make?（2009 Math Kangaroo Problem,Question#19）3111 A.10 B.21 C.20 D.15【答案】A【解析】(31−11)÷2=10.583.Wendy had stickers.First,she gave Aiden stickers.Then,she gave Terry stickers.Now,each of the three people has the same number of stickers.At the beginning,how many stickers did they have in total?3037 A.120 B.90 C.85 D.60 E.55【答案】D【解析】Now,Wendy has stickers.Thus,all of them have stickers,which is equal to the total number of stickers they had at the beginning.30−3−7=2020×3=60。
