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1.A pack of 24 pencils is shared equally among 4 children. Each child then gives 2 pencils to a teacher. How many pencils do the children have left altogether?[4]
A4
B6
C16
D18
E22
2.Ravi cycles 12 km at 24 km per hour, then walks 6 km at 4 km per hour. How many minutes does the whole journey take?[4]
A30
B90
C105
D120
E150
3.One tap fills a tank in 6 hours and another fills it in 3 hours. With both running, how long does the tank take to fill?[4]
A1 hour
B2 hours
C4.5 hours
D9 hours
E3 hours
4.A mother is 32 and her child is 8. In how many years will the mother be exactly three times as old as the child?[4]
A2
B4
C8
D12
E24
5.There are 5 boxes with 12 pencils in each. 17 pencils are given away and the rest are shared equally between 2 children. How many does each child get?[4]
A21
B21.5
C26
D43
E60
6.One pipe fills a pool in 12 hours and another fills it in 4 hours. With both running, how many hours does the pool take to fill?[4]
A3
B4
C6
D8
E16
7.A train covers 150 km at a steady 60 km per hour. How many minutes does the journey take?[4]
A25
B90
C150
D210
E9000
8.Four litres of a solution that is 25 percent acid are mixed with six litres of a solution that is 50 percent acid. What percentage of the mixture is acid?[4]
A40 percent
B37.5 percent
C75 percent
D35 percent
E30 percent
9.A driver travels from one town to another at an average of 60 km/h and returns along the same road at an average of 40 km/h. What is the average speed for the whole journey?[4]
A48 km/h
B50 km/h
C52 km/h
D24 km/h
E100 km/h
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Answer key — Math Kangaroo practice
Each wrong choice carries the thinking that produces it. When a student picks C, this is what they were doing.
1.C — 16KA-0019Multi-step arithmetic word problems
AI found what one child has left and gave that instead of the total for all four.
BI divided 24 by 4 and then subtracted 2 twice, mixing up per-child steps with total steps.
DI subtracted 2 pencils once from the whole pack instead of once from each of the four children.
EI subtracted the 2 before sharing, so only one lot of 2 ever came out of the total.
2.D — 120KA-0036Rate, time, distance
AI worked out the cycling leg and gave that as the answer, forgetting the walk entirely.
BI worked out the walking leg and gave that as the answer, forgetting the cycling entirely.
CI wrote half an hour as 15 minutes instead of 30 and added it to the 90 minute walk.
EI rounded the cycling leg up to a whole hour instead of keeping it as half an hour.
3.B — 2 hoursKA-0044Combined work rates
AI subtracted the two times from each other rather than adding the rates.
CI averaged the two times, which would only be right if the taps took turns instead of running together.
DI added the two times together, which makes the tank slower with two taps than with one.
EI used the faster tap's time alone and ignored the contribution of the slower one.
4.B — 4KA-0111Age problems
AI aged only the child and left the mother's age unchanged.
CI looked for when the mother is four times as old rather than three times.
DI used the age difference of 24 and halved it, without checking the ratio it gives.
EI gave the difference between their ages, which never changes, instead of a number of years.
5.B — 21.5KA-0115Multi-step arithmetic word problems
AI halved the 60 pencils before giving any away.
CI subtracted 17 from one box of 12 rather than from the whole 60.
DI gave the number of pencils left over rather than what each child gets.
EI gave the starting number of pencils without doing either of the steps.
6.A — 3KA-0116Combined work rates
BI gave the faster pipe's time on its own, forgetting the slower one helps as well.
CI halved the slower pipe's time rather than adding the two rates.
DI averaged the two times, which would only be right if the pipes took turns.
EI added the two times, which makes two pipes slower than one - an impossible answer.
7.C — 150KA-0117Rate, time, distance
AI divided 150 by 60 and read the answer as minutes rather than hours.
BI used 1.5 hours instead of 2.5, dividing 90 by 60 rather than 150.
DI converted 2.5 hours as two hours and fifty minutes.
EI multiplied the distance by 60 instead of dividing, then converted.
8.A — 40 percentKA-0165Mixtures and weighted averages
BI averaged 25 and 50 without weighting by how much of each solution there was.
CI added the two percentages together, which cannot be right because a mixture can never be stronger than its strongest ingredient.
DI weighted the percentages by the wrong volumes, giving the 25 percent solution the larger share.
EI used only the acid from the weaker solution and spread it over all ten litres.
9.A — 48 km/hKA-0174Rate, time, distance
BI averaged the two speeds, which would only be right if equal TIME were spent at each, not equal distance.
CI weighted the two speeds by their own values instead of by the time each leg took.
DI halved the correct answer, dividing by the total distance twice.
EI added the two speeds together, which gives a number faster than either leg and so cannot be an average of them.