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1.A rope is 3.5 metres long. A second rope is 240 centimetres long. How much longer is the first rope, in centimetres?[3]
A1.1
B11
C110
D236.5
E590
2.Two towns are 300 km apart. A car leaves each town at the same moment driving toward the other, one at 60 km/h and the other at 90 km/h. How long until they meet?[3]
A2 hours
B3 hours 20 minutes
C4 hours
D5 hours
E1 hour
3.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
4.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
5.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
6.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
7.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
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 class of 12 scored an average of 8. Another class of 18 scored an average of 13. What is the average for all 30 students together?[5]
A10.5
B11
C11.5
D12
E21
10.A jug holds 900 ml of juice. A third is poured out, then 150 ml is added. How many millilitres are in the jug?[5]
A450
B600
C750
D900
E1050
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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 — 110KA-0029Unit conversion
AI subtracted correctly in metres but then gave the answer in metres when centimetres were asked for.
BI converted 3.5 metres to 35 centimetres instead of 350.
DI subtracted without converting at all, taking 3.5 away from 240.
EI added the two lengths instead of finding the difference between them.
2.A — 2 hoursKA-0162Rate, time, distance
BI used only the slower car's speed and divided 300 by 90 the wrong way round.
CI averaged the two speeds to 75 km/h and divided 300 by it, which ignores that both cars move at once.
DI divided 300 by 60, using only the slower car.
EI halved the distance to 150 and then divided by 150, applying the closing speed twice.
3.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.
4.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.
5.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.
6.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.
7.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.
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.B — 11KA-0112Mixtures and weighted averages
AI averaged the two averages, ignoring that the classes are different sizes.
CI weighted the averages but used the wrong class size against each one.
DI leaned towards the larger class's average without computing the totals.
EI added the two averages together instead of combining them.
10.C — 750KA-0137Multi-step arithmetic word problems
AI poured out half instead of a third and then forgot to add the 150 ml back.
BI poured out the third correctly but never added the 150 ml.
DI assumed the 150 ml added back was the same as the amount poured out, so nothing changed.
EI added the 150 ml to the full jug without pouring anything out first.