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1.A bag of flour holds 2.5 kg. 1750 g are used. How many grams are left?[3]
A0.75
B75
C750
D1250
E1747.5
2.Three notebooks cost 240 cents each. You pay with a 10 euro note. How many cents change do you get? One euro is 100 cents.[3]
A240
B280
C520
D720
E760
3.The chart shows how many books four children read. How many did they read altogether?[3]
Text description of the figure
A bar chart with four bars labelled Ana, Bo, Cal and Dee. The vertical axis is marked in steps of 5 from 0 to 25. The bars reach 10, 25, 5 and 15.
A11
B25
C45
D55
E60
4.Three more than twice a number is 19. What is the number?[3]
A8
B11
C16
D22
E41
5.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
6.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
7.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
8.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
9.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
10.One tap fills a tank in 6 hours. A second tap fills the same tank in 4 hours. Both taps are opened together on an empty tank. How long does it take to fill?[5]
A2 hours 24 minutes
B5 hours
C10 hours
D2 hours
E1 hour 12 minutes
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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 — 750KA-0113Unit conversion
AI worked in kilograms and gave the answer in kilograms when grams were asked for.
BI converted 2.5 kg to 250 g rather than 2500 g.
DI subtracted 1750 from 3000, mis-converting 2.5 kg as three thousand grams.
EI subtracted without converting at all, taking 2.5 away from 1750.
2.B — 280KA-0114Money and change
AI subtracted the cost of one notebook rather than all three.
CI bought two notebooks instead of three.
DI gave the total cost of the notebooks instead of the change.
EI converted the 10 euro note to 1000 cents but subtracted the price of only one notebook after doubling it.
3.D — 55KA-0118Reading tables, charts, and graphs
AI read the axis as going up in ones and added the gridline heights instead of the values.
BI gave the tallest bar rather than the total of all four.
CI added only three of the four bars, missing the shortest one.
EI read the shortest bar as 10 rather than 5, because the axis steps in fives.
4.A — 8KA-0144Translating a sentence into an equation
BI subtracted 8 from 19 rather than working the two steps backwards.
CI subtracted the 3 from 19 and gave that without halving it.
DI added the 3 to 19 instead of subtracting it.
EI doubled 19 and added 3, applying the machine forwards instead of undoing it.
5.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.
6.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.
7.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.
8.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.
9.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.
10.A — 2 hours 24 minutesKA-0159Combined work rates
BI averaged the two times, but two taps together must be faster than either one alone.
CI added the two times, which would be right for filling two tanks one after the other.
DI halved the smaller of the two times, guessing that two taps must simply be twice as fast as one.
EI found 2 hours 24 minutes correctly and then halved it a second time.