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1.Ana, Bo and Cal each keep a different pet: a cat, a dog and a fish. Ana does not keep the cat. Bo keeps neither the cat nor the fish. Who keeps the cat?[4]
AAna
BBo
CCal
Dit cannot be decided
Eeither Ana or Cal
2.Five children queue up. Ana is somewhere ahead of Bo. Cal is behind Bo but ahead of Dee. Eve is last. Who is second in the queue?[4]
AAna
BBo
CCal
DDee
Eit cannot be decided
3.Ana says: "Bo and I are both liars." Each child is either always truthful or always a liar. Who is telling the truth?[4]
AAna only
BBo only
Cboth of them
Dneither of them
Eit cannot be decided
4.A number is doubled, then 6 is added, then the result is halved. The answer is 11. What was the original number?[4]
A4
B8
C11
D16
E22
5.Cards numbered 1 to 10 lie face up. You take any six of them. Must two of your cards add up to 11?[4]
AYes, always
BYes, but only if you take the card numbered 1
CNo, six cards can be chosen that avoid it
DOnly if the six numbers are consecutive
EIt cannot be decided without knowing the cards
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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 — CalKA-0091Elimination grids
AI used Bo's clue and forgot the very first clue, which rules Ana out directly.
BI read Bo's clue as telling me what Bo has rather than what Bo does not have.
DI stopped after using each clue once, without going back to see what the ticks had ruled out.
EI applied Bo's clue but never came back to Ana's, so I left two people in the running.
2.B — BoKA-0092Ordering and ranking from clues
AI gave the child who is first rather than the one who is second.
CI placed Cal directly after Ana, reading ahead of Dee as meaning immediately ahead.
DI built the order backwards from the last position instead of forwards from the first.
EI assumed the clues left several orders open without checking that they chain into a single one.
3.B — Bo onlyKA-0096Truth-tellers and liars
AI took Ana's statement at face value without checking whether a truthful person could say it.
CI decided nobody was lying without testing Ana's statement against that assumption.
DI believed Ana's statement even after concluding she was a liar, which is what a liar's statement cannot be.
EI gave up when Ana's statement looked circular, instead of testing one assumption all the way through.
4.B — 8KA-0100Working backwards
AI undid the operations in the order they were written instead of in reverse order.
CI gave the final answer back, assuming the three steps cancelled each other out.
DI doubled the 11 and subtracted the 6 but forgot the final halving that undoes the doubling.
EI undid only the halving and stopped there without touching the other two steps.
5.A — Yes, alwaysKA-0102Informal proof by contradiction
BI found one pair that works and assumed the argument depended on that particular card.
CI tried a couple of selections, did not find a pair, and stopped looking.
DI looked for a pattern in the numbers rather than at how many pairs there are to avoid.
EI thought the answer depended on which six were taken, when the counting settles it for every choice.