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Pick what you want, print the page. The answer key comes with it, on its own sheet, and it tells you the mistake behind every wrong choice — not just which letter is right.
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1.Toma spent 4 euros, then spent half of what was left, and now has 6 euros. How much did she start with?[3]
A10
B14
C16
D20
E24
2.Two apples balance three pears. One apple weighs 90 grams. How many grams does one pear weigh?[4]
A45
B60
C90
D135
E180
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.All the red boxes are heavy. Box X is not heavy. What must be true?[4]
ABox X is red
BBox X is not red
CBox X is blue
DSome red boxes are light
ENothing can be said about box X
5.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
6.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
7.Ana says "Bo is lying." Bo says "Cal is lying." Cal says "Ana and Bo are both lying." How many of the three are telling the truth?[5]
A0
B1
C2
D3
Eit cannot be decided
8.Seven cups all stand upside down. In one move you must turn over exactly two cups. Can all seven ever stand the right way up?[5]
AYes, in 4 moves
BYes, in 7 moves
CYes, but it takes many moves
DIt depends which two cups you pick
ENo, it is impossible
9.A bag holds 5 black and 6 white stones. You repeatedly remove two stones: if they match you put a black one in, if they differ you put a white one in. What colour is the last stone?[5]
Ablack
Bwhite
Cit depends on the order of the moves
Dthe bag never gets down to one stone
Ewhite if the first two stones match
10.One of nine identical-looking coins is slightly heavier. Using only a balance, what is the smallest number of weighings that is certain to find it?[5]
A1
B2
C3
D4
E8
Math Kangaroo Star · https://kangaroo-atlas.vercel.app · seed 8 · CC BY-NC-SA 4.0 · Independent project, not affiliated with Math Kangaroo in USA, NFP.
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-0050Working backwards
AI added the 4 and the 6 and stopped, forgetting to undo the halving.
BI doubled the 6 first and then added the 4, reversing the steps in the wrong order.
DI doubled the total at the end rather than doubling only the amount left after the first spend.
EI doubled twice because spending half felt like it needed undoing more than once.
2.B — 60KA-0093Weighing and balance puzzles
AI halved the apple's weight, as if one apple balanced two pears.
CI assumed a pear must weigh the same as an apple because the two sides balance.
DI multiplied the apple's weight by three halves the wrong way round, making the pear heavier.
EI gave the total weight of the two apples rather than the weight of one pear.
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 — Box X is not redKA-0099Reading a logical statement precisely
AI read the rule backwards, as if being heavy were what makes a box red.
CI assumed not red must mean one particular other colour, when the rule says nothing about which.
DI contradicted the rule I was given rather than applying it to box X.
EI decided one fact could not settle anything, without testing what would follow if X were red.
5.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.
6.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.
7.B — 1KA-0017Truth-tellers and liars
AI assumed everyone could be lying at once without checking that Cal's statement would then be true.
CI found one consistent truth-teller and added another without testing whether both could hold together.
DI assumed everyone was telling the truth without noticing that Ana's statement then contradicts Bo's.
EI gave up after one assumption led to a contradiction, instead of trying the other assumption.
8.E — No, it is impossibleKA-0028Parity arguments
AI found a sequence that turned over most of the cups and assumed the last one could be fixed somehow.
BI matched the number of moves to the number of cups without checking whether the target is reachable at all.
CI assumed that with enough moves any arrangement can be reached.
DI thought the choice of which cups to flip could change whether the target is reachable.
9.A — blackKA-0043Invariants and monovariants
BI noticed there are more white stones than black ones and guessed the majority colour would survive.
CI tried a few orders, saw different-looking positions along the way, and assumed the ending must vary too.
DI did not notice that every move takes two stones out and puts one back, so the count falls by exactly one each time.
EI assumed the first move settles the outcome instead of looking for a quantity that no move can change.
10.B — 2KA-0094Weighing and balance puzzles
AI assumed one weighing could separate nine possibilities, but it has only three outcomes.
CI split the coins into halves each time, which wastes the balance's third outcome.
DI weighed the coins one against another in pairs rather than in groups.
EI compared each coin with a known good one in turn, which always works but is nowhere near the fewest.