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.Nadia gave half her stickers to her brother, then 6 more to a friend. She has 9 left. How many stickers did she start with?[4]
A15
B21
C24
D30
E36
3.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
4.Two apples balance three pears. One apple weighs 90 grams. How many grams does one pear weigh?[4]
A45
B60
C90
D135
E180
5.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
6.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
7.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
8.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
9.Four children stand in a line. Ana is not first. Bo stands directly behind Ana. Cal is last. Who is first?[5]
AAna
BBo
CCal
DDee
Eit cannot be decided
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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-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.D — 30KA-0007Working backwards
AI added the 6 and the 9 and stopped, forgetting to undo the halving at the start.
BI undid the steps in the order they were written instead of reversing the order as well as the operations.
CI doubled the 9 first and then added the 6, which reverses the steps in the wrong order.
EI doubled twice because giving half away felt like it should be undone more than once.
3.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.
4.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.
5.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.
6.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.
7.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.
8.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.
9.D — DeeKA-0136Ordering and ranking from clues
AI ignored the very first clue, which rules Ana out of the front directly.
BI put Bo at the front, but Bo must have Ana immediately in front of him.
CI forgot that Cal is fixed at the back of the line.
EI stopped once two arrangements seemed possible, without testing whether the second one actually fits every clue.