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5 on the sheet, 22 match these filtersReshuffle Start overseed 9

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Math Kangaroo practice

Name: ______________________Date: ____________5 questions · 22 points

1.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
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.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
4.One hundred apples are packed into twelve boxes. What is the largest number n for which you can always be sure that some box holds at least n apples?[5]
- A8
- B9
- C10
- D12
- E100
5.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

Math Kangaroo Star · https://kangaroo-atlas.vercel.app · seed 9 · 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.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.
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 — 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.
4.B — 9KA-0095The extremal principle
- AI divided 100 by 12 and rounded down instead of up.
- CI rounded the division to a convenient number without checking that a packing with a smaller maximum exists.
- DI gave the number of boxes as the answer rather than a number of apples.
- EI described the case where one box holds everything, which is possible but not guaranteed.
5.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.

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