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Math Kangaroo practice

Name: ______________________Date: ____________5 questions · 20 points

1.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
2.Everyone at a meeting shakes hands with everyone else exactly once. There are 66 handshakes in total. How many people are there?[4]
- A11
- B12
- C22
- D33
- E66
3.Ana has exactly 5 coins, each worth either 2 cents or 5 cents. Which of these could NOT be her total?[4]
- A13
- B16
- C19
- D21
- E25
4.A photograph measures 8 cm by 12 cm. It is enlarged so that the shorter side becomes 20 cm, and the shape is not distorted. How long is the longer side of the enlargement?[4]
- A24 cm
- B30 cm
- C32 cm
- D4.8 cm
- E18 cm
5.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

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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.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.
2.B — 12KA-0121Try small cases first
- AI used the number of hands each person shakes rather than the number of people.
- CI doubled the answer, forgetting that the halving has already been done.
- DI halved 66 and treated that as the number of people.
- EI gave the number of handshakes back as the number of people.
3.D — 21KA-0132Eliminate impossible choices by bounding
- AI did not try one five and four twos, so I judged this total impossible.
- BI missed the combination of two fives and three twos.
- CI stopped listing after two fives and never reached three fives and two twos.
- EI forgot the case where every coin is a five, which is allowed by the wording.
4.B — 30 cmKA-0155Scaling and similar figures
- AI kept the difference of 4 cm between the two sides instead of keeping their ratio.
- CI added 20 to 12 rather than scaling 12.
- DI used the scale factor upside down and multiplied 12 by 8/20 instead of 20/8.
- EI multiplied 12 by 1.5, the ratio between the original sides, instead of by the enlargement factor.
5.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.

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