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Math Kangaroo practice

Name: ______________________Date: ____________3 questions · 12 points

1.A committee of 4 must be formed from 5 boys and 4 girls, and it must contain exactly 2 boys and 2 girls. How many different committees are possible?[4]
- A60
- B126
- C20
- D240
- E40
2.Each of the four edges of a square is painted either black or white. Two paintings count as the same if one can be rotated onto the other. How many genuinely different paintings are there?[4]
- A6
- B16
- C4
- D8
- E5
3.A driver travels from one town to another at an average of 60 km/h and returns along the same road at an average of 40 km/h. What is the average speed for the whole journey?[4]
- A48 km/h
- B50 km/h
- C52 km/h
- D24 km/h
- E100 km/h

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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.A — 60KA-0172Selections of a few objects
- BI chose any 4 from all 9 people and ignored the two-and-two requirement.
- CI added the two counts instead of multiplying them.
- DI treated the choices as ordered, counting the same committee several times.
- EI used 5 x 4 x 2 or a similar shortcut rather than counting each selection properly.
2.A — 6KA-0173Counting up to symmetry
- BI counted every colouring of the four edges and forgot that rotations make some of them identical.
- CI divided 16 by 4, but that only works when no painting is left unchanged by a rotation, and some are.
- DI halved 16, treating only the 180 degree turn as a symmetry.
- EI listed by how many edges are black but forgot that two black edges can be adjacent or opposite.
3.A — 48 km/hKA-0174Rate, time, distance
- BI averaged the two speeds, which would only be right if equal TIME were spent at each, not equal distance.
- CI weighted the two speeds by their own values instead of by the time each leg took.
- DI halved the correct answer, dividing by the total distance twice.
- EI added the two speeds together, which gives a number faster than either leg and so cannot be an average of them.

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