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Math Kangaroo practice

Name: ______________________Date: ____________2 questions · 9 points

1.In a class of 30 students, 18 play football and 15 play chess. Exactly 7 students do both. How many students play neither?[4]
- A4
- B26
- C3
- D11
- E7
2.A drawer holds 12 red socks, 10 blue socks and 8 green socks, all mixed up. You take socks out one at a time in the dark. What is the smallest number of socks you must take to be certain of having three of the same colour?[5]
- A4
- B7
- C9
- D13
- E3

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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 — 4KA-0154Inclusion–exclusion with two sets
- BI found how many students play at least one of the two and answered with that instead.
- CI added 18 and 15 to get 33, subtracted the 30 in the class, and used the 3 left over.
- DI removed the 7 from both groups and subtracted 11 and 8 from 30, taking the overlap away twice.
- EI answered with the number who play both, which is what the question gave me rather than what it asked for.
2.B — 7KA-0157The pigeonhole principle
- AI thought that one more than the number of colours must give three of a kind, which only guarantees a PAIR.
- CI got to two of each colour, then added one more for each colour instead of one more in total.
- DI assumed the worst case meant emptying the largest pile of 12 reds first.
- EI answered with the number of socks I want rather than the number I must take to be sure of them.

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