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Math Kangaroo practice

Name: ______________________Date: ____________3 questions · 15 points

1.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
2.What is the last digit of 3 multiplied by itself 2026 times, that is, of 3 to the power 2026?[5]
- A3
- B9
- C7
- D1
- E6
3.One tap fills a tank in 6 hours. A second tap fills the same tank in 4 hours. Both taps are opened together on an empty tank. How long does it take to fill?[5]
- A2 hours 24 minutes
- B5 hours
- C10 hours
- D2 hours
- E1 hour 12 minutes

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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 — 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.
2.B — 9KA-0158Last-digit behavior of products and powers
- AI used the first entry of the cycle because 2026 is even, without working out where in the cycle it lands.
- CI counted the cycle starting from zero, so a remainder of 2 put me one place too far along.
- DI assumed a power that large must end in 1.
- EI multiplied 3 by 2 and used the last digit of that.
3.A — 2 hours 24 minutesKA-0159Combined work rates
- BI averaged the two times, but two taps together must be faster than either one alone.
- CI added the two times, which would be right for filling two tanks one after the other.
- DI halved the smaller of the two times, guessing that two taps must simply be twice as fast as one.
- EI found 2 hours 24 minutes correctly and then halved it a second time.

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