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Math Kangaroo practice

Name: ______________________Date: ____________3 questions · 15 points

1.What is the units digit of 7 multiplied by itself 2026 times, that is 7 to the power 2026?[5]
- Ait cannot be found without a calculator
- B1
- C3
- D7
- E9
2.The numbers 1 to 9 are placed in a row in some order. Can every neighbouring pair add up to an odd number?[5]
- AYes, and many orders work
- BYes, but only one order works
- CNo, there are too many odd numbers
- DNo, nine places is an odd number of places
- EOnly if the row starts with an even number
3.A and B are different digits. The two-digit number AB added to the two-digit number BA gives 132. What is A + B?[5]
- A3
- B6
- C11
- D12
- E13

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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.E — 9KA-0037Last-digit behavior of products and powers
- AI assumed a number this large has no reachable last digit and gave up on the cycle.
- BI found the cycle 7, 9, 3, 1 but used a remainder of 0 when the remainder is actually 2.
- CI found the cycle but counted its positions starting at zero, shifting my answer along by one.
- DI assumed the units digit of any power of 7 is always 7.
2.A — Yes, and many orders workKA-0049Parity of numbers (odd/even behavior)
- BI found one arrangement that works and assumed a problem this fiddly could only have one answer.
- CI saw five odd numbers against four even ones and called that a mismatch, when a row of nine needs exactly five of one and four of the other.
- DI blamed the length of the row rather than checking how many odd and even numbers it has to hold.
- EI decided the first number settles it without checking that starting even would need five even numbers, and only four exist.
3.D — 12KA-0060Operation puzzles and cryptarithms
- AI added the digits of 132 instead of working out what A and B must be.
- BI found A + B correctly and then halved it, as if the question wanted one digit.
- CI spotted the 11 in the working and gave that instead of the sum it multiplies.
- EI found a pair of digits by trial and misadded them by one.

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