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2008/09 AHSMC Part 1 Problem 2

Problem 2 of 16

When the positive integers aa, bb and cc are divided by 1313, the respective remainders are 99, 77 and 1010. When a+2b+3ca + 2b + 3c is divided by 1313, the remainder is

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Solution

When a+2b+3ca+2b+3c is divided by 1313, the remainder will be the same as when 9+2×7+3×10=539 + 2 \times 7 + 3 \times 10 = 53 is divided by 1313. The latter is clearly 11. The answer is (A).

University of Alberta