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2008/09 AHSMC Part 1 Problem 5

Problem 5 of 16

If a certain positive integer is divided by 77, the remainder is 66. If it is divided by 44, the remainder is 11. The remainder when it is divided by 2828 is

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Solution

From the first condition, the desired remainder is one of 66, 1313, 2020 and 2727. From the second condition, the desired remainder is one of 11, 55, 99, 1313, 1717, 2121 and 2525. The only common value is 1313. The answer is (D).

University of Alberta