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2008/09 AHSMC Part 1 Problem 1

Problem 1 of 16

The numbers mm and nn are related by m=9n5+32m = \dfrac{9n}{5} + 32. If nn is an integer between 11 and 9999, the number of corresponding values of mm which are also integers is

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Solution

In order for mm to be an integer, nn must be a multiple of 55. Since there are 1919 integer values of nn within range, the number of corresponding values of mm that are integers is also 1919. The answer is (B).

University of Alberta