2017/18 AHSMC Part 1 Problem 2

Problem 2 of 16

A math teacher is given a big bag of $300$ candies by a grateful parent. The teacher distributes as many of the candies as possible to her students so that each student gets the same number of candies. There are $14$ candies left over. How many students are there in her class, if each class in the school has at most $30$ students?

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Solution

If $x$ represents the number of students in the class and $c$ the number of candies received by each student, then $14 < x \le 30$ and $x \cdot c = 300 - 14 = 286 = 2 \cdot 11 \cdot 13.$ There are two possible solutions, $x = 22$ or $x = 26$ . The answer is (E).

University of Alberta

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