2013/14 AHSMC Part 1 Problem 2

Problem 2 of 16

The total score of four students in a test is $2013$ . Ace scores $1$ point more than Bea, Bea scores $3$ points more than Cec, and Cec scores $2$ points more than Dee. None of their scores is divisible by

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Solution

Since the average score is just over $500$ , we try $500$ as a score for Dee. Then Cec's score is $502$ , Bea's is $505$ and Ace's $506$ . The total is indeed $2013$ , so that no adjustment is necessary. Now $500$ is divisible by $4$ , $500$ and $505$ are divisible by $5$ , and $506$ is divisible by $11$ and $23$ . The answer is (A).

University of Alberta

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