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Question

If x and yare positive integers and x ÷ y has a remainder of 5, what is the smallest possible value of xy ?
  1. 50
  2. 60
  3. 40
  4. 30

A
40
B
30
C
60
D
50
Solution
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30:
The remainder must always be smaller than the divisor. In this problem, 5 must be smaller than y. Additionally, y must be an integer, so y must be at least 6. If y is 6, then the smallest possible value of x is 5. (Other values of x that leave a remainder of 5 when divided by 6 would be 11, 17, 23, etc.) If y is chosen to be larger than 6, then the smallest possible value of x is still 5. Thus, you will get the smallest possible value of the product xy by choosing the smallest x together with the smallest y. The smallest possible value of xy is 5×6=30.

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