Question

If x and yare positive integers and x $÷$ y has a remainder of 5, what is the smallest possible value of xy ?

• A. $40$
• B. $50$
• C. $30$
• D. $60$

Answer 1

Answer: (C)

$30$

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 $5\times 6=30.$