When a positive integer $N$ is divided by 60 , the remainder is 49 . When $N$ is divided by 15 , the remainder is
(A) 0
(B) 3
(C) 4
(D) 5
(E) 8
When a positive integer $N$ is divided by 60 , the remainder is 49 . When $N$ is divided by 15 , the remainder is
(A) 0
(B) 3
(C) 4
(D) 5
(E) 8

## Solution

This problem can be done in a number of ways. The easiest way is to consider that if $N$ is divided by 60 to achieve a remainder of 49 , it must be a number of the form, $60 k+49, k=0,1,2, \ldots$.

This implies that the smallest number to meet the requirements is 49 itself. If we divide 49 by 15 we get a remainder of 4 . Or, if $k=1$ in our formula then the next number to satisfy the requirements is 109 which when divided by 15 gives 4 as the remainder.

ANSWER: (C)