Integers and divisibility

[fighting_cax]

When integer m is divided by 13, the quotient is q and the remainder is 2. When m is divided by 17, the remainder is also 2. What is the remainder when q is divided by 17?

A. 0
B. 2
C. 4
D. 9
E. 13

OA is A

Please explain.

[Zipper]

m/13=q and 2 remainder
m/17=x and 2 remainder

so m-2 is a multiple of 13 and 17
m-2/13=q with no remainder but we don't need it anyway.

so q must be a multiple of 17

hence, A=0