difficult - remainder remainder questions

[cgc]

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

Anyone have a good strategy for remainder questions like this one or others in general?

[ace_gre]

Hi, Here is my approach.

m= 13*q +2
m= 17 *k + 2

Now both the above equations will be satisfied, if m=2, or multiples of (13 * 17 ) + 2.
Or where q=0 or q= 17*1, 17*2,17*3...
k =0 or k= 13*1, 13*2, 13*3...

In any case, remainder when q is divided by 17 is 0.

IMO A.

Please post OA.

[cgc]

You are correct! the answer is 0.

I couldnt see the relationship until you pointed it out. Thanks.

[sg1978]

I agree the answer should be A since the remainder when q divided by 17 or k divided by 13 will be 0.
Maybe my approach is not very intuitive, but 13q=17k so for q,k to be integers the remainder when q/17
will be 0 as k should be a multiple of 13.