Need quick way to solve this DS

gmatme wrote:What is the remainderwhen a positive integer x is divided by 8?
a) When x is divided by 12 the remainder is 5
b) When x is divided by 18 the remainder is 7

What is the best and quick way to solve this problem?

Not sure if this is THE most optimal but here goes...

1 - insufficient.
x = 12*t + 5
We have to find remainder of x / 8
For even values of t, remainder = 5. For odd values of t, remainder = 1


2 - insufficient.
x = 18*s + 7
Try s=0, s=1, s=2, s=3. We get remainders of 7, 1, 3 and 5 resp.

Together they are insufficient as well since remainder can be 1 or 5.

Hence E

What is the remainder when a positive integer x is divided by 8?
a) When x is divided by 12 the remainder is 5
b) When x is divided by 18 the remainder is 7

Statement A
x can belong to {17,29,41,53,65,77...}
x/8 can give a remainder of {1,5,1,5,1,5} hence either 1 or 5

Statement B
x can belong to {25,43,61,79,95...}
x/8 can give a remainder of {1,3,5,7,...}

I think it should be E