Data Sufficiency

rafodr wrote:Please help with this one...

If x and y are positive integers, is xy a multiple of 8?

(1) The greatest common divisor of x and y is 10
(2) The least common multiple of x and y is 100

I thought that A was the answer, but it says that the answer is C

The answer is C.
(1) INSUFFICIENT - two conflicting sets of values:
a) x=10, y=10 xy is not divisible by 8
b) x=20, y=10 xy is divisible by 8

(2) INSUFFICIENT - two conflicting sets of values:
a) x=100, y=10 xy is divisible by 8
b) x=25, y=4 xy is not divisible by 8

(1)&(2)
(1) tells us that x and y both have a 2 and a 5 in their prime factorizations.
(2) tell us that, in addition to the 2 and 5 that x and y share in their prime factorizations, one of the values has an additional 2 in its prime factorization and the other has an addditional 5.

To solve this question(and understant my solution , it is useful to know the systematic approach to finding GCD and LCM. I have created a video tutorial at https://www.leapeducation.ca/gcd-lcm.mp4
You might want to review this video to better understand my reasoning above.