Data Sufficiency

If w, x and y are different positive integers, and wxy = 24, is xy divisible by 6?

(1) wy is not divisible by 6.

(2) x is even.

Solution by author:




Author just came up with "good" examples (counter cases) in BOTH cases. Good because both ARE SAME. How I indistinctly come up with them? [/img]

And I think it is "good" also because the author came up with way too fast. Any input? Thanks.

towerSpider wrote:If w, x and y are different positive integers, and wxy = 24, is xy divisible by 6?

(1) wy is not divisible by 6.

(2) x is even.

List combinations of 3 distinct positive integers with a product of 24:
1*2*12.
1*3*8
1*4*6
2*3*4.

Statement 1: wy is not divisible by 6
Case 1: w=1 and y=2, implying that x=12.
In this case, xy = 24, which is divisible by 6.

Case 2: w=1 and y=3, implying that x=8.
In this case, xy=24, which is divisible by 6.

But if w and y swap values in Case 2, xy will NOT be divisible by 6.
Case 3: w=3 and y=1, implying that x=8.
In this case, xy=8, which is NOT divisible by 6.
INSUFFICIENT.

Cases 1 and 3 also satisfy Statement 2.
Thus, even when both statements are satisfied, it's possible that xy is divisible by 6 or that xy is not divisible by 6.

The correct answer is E.