If x, y, and z are positive integers, is xy divisible by z ?

Question

(1) x is not divisible by z
(2) y is not divisible by z

gmatophobia · Answer

The statements are individually not sufficient to answer the question if  \frac{xy }{ z}  will result in an integer.

Statement 1

We know x is not divisible by 6, there is no information regarding the divisibility of y.

Hence this statement is not sufficient on its own. Eliminate A and D

Statement 2

We know y is not divisible by 6, there is no information regarding the divisibility of x.

Hence this statement is not sufficient on its own. Eliminate B.

Combination

While x and y may not be individually divisible by z, the product can still be divisible, however that's not guaranteed to happen.

Hence the combination of both the statements doesn't help us determine if  \frac{xy }{ z}   is an integer.

IMO E

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