MathRevolution wrote:

[GMAT math practice question]

For the integers \(x\) and \(y\), if \(xy\) is a multiple of \(25\), is \(y\) a multiple of \(5\)?

1) \(x-y\) is a multiple of \(5\)

2) \(x\) is a multiple of \(2\)

x*y is a multiple of 25, which is 5^2. This means Either both x and y have at least one '5' each in their prime factorisation, Or its also possible that one of x/y does not have any '5' and the other one of x/y has at least two 5's in its prime factorisation.

(then only x*y will be a multiple of 5^2)

Also if sum (or difference) of two integers is a multiple of 5, then Either each one of them is a multiple of 5 Or none of the two integers is a multiple of 5.

(1) x-y is a multiple of 5, so either each of them is a multiple of 5 Or none of the two integers is a multiple of 5. But the latter case is Not possible here since x*y is divisible by 5^2. So it means each of x/y must have at least one 5, so 'y' is a multiple of 5.

Sufficient.

(2) x is a multiple of 2, this doesn't tell anything about divisibility by 5 of y.

Not sufficient.

Hence

A answer