GMAT question - If x and y are integers... - Review

If and are integers, is divisible by 7?

1. When is divided by 7, the remainder is 2
2. When is divided by 7, the remainder is 5

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
4. EACH statement ALONE is sufficient
5. Statements (1) and (2) TOGETHER are NOT sufficient

Explanation

Simplify the question

In this case it is possible to express the question in a different way to make it easier to answer.

So the question is asking whether is divisible by 7.

Is statement (1) sufficient?

It should be clear that since this only tells us about and not that it is not sufficient

Is statement (2) sufficient?

It should be clear that since this only tells us about and not that it is not sufficient

Are both together sufficient?

Since neither on its own is sufficient we are left with two answer choices C (Together) and E (Neither) so we need to determine whether both statements together are sufficient.

We know that leaves a remainder of 2 when divided by 7 so let us express it as .

We know that leaves a remainder of 5 when divided by 7 so let us express it as .

So

Dividing this by 7 gives us

Which is not an integer and therefore is not divisible by 7.

This means that both statements together are sufficient to answer the question and the answer is C (Together).