Aple wrote:

Is N divisible by 7?

(1) N = x-y, where x and y are integers

(2) x is divisible by 7, and y is not divisible by 7

Hi guys, my question is not in regards to how to solve this problem, but how to know if the answer is required to be an integer or not? For example, the question above does not mention any requirements for the answer to be an integer, yet that is exactly what the outcome requires. Any help would be greatly appreciated.

Thanks

N to be divisible by 7, it MUST be an integer (at least on the GMAT) because the question makes no sense if N is not an integer.

On the GMAT divisibility is applied only to the integers. Also on GMAT when we are told that a is divisible by b (or which is the same: "a is multiple of b", or "b is a factor of a"), we can say that:1.

a is an integer;

2.

b is an integer;

3.

\frac{a}{b}=integer.

As for the question:

Is N divisible by 7?(1) N = x-y, where x and y are integers. Clearly insufficient.

(2) x is divisible by 7, and y is not divisible by 7. Clearly insufficient.

(1)+(2) N={multiple of 7}-{not a multiple of 7}={not a multiple of 7}. Sufficient.

Answer: C.

Below might help to understand this concept better.

If integers a and b are both multiples of some integer k>1 (divisible by k), then their sum and difference will also be a multiple of k (divisible by k):Example:

a=6 and

b=9, both divisible by 3 --->

a+b=15 and

a-b=-3, again both divisible by 3.

If out of integers a and b one is a multiple of some integer k>1 and another is not, then their sum and difference will NOT be a multiple of k (divisible by k):Example:

a=6, divisible by 3 and

b=5, not divisible by 3 --->

a+b=11 and

a-b=1, neither is divisible by 3.

If integers a and b both are NOT multiples of some integer k>1 (divisible by k), then their sum and difference may or may not be a multiple of k (divisible by k):Example:

a=5 and

b=4, neither is divisible by 3 --->

a+b=9, is divisible by 3 and

a-b=1, is not divisible by 3;

OR:

a=6 and

b=3, neither is divisible by 5 --->

a+b=9 and

a-b=3, neither is divisible by 5;

OR:

a=2 and

b=2, neither is divisible by 4 --->

a+b=4 and

a-b=0, both are divisible by 4.

Hope it's clear.

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