Data Sufficiency

BTGmoderatorDC wrote:Is the sum of integers a and b divisible by 7?

(1) a is not divisible by 7
(2) a - b is divisible by 7

OA C

Source: Manhattan GMAT

Question: Is the sum of integers a and b divisible by 7?

Let's take each statement one by one.

(1) a is not divisible by 7.

We know nothing about b. Insufficient.

(2) a - b is divisible by 7.

We cannot get to know whether (a + b) is divisible by 7. Insufficient.

(1) and (2) together

Say (a - b) = 7k, where k is any integer and a = 7m + r, where m is any integer and r is the remainder (we know that a is not divisible by 7)

From (a - b) = 7k and a = 7m + r, we have b = 7m + r - 7k = 7(m - k) + r

Thus, a + b = [7m + r] + [7(m - k) + r] = 7(2m - k) + 2r

Since r is the remainder and 2r is an even number, it is also not divisible by 7. Thus, 7(2m - k) + 2r = a + b is not divisible by 7. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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