Data Sufficiency

gmatdriller wrote:If a and b are two integers greater than zero such that a = 7m and
b = 6n + 1 for some integers m and n, what is the value of a?

(1)m = n
(2)When a is divided by b, the remainder is a prime number

Target question: What is the value of a?

Given: a = 7m, and b = 6n + 1 for some integers m and n

It probably won't take long to conclude that each statement alone is not sufficient. This leaves us with . . .

Statements 1 and 2 combined:
If m = n, then we can say that a = 7m, and b = 6m + 1
We want values of m such that 7m (aka a) divided by 6m + 1 (aka b) leaves a prime remainder.
From here, we can plug in m values to see which ones leave a prime remainder.
Try m = 1: we get 7 divided by 7 leaves remainder 0 (not prime)
Try m = 2: we get 14 divided by 13 leaves remainder 1 (not prime)
Try m = 3: we get 21 divided by 19 leaves remainder 2 (prime)
Aside: notice the pattern emerging?
Try m = 4: we get 28 divided by 25 leaves remainder 3 (prime)
Stop here.

We can see that a could equal 21 or a could equal 28

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent