metallicafan wrote:In the fraction x/y , where x and y are positive integers, what is
the value of y ?
(1) x is an even multiple of y.
(2) x - y = 2

Target question: What is the value of y ?

Statement 1: x is an even multiple of y.
I'm not crazy about the term "even multiple." There are other ways that we could word this.
Presumably, this means that x = ky, (where k is an even integer)
Is this enough information to answer the target question? No, there are several possible pairs of numbers that satisfy this condition. Here are two:
Case a: x=10, y=5
Case b: x=12, y=3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x - y = 2
There are several possible pairs of numbers that satisfy this condition. Here are two:
Case b: x=4, y=2
Case b: x=5, y=3
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
Statement 1 says that x = ky (for some even integer k)
Statement 2 says that x - y = 2

Take statement 2 and replace x with ky to get: ky - y = 2
Factor to get y(k-1) = 2
So, we have: (positive integer)(positive integer) = 2
This means that one integer must be 1 and one integer must be 2
If we focus on k-1, we can see that k-1 cannot equal 2 since we are know that k is even, and an even number minus 1 (an odd number) cannot equal 2 (an even number).
So, it must be the case that k-1 = 1. In other words, k = 2
This means that y must equal 2
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent