If x and y are positive integers, what is the value of x y?

Even if we consider x=y, still other cases will also work so we have multiple answers for x-y, that is why statement is not sufficient
Statement is only sufficient if it gives only 1 answer under any and all circumstances

Given: \(x\) and \(y\) are positive integers

Target question: What is the value of \(x – y\)?

Statement 1: The greatest common divisor of \(x\) and \(y\) is \(1\)
There are several values of x and y that satisfy statement 1. Here are two:
Case a: If x = 1 and y = 1, then the greatest common divisor of x and y is 1. In this case, the answer to the target question is x - y = 1 - 1 = 0
Case b: If x = 1 and y = 2, then the greatest common divisor of x and y is 1. In this case, the answer to the target question is x - y = 1 - 2 = -1
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: \(\frac{13x}{y}\) is a positive integer with exactly two positive divisors.
In other words, \(\frac{13x}{y}\) is a prime number.
There are several values of x and y that satisfy statement 2. Here are two:
Case a: If x = 1 and y = 1, then 13x/y = (13)(1)/(1) = 13, which is prime. In this case, the answer to the target question is x - y = 1 - 1 = 0
Case b: If x = 5 and y = 13, then 13x/y = (13)(5)/(13) = 5, which is prime. In this case, the answer to the target question is x - y = 5 - 13 = -8
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are several values of x and y that satisfy BOTH statements. Here are two:
Case a: x = 1 and y = 1. In this case, the answer to the target question is x - y = 1 - 1 = 0
Case b: x = 5 and y = 13.In this case, the answer to the target question is x - y = 5 - 13 = -8

Answer: E

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.