nipunranjan wrote:If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y.
1. y = 12m, where m is an integer.
2. x = 12n, where n is an integer.

OA=A

This question is very similar to an official GMAT question. Mitch has inadvertently answered the other question.

One solution to the question you have posed is as follows:

Target question: What is the greatest common divisor of x and y?

Given: x = 8y + 12

Statement 1: y = 12m, where m is an integer
If y = 12m and x = 8y + 12, then we can replace y with 12m to get:
x = 8(12m) + 12, which means x = 96m + 12, which means x = 12(8m + 1) [if we factor]
So, rather than ask "What is the GCD of x and y?", we can ask "What is the GCD of 12m and 12(8m + 1)?"
Well, we can see that they both share 12 as a common divisor, but what about m and 8m+1?
Well, there's a nice rule that says: If n and k are positive integers, the GCD of n and kn+1 is always 1
So, the GCD of m and 8m+1 is 1, which means the GCD of 12m and 12(8m + 1) is 12.
This means that the GCD of x and y is 12
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x = 12n, where n is an integer.
There are several pairs of values that satisfy the given conditions. Here are two:
Case a: x=36 and y=3, in which case the GCD of x and y is 3
Case b: x=60 and y=6, in which case the GCD of x and y is 6
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent