enigma123 wrote:

If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y?

(1) x = 12u, where u is an integer.

(2) y = 12z, where z is an integer.

x = 8y + 12

(1) x = 12u, where u is an integer.

If x is a multiple of 12, it means 8y is a multiple of 12. Since 8 already has three 2s, we NEED y to have a 3 but it COULD have 2s and/or other factors too.

So we cannot say what the GCD of x and y is.

Not sufficient.

(2) y = 12z, where z is an integer.

If y is a multiple of 12, x is a multiple of 12 too. So they certainly have 12 common. Let's see what else they could have common.

x is 12 more than a multiple of y so the only common factors they could have are the factors of 12. We already know that they both have 12 in them. So GCD must be 12.

(This concept has been discussed in detail here:

https://www.veritasprep.com/blog/2015/0 ... -the-gmat/)

Sufficient.

Answer (B)

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Karishma

Veritas Prep GMAT Instructor

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