What is the greatest common divisor of positive integers x and y? (1)

Question

What is the greatest common divisor of positive integers x and y?

(1) x = y + 6
(2) y/6 is an integer

freedom128 · Answer

1) (y, x) can be (1,7), (2,8), etc. Each has different GCD.
NOT SUFFICIENT

2) we don't know about x
NOT SUFFICIENT

1) (y, x) can be (6,12), (18,24). The GCD is always 6.
SUFFICIENT.

Final answer is (C).

TestPrepUnlimited · Answer

We are finding the GCF of x and y.

Statement 1: 
We can have y = 3, x = 9 (GCF = 3) or y = 6, x = 12 (GCF = 6). Insufficient.

Statement 2: 
y has a factor of 6. Insufficient.

Combined: 
We know that both x and y are multiples of 6. We could have GCF's 6, 12, 18 etc. x is 6 directly higher than y however, so the GCF is only 6 at most. Therefore the GCF can only be 6.

Ans: C

madgmat2019 · Answer

(1) x = y + 6........many possibilities - INSUFFICIENT
(2) y/6 is an integer........y=6a - INSUFFICIENT

combining both x = y + 6, y=6a

x = 6(a+1) , y=6a 
so the gcd of x,y is 6

OA:C

North1South · Answer

I got this incorrect, maybe there's something I'm missing?

1) & 2) alone are insufficient.

Together, it would seem that the GCF is 6, but not necessarily, if there were greater (hidden) prime factors, it would make 1) and 2) together insufficient.

Prime factors of x: 2, 3, a + 1, (n?)
Prime factors of y: 2, 3 , a, (n?)

If n were, say, 13, then the GCD would no longer be 6.

Am I missing something here?

TestPrepUnlimited · Answer

Hi  North1South  ,

You proposed a great question! We have x = y + 6 though so if y has a factor of 13 then x cannot have a factor of 13, they only have a difference of 6. We can use statement 1 to conclude the GCF must be a factor of 6, hence their GCF is 1, 2, 3, or 6.

bumpbot · Answer

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What is the greatest common divisor of positive integers x and y? (1)

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