Is the integer z divisible by 15?

Is integer z divisible by 15?

Statement 1: The greatest common factor of z and 10 is 5. This means there is atleast one 5 in z but no info about a 3. We can't say whether z is divisible by 15. INSUFFICIENT

Statement 2: The greatest common factor of z and 15 is 5.

This means there is atleast one 5 in z but no 3. If z also had a 3 then the GCF would be 5*3 which is 15.

So we can conclude z is not divisible by 15. SUFFICIENT.

Ans:B

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I think the answer is B.

Statement 1
x = 10, z = 15 YES
x = 10, z = 25 NO

Statement 2
x = 15, z = 5 NO
x = 15, z = 20 NO
The only way for z/15 to be divisible by 15 is if it is some multiple of 15 (e.g. 15, 30, 45, 60). But, if it's a multiple of 15 then that multiple would violate the condition in statement 2.
e.g. x = 15, z = 30 <--GCF(15,30) = 15 NOT 5

Is the integer z divisible by 15?

(1) The greatest common factor of z and 10 is 5.
(2) The greatest common factor of z and 15 is 5.


1) The greatest common factor of z and 10 is 5.

a) z can be 5
b) z can be 15 itself
Insufficient

(2) The greatest common factor of z and 15 is 5.

for integer z to be divisible by 15, z and 15 gcd should be 15 itself

z is not divisible by 15. Sufficient

IMO (B)

Is the integer z divisible by 15?

(1) The greatest common factor of z and 10 is 5.
Z can be 15, which is divisble by 15
Z can be 25 ,which is not divisble by 15

We get 2 different answers. Option A - Not Sufficient.

(2) The greatest common factor of z and 15 is 5.
We know that Z has to be less than 15, to have 5 as GCF. Because if z is equal to greater than 15 , then GCF of Z and 15 will be minimum 15.

So Z is not divisble by 15.

Option B alone is sufficient.

Ans: B

(1) If z=10 then \(NO\), if \(z=15\) then \(YES\). Insufficient.

(2) Again z=10
The GCF of 10 and 15 is 5;
\(z<15\) to have GCF 5. So, z is not divisible by 15

Sufficient.

The answer is B

Hi Bunuel , if the second statement was like -

"The greatest common factor of z and 15 is 3"

then the question's answer would have been E right?

Just a curious doubt to understand the question better. Thanks, Bunuel!

No, (2) would still be sufficient.

The question asks: Is the integer z divisible by 15?

(2) sys that the greatest common factor of z and 15 is 5. Now, IF z were divisible by 15 (15, 30, 45, 60, ...), then the greatest common factor of z = 15k (for some integer k) and 15 would have been 15, not 5. Here z can be ..., -20, -10, -5, 5, 10, 20, 25, 35, ... So, z can be any multiple of 5, which is NOT a multiple of 3!

Similarly, IF (2) were the greatest common factor of z and 15 is 3 it would mean that z is NOT divisible by 5, so not divisible by 15 either. IF z were divisible by 15 (15, 30, 45, 60, ...), the the greatest common factor of z = 15k (for some integer k) and 15 would have been 15, not 3. Here z can be ..., -12, -9, -6, -3, 3, 6, 9, 12, 18, ... So, z can be any multiple of 3, which is NOT a multiple of 5!

Hope it's clear.

Thank you Bunuel, my doubt is clear. Grateful for your detailed explanations! Always! Thanks­

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