Is the integer z divisible by 15?

Question

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

Bryan180599 · Answer

Is the integer z divisible by 15?

15 = 3*5 so to be divisible by 15, z must have the factors 3 and 5

(1) The greatest common factor of z and 10 is 5.
 Inssuficient  10=5*2. So we know that z has a factor 5 (greatest common factor), but we know nothing about other factors.

(2) The greatest common factor of z and 15 is 5.
 Insufficient  15=3*5. So again we know that z has a factor 5, but we know nothing about other factors.

Answer E

carouselambra · Answer

Is the integer z divisible by 15?

(1) The greatest common factor of z and 10 is 5.
Example :
z=50 (Not divisible by 15)
z=30 (Satisfies)
 (A) is not sufficient

(2) The greatest common factor of z and 15 is 5.
Example :
z=50 (Not divisible by 15)
z=30(Satifies)

We see that there are multiple numbers that can satisfy the above criteria hence (E) is the correct answer.

mcmoorthy · Answer

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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CEdward · Answer

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

dushyanta · Answer

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)

akadiyan · Answer

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

MHIKER · Answer

(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

raghav1708 · Answer

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 !

Bunuel · Answer

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.

raghav1708 · Answer

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

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Is the integer z divisible by 15?

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Is the integer z divisible by 15?

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