raghav1708 wrote:
Bunuel wrote:
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.
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.
, my doubt is clear. Grateful for your detailed explanations! Always! Thanks