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stonecold
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stonecold
Is the integer z divisible by 6?

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

Similar question to practice: is-the-integer-z-divisible-by-128030.html
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Here is what i did on this one =>

We need to see if Z is divisible by 6 or not.
Statment 1 =>
Z=2 => NO
Z=6 => YES
Not sufficient.

Statment 2 =>
As GCD=5
Hence can never have a three.
So it is not divisile by 3.
Hence Z can never be divisible by 6.

Sufficient.

SMASH THAT B.
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For statement 2, is it possible that z and 15 have 3 as a common factor, but the greatest common factor is 5. In which case, statement 2 is not sufficient?
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For statement 2, is it possible that z and 15 have 3 as a common factor, but the greatest common factor is 5. In which case, statement 2 is not sufficient?

No. If z were divisible by 3 too, then the greatest common factor of z and 15 would be 15, not 5.

Check the following question for more: https://gmatclub.com/forum/is-the-integ ... 28030.html
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