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23 Nov 2016, 03:14
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If x is an integer, is 6 a factor of x^3?
(1) x is divisible by 12.
(2) x^2 is a multiple of 3 and 2.
(1) x is divisible by 12.
(2) x^2 is a multiple of 3 and 2.
Vinayak Shenoy
Joined: 06 Jun 2016
Last visit: 27 Jun 2017
Posts: 233
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Location: India
Concentration: Operations, Strategy
Schools: ISB '18 (D)
GMAT 1: 600 Q49 V23
GMAT 2: 680 Q49 V34
GPA: 3.9
23 Nov 2016, 03:46
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Bunuel
If x is an integer, is 6 a factor of x^3?
(1) x is divisible by 12.
(2) x^2 is a multiple of 3 and 2.
(1) x is divisible by 12.
(2) x^2 is a multiple of 3 and 2.
IMO D
From statement 1
x is divisible by 12, that means x is also divisible by 6
hence x^3 will also have 6 as a factor
Sufficient
From statement 2
x^2 is a multiple of 3 and 2
we know x is an integer
hence x^2 must be of the form x^2 = 2^2* 3^2 = 36, 2^4*3^4=1296
Sufficient
Hence D
23 Nov 2016, 04:12
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Bunuel
If x is an integer, is 6 a factor of x^3?
(1) x is divisible by 12.
(2) x^2 is a multiple of 3 and 2.
(1) x is divisible by 12.
(2) x^2 is a multiple of 3 and 2.
IMO : D
Correct me if I'm wrong~
(1) X is divisible by 12
so... x = 12, 24, 36....
and x should be divisible by 6.. thus x^3 should be divisible by 6
(2) x^2 is multiple of 3 and 2.
or 6 is a factor of x^2
thus (x)(x^2) should be divisible by 6
So both options are independently sufficient.
can someone explain why the ans. is E 
