If x is an integer, is 6 a factor of x^3?

Question

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.

Vinayak Shenoy · Answer

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

PrincessPanda · Answer

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.

nks2611 · Answer

can someone explain why the ans. is E

chetan2u · Answer

Bunuel  answer should be D, seems some typo error

stonecold · Answer

Given info --> 
x is an integer.
We need to check if x^3 is divisible by 6 or not.
Notice 6=2*3
RULE-> Both x and x^n always have the exact same prime factors.
Hence if x^3 is to be divisible by 6=> x^3 must have both 2 and 3 as its prime factor.
Hence if x must have both 2 and 3 as its prime factors for ^3 to be divisible by 6.

Statement 1
x is divisible by 12.
Hence 2 and 3 must be prime factors of x

hence Sufficient

Statement 2
x^3 is divisible by both 2 and 3
Remember x and x^n have the exact same prime factors.
Hence x must have 2 and 3 as its prime.
Hence sufficient .

Hence D

Shiv2016 · Answer

Is the answer D or E?

Bunuel · Answer

It's D. Edited. Sorry.

If x is an integer, is 6 a factor of x^3?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards