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## Interget Power DS (GMATPrep)

Bhupisuhag Just gettin' started!
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Interget Power DS (GMATPrep) Sat Jun 23, 2012 9:24 am
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• Lap #[LAPCOUNT] ([LAPTIME])
If X is an integer greater than 1, is X equal to the 12th power of an integer ?

(1) X is equal to the 3rd Power of an integer

(2) X is equal to the 4th Power of an integer.

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Sat Jun 23, 2012 4:08 pm
Bhupisuhag wrote:
If X is an integer greater than 1, is X equal to the 12th power of an integer ?

(1) X is equal to the 3rd Power of an integer

(2) X is equal to the 4th Power of an integer.

Statement 1: x = a³, where a is an integer

If a=2, then x = 2³, which is not the 12th power of an integer.
If a=2^4, then x = (2^4)³ = 2^12, which is the 12th power of an integer.
INSUFFICIENT.

Statement 2: x = b^4, where b is an integer
If b=2, then x = 2^4, which is not the 12th power of an integer.
If b=2³, then x = (2³)^4 = 2^12, which is the 12th power of an integer.
INSUFFICIENT.

Statements 1 and 2 combined:

Since x = a³ and x = b^4, we get:
a³ = b^4
a³ = (b³)b
b = (a/b)³.
Since b is an integer, (a/b)³ is an integer.
Since a/b = integer/integer -- the definition of a rational number -- it is not possible that a/b is equal to an irrational value such as ³√2.
Thus, in order for (a/b)³ to be an integer, a/b must be an integer, implying that b is the CUBE OF AN INTEGER.
Thus, x = b^4 = (integer³)^4 = integer^12.
SUFFICIENT.

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sandeep_thaparianz Rising GMAT Star
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Sun Jun 24, 2012 5:55 am
Great explanation above OA is C

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