If x

Question

If x < 200, what is the value of x?

(1) 2x is a perfect square and a perfect cube
(2) x has an odd number of distinct prime factors

EDIT: Original post did not contain a solution. Detailed explanation will be posted in several days.

GMATinsight · Answer

Question: x = ?

Statement 1 : 2x is a perfect square and a perfect cube

i.e.  2x = 2^6  (in range < 200) OR i.e.  2x = 1^6  (in range < 200)
i.e. x = 32 or 1/2

NOT SUFFICIENT

Statement 2 : x has an odd number of distinct prime factors

As per the statement, x has either one prime factor or 3 prime factors or 5 prime factors etc.

i.e. x may be {4, 9, 16, 25... etc.}

NOT SUFFICIENT

Combining the statements

2X is a perfect square, a perfect cube and x has odd Number of Prime factors

i.e. x can be only 32 now

SUFFICIENT

Answer: Option C

rmnsr · Answer

Hey you didn't consider the possibility of X=0.5 which would make C option the correct answer.

Posted from my mobile device

IanStewart · Answer

"Odd number of distinct prime factors" means something completely different from "odd number of factors". It is not true here, from Statement 2, that x needs to be a perfect square. From Statement 2, x could be 2 (which has one prime factor, so an odd number of prime factors) or 30 (which has three prime factors) among many other possibilities.

The question, though:

does not make sense. The concepts of "perfect square" and "perfect cube" only mean anything if you know what set of numbers you're talking about. If you're talking about integers, then any sixth power is both a perfect square and perfect cube, so 1^6 = 1, 2^6 = 64, 3^6 = 729, and so on are both perfect squares and perfect cubes. But if you might instead be talking about 'rational numbers' (fractions involving integers only), then numbers like 1/64 become perfect squares and perfect cubes, because 1/64 = (1/8)^2 = (1/4)^3. There is no way to interpret Statement 1 unless you know to which set x belongs.

The same is true of Statement 2; a question can never use a Statement like this to convey the information "x is an integer", because it's not clear what Statement 2 would even mean if x could be a non-integer. If a question is going to talk about prime factors of a number, the question will always tell you in advance that the number is an integer, because a GMAT question never risks discussing something potentially undefined (in the same way that a question containing the fraction 1/x will tell you x is nonzero).

So you simply can't see a question set up this way on the GMAT, unless it tells you in the stem that x is an integer. Then the answer is A, not C.

mSKR · Answer

x<14

1. 2x = perfect square and a perfect cube
>> means 2x can be 4(2x= 2),32 ( 2x= 4)
not sufficient

2. x = odd number of distinct prime factors
in this way, x can be 2,5,13,7, etc.
not sufficient

combine 1 and 2:
2x= 4
means x = 2( 1 distinct prime factor)

hence ,C

If x < 200, what is the value of x?

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

GMAT Data Sufficiency (DS) Questions

If x < 200, what is the value of x?

Prep Toolkit

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