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Is the positive integer z a prime number

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Is the positive integer z a prime number

by saxenashobhit » Thu Jul 07, 2011 5:17 am
Is the positive integer z a prime number?

1) z and the square root of integer y have the same number of unique prime factors.
2) z and the perfect square y have the same number of unique factors.

Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.

Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.

Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.

EITHER statement BY ITSELF is sufficient to answer the question.

Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

Kaplan quiz 6, question 6, https://www.scribd.com/doc/58999877/GMAT ... et-6-Quant
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by Frankenstein » Thu Jul 07, 2011 5:38 am
Hi,
From(1):
if y = 3^2, sqrt(y) = 3 and z can be either 3 or 3^3(Both have only 3 as prime factor)
So, z can be prime or not
Not sufficient

From(2):
if y is a perfect square. It has at odd number of factors. So, z has odd number of factors.
So, z is definitely not prime because a prime has only 2 factors(1 and itself)
Sufficient

Hence, B
Last edited by Frankenstein on Thu Jul 07, 2011 5:56 am, edited 1 time in total.
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by Ian Stewart » Thu Jul 07, 2011 5:46 am
saxenashobhit wrote:Is the positive integer z a prime number?

1) z and the square root of integer y have the same number of unique prime factors.
2) z and the perfect square y have the same number of unique factors.
Statement 1 is not sufficient; if y is 9, then z could be 3 or 9, so z could be prime or not.

Does Statement 2 say 'unique factors', or 'unique prime factors'? If the question only says 'unique factors' in Statement 2, then Statement 2 is sufficient alone. Perfect squares must have an odd number of factors in total, whereas prime numbers always have 2 factors in total, so if Statement 2 is true, then z cannot be prime, and Statement 2 is sufficient to give a 'no' answer to the question.
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by Ian Stewart » Thu Jul 07, 2011 5:48 am
Frankenstein wrote:
if y is a perfect square. It has at least 3 factors.
Careful here - that's true for every positive perfect square with one exception: 1 has only 1 positive factor.
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by saxenashobhit » Thu Jul 07, 2011 6:05 am
Hi Ian,
Option B in Kaplan test says 'unique factors'. I had marked B by thinking on same lines as you but Kaplan said B its wrong. I don't have OA but I feel this one question's answer may be wrong in Kaplan's system
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by Frankenstein » Thu Jul 07, 2011 6:09 am
Ian Stewart wrote:
Frankenstein wrote:
if y is a perfect square. It has at least 3 factors.
Careful here - that's true for every positive perfect square with one exception: 1 has only 1 positive factor.
Thanks Ian. As soon as I posted, I actually thought of changing and adding that z is a perfect square. But, I have been having problem with my internet. So, I couldn't edit earlier.
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