Data Sufficiency

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

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

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

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.