Bunuel wrote:

If y is an integer such that 2 < y < 100 and if y is also the square of an integer, what is the value of y ?

(1) y has exactly two distinct prime factors

(2) y is even.

Kudos for a correct solution.

Question says, that y is between 2 and 100. And Y is square of an integer. In that case we have following squares below 100.

Y should be either of 4,9,16,25,36,49,64,81.

Statement-1 : It says Y has 2 DISTINCT Prime Factors. So eliminate all the odd numbers as they have only one prime factors(3 apart from prime factorization of 49 which has 7) in it.

We are left with even numbers(4,16,36,64)-- In this eliminate 4, 16 and 64. These got 2 has their only prime factor. But when we do prime factorization,

\(36= 2^2 * 3^2\). We get 2 distinct prime factors- 2 and 3.

So sufficient.

Statement-2 : Doesn't say anything other than y is even number. Not sufficient as we have 48 even numbers between 2 and 100,

So Statement-1 is sufficient. Answer is A.

Also, we can verify that our answer (y=36) is correct as statement-2 says y is even. And in GMAT DS, the statements never contradicts each other.

Bunuel, Please post your explanation

Hope i made my choice justifiable :D

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