Number properties - prime factors

Given: 2< y < 100 and y = perfect square
S1. Exactly two factors.
Writing down all the squares < 100 we get that 36 is the only square which satisfies the given condition,, Sufficient
S2. Even Number, Many even squares are there between given limits, Not Sufficient

(A) is answer.

This would be a typical word translation problem for which we will fall trap for....nice problem

I also assumed that two factors would be 2 different ones. Do not think that such a problem will appear on the actual GMAT.

C the Answer.

If the problem meant distinct prime factors, it would use the word distinct.

+1 C

IMO is A

Taking one fact at a time.
Fact 1 (from the Q): 2 < y < 100
Fact 2 (from the Q): y is square of a number

just from this info the possible answers are 1, 4, 9, 16, 25, 49, 64, 81

Fact 3 (from Statement 1): y has exactly 2 prime factors
from the numbers listed about only 36 uniquely satisfies the condition. Hence Sufficient

Hence the only possible answers now are A and D

Statement 2 gives multiple choices. It could be 4, 16 or 64 and hence insufficient

The correct answer is A

OA?

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 prime factors.
2. y is even.
IMO: A
Reason:
Question Stem: Y is between 2 and 100 and also the square of an integer.
So, y may be one of 4,9,16,25,36,49,64,81

St. 1 y has exactly two prime factors. (36 has two prime nos: 2 and 3) Sufficient
Sr. 2 y is even.(Y may be 4, 16, 36, and 64) Not sufficient

Can anyone post the OA for this question.

I believe it should be C for number y=4

but we can't deny y=36 with 2 prime factors 2 & 3 and Answer to be A

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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 prime factors.

(2) y is even.

In the original condition, there is 1 variable (y) and thus we need 1 equation to match the number of variable and equation. Since there is 1 each in 1) and 2), D is likely the answer.

In case of 1), y=4,9,25,49 and the answer is not unique. Therefore it is not sufficient.
In case of 2), y=4,16, 36, 64 the answer is not unique. Therefore it is not sufficient.
Using both 1) & 2) together, y=4 is unique. Therefore it is sufficient and the answer is C.


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4 = 2 x 2 (factors of 4 = 1, 2, & 4)...only 1 prime factor(2)
9 = 3 x 3 (factors of 9 = 1, 3, & 9)...only 1 prime factor(3)
16 = 4 x 4(factors of 16 = 1,2,4,8,& 16)...only 1 prime factor(2)
25 = 5 x 5 (factors of 25 = 1,5, & 25)....only 1 prime factor(5)
36 = 4 x 9 (factors of 36= 1,2,3,4,6,8,12,18,& 36) 2 prime factors (2 and 3)
...... until we get to 81, which also 1 prime factor (3)

That 4 = 2 x 2 does not imply 4 has 2 prime factors. Else, how many factors does it have?
In this case, I feel A should be the answer, right?

Pls what is the OA and explanations.

gmatdriller, I'm with you: if the question doesn't specify, then "two prime factors" (for me, at least) should be taken as two distinct prime factors. (For instance, 4 has three factors: 1, 2, and 4. One of those is prime.)

This question showed up in my e-mail inbox as a "Question of the Day."

To the people who choose the Question of the Day: questions like these, with clear ambiguity, aren't helping anyone. This is a recurring issue in the questions that have been selected and make their way to my inbox. I hope this can be cleaned up.

I appreciate the viewpoints of the regular experts on this site, they will keep me coming back regardless.