If x and y are positive integers, is y a prime number?

Question

(1) xy is a prime number.

(2)  y^2  is even.

adityan92 · Answer

Statement 1 : NOT SUFFICIENT

Y can be 1 or a prime number

Statement 2 : NOT SUFFICIENT

Y can be any even number

Combined : Yes.

Why is the OA B? Can you please explain?

Kurtosis · Answer

St1: xy is a prime number --> 1 * 3 = prime --> y is prime
3 * 1 = prime --> y is not prime
Not Sufficient

St2: y^2 = even --> y is even but we do not know whether it is prime.
Not Sufficient.

Combining St1 and St2, xy is prime and y is even --> x = 1 and y = 2
Sufficient

Answer: C

anugrahs · Answer

IMO: C

St 1: NOT SUFFICIENT
X Y Is Y Prime
5 1 No
1 5 Yes

St 2: NOT SUFFICIENT
 y^2  is even means Y is even
So Y = 2,4 ---- both even and composite

Together: only 1 condition X =1 and Y =2
thus SUFFICIENT

Whats the OA ?

Regards
Anugrah

GMATBusters · Answer

You are right, OA = C.

Same has been updated in the question.

Posted from my mobile device

adkikani · Answer

Bunuel   gmatbusters   niks18   chetan2u   VeritasPrepKarishma

Is there any better approach than plugging numbers for this Q?

niks18 · Answer

hi  adkikani

Solve the question logically.

Statement 1: x*y = Prime No, implies either y=Prime or y=1, because x is a positive integer

Statement 2:  y^2 =Even implies, y can be any EVEN number

Combining 1 & 2: we know y is even, hence it cannot be 1. So y is Prime

adkikani · Answer

niks18

Let me know if we are on same page.

You used basic properties of prime numbers here:
1. A prime no is one whose factors are 1  and  number itself.
2. 1 is  not  a prime no.

Eg : 2 * 1 = 2 or 1 * 2 = 2
I get both conditions in question and St 1 satisfied, but am not getting unique answer for y :
I get answer as y is prime in second case and y is not prime in first case. Hence insuff.

A square of an even integer will be even and likewise for odd. Clearly insuff.

GMATBusters · Answer

You got it right, niks18 has explain it very well.

Daikon123 · Answer

Thanks for the well-explained answers. But here I would like to point out one thing:

In GMAT, Data Sufficiency questions require the exam takers to decide whether either statement (or both statements) gives data that is sufficient for finding  an answer , NOT necessarily  a positive answer .

Hence in this case, since the second statement can help us prove the statement wrong, I think it should be recognized as sufficient for finding the answer to the question of whether y is a prime number or not.

In conclusion, I think the answer to this question is B.

Is there any chance that the official answer is wrong?

kingcrimson282 · Answer

Hello!

In the primary Question stem, the given info. is that both X & Y are +ve. We are req. to find out whether "Y" is a prime number. In Statement 2, it is given that "Y^2 is even". Thus, we can conclude that "Y" can be any even number. From the given statements together, we can say that option C would be sufficient to answer the question. Hope this helps.

If x and y are positive integers, is y a prime number?

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GMAT Data Sufficiency (DS) Questions

If x and y are positive integers, is y a prime number?

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