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

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adkikani
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If x and y are positive integers, is y a prime number? [#permalink] New post   Updated on: 25 Apr 2018, 21:24
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If x and y are positive integers, is y a prime number?

(1) xy is a prime number.

(2) \(y^2\) is even.
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Official Answer
C

Originally posted by adkikani on 25 Apr 2018, 18:21.
Last edited by Bunuel on 25 Apr 2018, 21:24, edited 1 time in total.
Edited the OA.
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Re: If x and y are positive integers, is y a prime number? [#permalink] New post   25 Apr 2018, 19:34
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?
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Re: If x and y are positive integers, is y a prime number? [#permalink] New post   25 Apr 2018, 19:45
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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
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Re: If x and y are positive integers, is y a prime number? [#permalink] New post   25 Apr 2018, 20:55
adkikani wrote:
If x and y are positive integers, is y a prime number?

(1) xy is a prime number.

(2) \(y^2\) is even.


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 ?

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Re: If x and y are positive integers, is y a prime number? [#permalink] New post   25 Apr 2018, 22:29
Expert Reply
You are right, OA = C.

Same has been updated in the question.

anugrahs wrote:
adkikani wrote:
If x and y are positive integers, is y a prime number?

(1) xy is a prime number.

(2) \(y^2\) is even.


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


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adkikani
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Re: If x and y are positive integers, is y a prime number? [#permalink] New post   26 Apr 2018, 03:09
Bunuel gmatbusters niks18 chetan2u VeritasPrepKarishma

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

(1) xy is a prime number.

(2) \(y^2\) is even.


Is there any better approach than plugging numbers for this Q?
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If x and y are positive integers, is y a prime number? [#permalink] New post   26 Apr 2018, 03:13
adkikani wrote:
Bunuel gmatbusters niks18 chetan2u VeritasPrepKarishma

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

(1) xy is a prime number.

(2) \(y^2\) is even.


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


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
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Re: If x and y are positive integers, is y a prime number? [#permalink] New post   26 Apr 2018, 04:25
niks18

Let me know if we are on same page.

Quote:
Solve the question logically.

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


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.

Quote:
Statement 2: \(y^2\)=Even implies, y can be any EVEN number


A square of an even integer will be even and likewise for odd. Clearly insuff.
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Re: If x and y are positive integers, is y a prime number? [#permalink] New post   26 Apr 2018, 05:10
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You got it right,
niks18 has explain it very well.

:thumbup:

adkikani wrote:
niks18

Let me know if we are on same page.

Quote:
Solve the question logically.

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


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.

Quote:
Statement 2: \(y^2\)=Even implies, y can be any EVEN number


A square of an even integer will be even and likewise for odd. Clearly insuff.
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If x and y are positive integers, is y a prime number? [#permalink] New post   08 Aug 2021, 03:20
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?
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Re: If x and y are positive integers, is y a prime number? [#permalink] New post   14 Aug 2021, 09:05
Daikon123 wrote:
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?



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.
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Re: If x and y are positive integers, is y a prime number? [#permalink]
14 Aug 2021, 09:05
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Bunuel
Math Expert
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