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# If x and y are positive integers, what is the value of y?

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
If x and y are positive integers, what is the value of y?  [#permalink]

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01 Oct 2018, 03:48
00:00

Difficulty:

25% (medium)

Question Stats:

83% (01:06) correct 17% (00:41) wrong based on 37 sessions

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If x and y are positive integers, what is the value of y?

(1) y − x = 3

(2) x and y are prime numbers

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Director
Joined: 18 Jul 2018
Posts: 679
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: If x and y are positive integers, what is the value of y?  [#permalink]

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01 Oct 2018, 03:56
From statement 1:

y = x+3
Clearly insufficient.

From statement 2:

x and y are prime. Y could be any number.

Combining both

If x = 2. y= 5.
Sufficient.

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Re: If x and y are positive integers, what is the value of y?  [#permalink]

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01 Oct 2018, 09:41
Top Contributor
Bunuel wrote:
If x and y are positive integers, what is the value of y?

(1) y − x = 3
(2) x and y are prime numbers

Target question: What is the value of y?

Statement 1: y − x = 3
Clearly NOT SUFFICIENT

Statement 2: x and y are prime numbers
Clearly NOT SUFFICIENT

Statements 1 and 2 combined
The GMAT loves to test us on the fact that, although there are infinitely many prime numbers, ONLY ONE of those primes is EVEN
That is, 2 is the only EVEN prime number. All other primes are ODD.

Statement 2 tells us that x and y are prime.
And statement 1 tells us that y − x = 3
Hmmm, y - x = 3, which is odd.
This means that one value is EVEN, and the other value is ODD (since this is the only way to get an odd difference)

If one number is EVEN, then that number must be 2.
So, if y - x = 3, it must be the case that y = 5 and x = 2
So, the answer to the target question is y = 5
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent
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Re: If x and y are positive integers, what is the value of y?   [#permalink] 01 Oct 2018, 09:41
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