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If x are y are positive integers, what is the value. . .

This topic has 1 expert reply and 0 member replies

If x are y are positive integers, what is the value. . .

Post Thu Sep 14, 2017 2:09 pm
If x are y are positive integers, what is the value of x+y?

(1) x and y are consecutive prime numbers
(2) x-y=1

The OA is C.

Any of the options alone is sufficient? Can any expert help me?

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Top Reply
Post Thu Sep 14, 2017 2:33 pm
Vincen wrote:
If x are y are positive integers, what is the value of x+y?

(1) x and y are consecutive prime numbers
(2) x - y = 1
Target question: What is the value of x+y?

Given: x are y are positive integers

Statement 1: x and y are consecutive prime numbers
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 2 and y = 3 (two consecutive primes), in which case x + y = 2 + 3 = 5
Case b: x = 19 and y = 23 (two consecutive primes), in which case x + y = 19 + 23 = 42
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of testing values when a statement doesn't feel sufficient, read my article: http://www.gmatprepnow.com/articles/data-sufficiency-when-plug-values

Statement 2: x - y = 1
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 3 and y = 2, in which case x + y = 3 + 2 = 5
Case b: x = 5 and y = 4, in which case x + y = 5 + 4 = 9
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x and y are consecutive primes
Statement 2 tells us that x and y differ by 1
If x and y differ by 1, then one number is ODD and the other is EVEN
Since there is only one EVEN prime number (2), then it must be the case that y = 2 and x = 3, in which case x + y = 3 + 2 = 5
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

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Brent Hanneson – Founder of GMATPrepNow.com
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Thanked by: Vincen
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