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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
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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?

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    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

    _________________
    Brent Hanneson – Founder of GMATPrepNow.com
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