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Algebra

This topic has 1 expert reply and 0 member replies

Algebra

Post Sat Sep 16, 2017 11:20 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    What is the value of x^2 - y^2 ?
    (1) x + y = 2y - 1
    (2) 5x - 5y = 1/(2x + 2y)

    a. statement 1 and 2 are sufficient
    b. statement 1 is not sufficient while statement 2 is sufficient
    c. Both are not sufficient
    d. statement 1 is sufficient while statement 2 is not sufficient
    e. All of the above

    OA is b.
    what is the best approach to use to determine that the two statement are sufficient and thus, agree with option A

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Sun Sep 17, 2017 7:28 am
    Roland2rule wrote:
    What is the value of x² - y² ?
    (1) x + y = 2y - 1
    (2) 5x - 5y = 1/(2x + 2y)

    Target question: What is the value of x² - y² ?

    Statement 1: x + y = 2y - 1
    Subtract 2y from both sides to get: x - y = -1
    There are several values of x and y that satisfy statement 1. Here are two:
    Case a: x = 0 and y = 1, in which case x² - y² = 0² - 1² = 0 - 1 = -1
    Case b: x = 1 and y = 2, in which case x² - y² = 1² - 2² = 1 - 4 = -3
    Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

    Statement 2: 5x - 5y = 1/(2x + 2y)
    Multiply both sides of the equation by (2x + 2y) to get: (2x + 2y)(5x - 5y) = 1
    ASIDE: If you recognize that x² - y² = (x+y)(x-y), then you'll see that we're well on our way to answering the target question
    Rewrite as: (2)(x + y)(5)(x - y) = 1
    Or we can write: (2)(5)(x + y)(x - y) = 1
    Simplify: (10)(x² - y²) = 1
    Divide both sides by 10 to get: x² - y² = 1/10
    Since we can answer the target question with certainty, statement 2 is SUFFICIENT

    Answer: B

    Cheers,
    Brent

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