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If x = 2t and y = t/3, what is the value

This topic has 2 expert replies and 0 member replies
jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
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24 Jul 2017
Posted:
83 messages

If x = 2t and y = t/3, what is the value

Post Wed Aug 02, 2017 10:44 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If x = 2t and y = t/3, what is the value of x^2 - y^2?
    (1) t^2 - 3 = 6.
    (2) t^3 = -27

    Official Guide question
    Answer: D

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    Post Wed Aug 02, 2017 11:31 am
    jjjinapinch wrote:
    If x = 2t and y = t/3, what is the value of x^2 - y^2?
    (1) t^2 - 3 = 6.
    (2) t^3 = -27

    Official Guide question
    Answer: D
    Target question: What is the value of x² - y²?

    Given: x = 2t and y = t/3

    Statement 1: t² - 3 = 6
    Add 3 to both sides to get: t² = 9
    So, EITHER t = 3 OR t = -3
    Let's test each case:
    Case a: t = 3. Since x = 2t and y = t/3, this means x = 6 and y = 1. So, x² - y² = 6² - 1² = 36 - 1 = 35
    Case b: t = -3. Since x = 2t and y = t/3, this means x = -6 and y = -1. So, x² - y² = (-6)² - (-1)² = 36 - 1 = 35
    So, x² - y² MUST equal 35
    Since we can answer the target question with certainty, statement 1 is SUFFICIENT

    Statement 2: t³ = -27
    This means t = 3
    Since x = 2t and y = t/3, this means x = 6 and y = 1. so, x² - y² = 6² - 1² = 36 - 1 = 35
    Since we can answer the target question with certainty, statement 2 is SUFFICIENT

    Answer: D

    Cheers,
    Brent

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    Post Fri Aug 04, 2017 11:22 am
    Hi jjjinapinch,

    Certain DS questions are really just a 'test' of your 'thoroughness', so it's important to do all of the necessary work (on the pad; NOT 'in your head') to prove what the correct answer is. Without having that 'proof', you might inadvertently choose the wrong answer (and miss out on some easy points on Test Day).

    We're told that X = 2T and Y = T/3. We're asked for the value of X^2 - Y^2

    1) T^2 - 3 = 6.

    With the equation in Fact 1, we can determine that T has 2 values...
    T^2 - 3 = 6
    T^2 = 9
    T = +3 or -3
    Many Test Takers would assume that these two values would lead to two different answers to the question (and assume that Fact 1 was insufficient).... but where is your PROOF that it's insufficient...?

    IF....
    T = 3, X=6, Y=1, then the answer to the question is 6^2 - 1^2 = 35
    IF....
    T = -3, X= -6, Y= -1, then the answer to the question is (-6)^2 - (-1)^2 = 35
    It turns out that both values of T lead to the SAME answer - and the answer to the question is ALWAYS 35.
    Fact 1 is SUFFICIENT

    2) t^3 = -27

    The equation in Fact 2 has just one solution: -3. With the work that we did in Fact 1, we know that there is only one answer to the question (35).
    Fact 2 is SUFFICIENT

    Final Answer: D

    GMAT assassins aren't born, they're made,
    Rich

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