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If 2^(x + y) = 4^8, then

This topic has 1 expert reply and 0 member replies
jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
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Posted:
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If 2^(x + y) = 4^8, then

Post Tue Aug 08, 2017 7:52 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If 2^(x + y) = 4^8, then what is the value of y?
    (1) x^2 = 81
    (2) x - y = 2

    Official Guide question
    Answer: B

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    Post Tue Aug 08, 2017 8:07 am
    jjjinapinch wrote:
    If 2^(x + y) = 4^8, then what is the value of y?
    (1) x² = 81
    (2) x - y = 2

    Official Guide question
    Answer: B
    Target question: What is the value of y?

    Given: 2^(x + y) = 4^8
    Rewrite right side with base of 2.
    So, first replace 4 with 2² to get: 2^(x + y) = (2²)^8
    Simplify right side: 2^(x + y) = 2^16
    We can conclude that x + y = 16

    Statement 1: x² = 81
    This tells us that EITHER x = 9 OR x = -9
    Let's test each case.
    Case a: If x = 9, then we can take x + y = 16 and replace x with 9 to get: 9 + y = 16. When we solve this equation for y, we get y = 7
    Case b: If x = -9, then we can take x + y = 16 and replace x with -9 to get: -9 + y = 16. When we solve this equation for y, we get y = 25
    Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

    Statement 2: x - y = 2
    Since we also know that x + y = 16 , we now have a system of 2 variables with equations, which we COULD solve for y (but we won't do because we don't want to waste valuable time).
    Since we COULD answer the target question with certainty, statement 2 is SUFFICIENT

    Aside: For "fun" let's solve the following system:
    x + y = 16
    x - y = 2

    If we SUBTRACT the bottom equation from the top equation, we get: 2y = 14, which means y = 7
    Voila!

    Answer: B

    Cheers,
    Brent

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