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If x and y are positive integers, what is

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jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
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Posted:
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If x and y are positive integers, what is

Post Tue Aug 01, 2017 10:08 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If x and y are positive integers, what is the value of √x + √y?
    (1) x + y = 15
    (2) √(xy) = 6

    Official Guide question
    Answer: C

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    Post Tue Aug 01, 2017 10:32 am
    jjjinapinch wrote:
    If x and y are positive integers, what is the value of √x + √y?
    (1) x + y = 15
    (2) √(xy) = 6

    Official Guide question
    Answer: C
    Target question: What is the value of √x + √y?

    Statement 1: x + y = 15
    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 = 14 and y = 1, in which case √x + √y = √14 + √1 = √14 + 1
    Case b: x = 9 and y = 6, in which case √x + √y = √9 + √6 = 3 + √6
    Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

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

    Statement 2: √(xy) = 6
    In other words xy = 36
    This statement doesn't FEEL sufficient either, so I'll TEST some values.
    There are several values of x and y that satisfy statement 2. Here are two:
    Case a: x = 1 and y = 36, in which case √x + √y = √1 + √36 = 1 + 6 = 7
    Case b: x = 4 and y = 9, in which case √x + √y = √4 + √9 = 2 + 3 = 5
    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 + y = 15
    Statement 2 tells us that √(xy) = 6
    Recognize that (√x + √y)² = x + 2√(xy) + y
    Rearrange to get: (√x + √y)² = 15 + 2(6)
    Evaluate: (√x + √y)² = 27
    So, √x + √y = √27
    Since we can answer the target question with certainty, the combined statements are SUFFICIENT

    Answer: C

    Cheers,
    Brent

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    Post Wed Aug 09, 2017 11:10 am
    jjjinapinch wrote:
    If x and y are positive integers, what is the value of √x + √y?
    (1) x + y = 15
    (2) √(xy) = 6

    Official Guide question
    Answer: C
    We need to determine the value of √x + √y.

    Statement One Alone:

    x + y = 15

    If x = 1 and y = 14, then √x + √y = 1 + √14. However, if x = 4 and y = 11, then √x + √y = 2 + √11. We see that we don’t have enough information to determine a unique value of √x + √y.

    Statement one alone is not sufficient to answer the question.

    Statement Two Alone:

    √(xy) = 6

    If x = 6 and y = 6, then √x + √y = 2√6. However, if x = 4 and y = 9, then √x + √y = 5. We see that we don’t have enough information to determine a unique value of √x + √y.

    Statement two alone is not sufficient to answer the question.

    Statements One and Two Together:

    Notice that (√x + √y)^2 = x + y + 2√(xy). From the two statements, we are given that x + y = 15 and √(xy) = 6, and thus (√x + √y)^2 = 15 + 2(6) = 27. Now, if we take the square root of both sides of the equation (√x + √y)^2 = 27, we have √x + √y = √27 = 3√3.

    Answer: C

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