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If n is an integer, is (0.1)^n greater than

This topic has 2 expert replies and 0 member replies
jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
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Posted:
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If n is an integer, is (0.1)^n greater than

Post Wed Aug 02, 2017 11:04 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If n is an integer, is (0.1)^n greater than (10)^n?
    (1) n > -10
    (2) n < 10

    Official Guide question
    Answer: E

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    Post Wed Aug 02, 2017 11:57 am
    When you don't have a calculator, it's often easier to convert decimals into fractions, particularly when dealing with exponents:
    Is (1/10)^n greater than (10)^n?

    Ask yourself: when would a fraction raised to a power be greater than an integer raised to the same power? If the exponent were negative! A negative exponent is equal to the reciprocal of the positive exponent:
    (1/10)^(-1) = 10
    10^(-1) = 1/10

    If n > 0, then (1/10)^n < 10^n
    If n = 0, then (1/10)^n = 10^n
    If n < 0, then (1/10)^n > 10^n

    Target question: is n < 0 ?

    (1) n > -10
    n could be negative, if n = -9, or it could be any integer greater than or equal to 0. Insufficient.

    (2) n < 10
    Again, n could be negative (this range includes all negatives), or any positive integer less than 10. Insufficient.

    (1) & (2) together:
    -10 < n < 10
    This range includes both negatives and non-negatives, so we do not get a definitive answer to our question. Insufficient.

    The answer is E.

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    Post Wed Aug 02, 2017 12:01 pm
    jjjinapinch wrote:
    If n is an integer, is (0.1)^n greater than (10)^n?
    (1) n > -10
    (2) n < 10

    Official Guide question
    Answer: E
    Target question: Is (0.1)^n > (10)^n?
    This is a good candidate for rephrasing the target question.
    Since (0.1)^n is always POSITIVE, we can safely divide both sides of the inequality by (0.1)^n to get: 1 > [(10)^n]/[(0.1)^n]
    There's a nice rule that says (a^n)/(b^n) = (a/b)^n
    When we apply this rule to the right side of the inequality, we get: 1 > (10/0.1)^n
    Simplify to get: Is 1 > 100^n?
    Notice that, when n = 0, then 100^n = 100^0 = 1
    So, when n > 0, then 100^n > 1, and when n < 0, then 100^n < 1
    So, we can REPHRASE the target question as....
    REPHRASED target question: Is n < 0?

    Aside: Here’s a video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100

    Statement 1: n > -10
    There are several values of n that satisfy statement 1. Here are two:
    Case a: n = -9, in which case n < 0
    Case b: n = 2, in which case n > 0
    Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

    Statement 2: n < 10
    There are several values of n that satisfy statement 1. Here are two:
    Case a: n = -9, in which case n < 0
    Case b: n = 2, in which case n > 0
    Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

    Statements 1 and 2 combined
    IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
    Since we cannot answer the REPHRASED target question with certainty, the combined statements are NOT SUFFICIENT

    Answer: E

    Cheers,
    Brent

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