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tricky 1 from Prep

This topic has 3 expert replies and 0 member replies
mukherjee.tanuj3@gmail.co Master | Next Rank: 500 Posts
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tricky 1 from Prep

Post Mon Apr 28, 2014 8:34 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    ttp://postimg.org/image/dattzf72l/" target="_blank">

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    Post Wed Apr 30, 2014 11:27 am
    There isn't an obvious way to rephrase this question. We can't cross-multiply because we don't know whether p is negative. (You could rephrase giving yourself a positive and negative case, but this can become confusing). The best thing to do it to try to PROVE INSUFFICIENCY when looking at the statements.

    Question: Is (1/p) > r/(r^2 + 2) ?

    1) p = r

    Test values to prove insufficiency:
    If p and r both equal 1: (1/1) > 1/(1^2 + 2) --> 1 > 1/3 yes.
    If p and r both equal -1: (1/-1) > -1/((-1)^2 + 2) --> -1 > -1/3 no.
    Insufficient.

    2) r > 0

    This tells us nothing about p. Insufficient.

    1 & 2) Together, if r > 0 then p > 0. We only need to test positive values:
    If p and r both equal 1: (1/1) > 1/(1^2 + 2) --> 1 > 1/3 yes.
    If p and r both equal 2: (1/2) > 2/(2^2 + 2) --> 1/2 > 2/6 yes.
    If p and r both equal 3: (1/3) > 3/(3^2 + 2) --> 1/3 > 3/11 yes.

    Any positive value we test would give us a "yes" result. The answer is C.

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    Post Thu May 01, 2014 3:11 am
    Quote:
    Is 1/p > r/(r^2 + 2) ?

    (1) p = r
    (2) r > 0
    Alternate approach:

    Statement 2 is clearly INSUFFICIENT.

    Statement 1: p=r
    Substituting p=r into the question stem, we get:
    1/r > r/(r² + 2)?

    (1/r) - r/(r² + 2) > 0?

    (r² + 2 - r²) / [r(r² + 2)] > 0?

    2 / [r(r² + 2)] > 0?

    1 / [r(r² + 2)] > 0?

    Case 1: r>0
    1 / [r(r² + 2)] > 0
    1/(positive*positive) > 0
    1/positive > 0.
    positive > 0.
    In this case, the answer is YES.

    Case 2: r<0
    1 / [r(r² + 2)] > 0
    1/(negative*positive) > 0
    1/negative > 0
    negative > 0.
    In this case, the answer is NO.
    INSUFFICIENT.

    Statements combined:
    Since only Case 1 is possible, the answer to the question stem is YES.
    SUFFICIENT.

    The correct answer is C.

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    sanju09 GMAT Instructor
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    Post Fri May 02, 2014 11:02 pm
    mukherjee.tanuj3@gmail.co wrote:
    ttp://postimg.org/image/dattzf72l/" target="_blank">
    (1) If p = r, let’s plug in p = r = 2, and ask if ½ > 2/6, we get a YES. Or if we plug in p = r = -2, and ask if -½ > -2/6, and we get a NO. Hence, insufficient!

    (2) It only tells about r, no info about p. Hence, insufficient!

    When taken together, since both p and r are equal and positive, even if we now try a fraction for p and r, like if we plug in p = r = ½, and ask if 1/(½) > (½) /(¼ + 2) or “Is 2 > 2/9”, we still get a YES. Hence Sufficient!

    Take C

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