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Qn #80 in OG12

This topic has 1 expert reply and 3 member replies
papgust Community Manager
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Qn #80 in OG12

Post Fri Feb 26, 2010 8:03 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If r > 0 and s > 0, is r/s < s/r?
    (1) r / 3s = 1/4
    (2) s = r + 4

    OA: D

    I know that statement 1 is sufficient, but i thought that II is insufficient. As the qn does not mention whether r and s are integers, i plugged in both fractions and integers and was convinced that i get 2 different answers.

    If r=2, then s = 4+2 = 6.
    2/6 < 6/2. YES

    If r=1/2, then s = 1/4.
    r/s = 4/2. s/r = 2/4. So, r/s > s/r. NO

    Can someone explain where i'm wrong?

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    arzanr Senior | Next Rank: 100 Posts Default Avatar
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    Post Fri Feb 26, 2010 8:16 pm
    Quote:
    If r=1/2, then s = 1/4.
    With s = r + 4, If r = 1/2 then S would be equal to 4 1/2 (1/2 + 4)

    Btw, for #2 you don't need to try any numbers, when s is greater than r then the fraction with s as the numerator would always be greater than the fraction with s as the denominator.

    kstv Legendary Member Default Avatar
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    Post Fri Feb 26, 2010 9:53 pm
    If r > 0 and s > 0, is r/s < s/r?
    (1) r / 3s = 1/4
    (2) s = r + 4


    (1) r/s = 3/4 so when r= 3 s = 4 , s/r =4/3

    or when r= 1/4 s= 1/3 s/r = 3/4 not suff

    (2) s= r + 4 or s/r = 1 + 4/r plug the same values r= 3 s = 4 , s/r =4/3
    s/r = 4/3 = 1+ 4/3 not possible

    s/r = 3/4 = 1+4*4 when r= 1/4 s= 1/3 s/r = 3/4 not possible

    so D.

    I read somewhere that (1) and (2) should be compatible if E is the option. Leads me think that we should use the same values in (1) and (2).

    papgust Community Manager
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    Post Fri Feb 26, 2010 10:01 pm
    arzanr wrote:
    Quote:
    If r=1/2, then s = 1/4.
    With s = r + 4, If r = 1/2 then S would be equal to 4 1/2 (1/2 + 4)

    Btw, for #2 you don't need to try any numbers, when s is greater than r then the fraction with s as the numerator would always be greater than the fraction with s as the denominator.
    True arzanr. I completely agree!

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    Testluv GMAT Instructor Default Avatar
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    Post Sun Feb 28, 2010 11:00 am
    Simplify the question stem.

    Because we know that both r and s are positive, we don't have to worry about the inequality sign flipping, and we can rearrange the inequality being asked about:

    Is r/s < s/r?

    Is r^2 < s^2?

    Is r < s?

    If we rephrase the question this way, then it is clear that both statements are sufficient by themselves.

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