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Is r greater than zero?

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islands80 Just gettin' started! Default Avatar
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Is r greater than zero? Post Tue Apr 24, 2012 10:40 pm
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  • Lap #[LAPCOUNT] ([LAPTIME])
    If t ≠ 0, is r greater that zero?

    (1) rt = 12
    (2) r + t = 7


    I apologize if this has been posted before. I couldn't find this problem on the forum.

    OA C

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    Post Tue Apr 24, 2012 10:46 pm
    islands80 wrote:
    If t ≠ 0, is r greater that zero?

    (1) rt = 12
    (2) r + t = 7


    I apologize if this has been posted before. I couldn't find this problem on the forum.

    OA C
    If t ≠ 0, is r > 0?

    (1) rt = 12
    If r = 3, t = 4, then rt = 3 * 4 = 12. Here r > 0.
    If r = -3, t = -4, then rt = -3 * -4 = 12. Here r < 0.
    No definite answer; NOT sufficient.

    (2) r + t = 7
    If r = 3, t = 4, then r+ t = 3 + 4 = 7. Here r > 0.
    If r = -5, t = 12, then r + t = -5 + 12 = 7. Here r < 0.
    No definite answer; NOT sufficient.

    Combining (1) and (2), rt = 12 and r + t = 7
    Substitute the value of t from r + t = 7 implies t = 7 - r, in rt = 12, we get
    r(7 - r) = 12
    7r - r² = 12
    r² - 7r + 12 = 0
    r² - 4r - 3r + 12 = 0
    r(r - 4) - 3(r - 4) = 0
    (r - 3)(r - 4) = 0
    r = 3, 4, both values are > 0; SUFFICIENT.

    The correct answer is C.

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    shantanu86 Rising GMAT Star Default Avatar
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    Post Tue Apr 24, 2012 10:55 pm
    islands80 wrote:
    If t ≠ 0, is r greater that zero?

    (1) rt = 12
    (2) r + t = 7


    I apologize if this has been posted before. I couldn't find this problem on the forum.

    OA C
    Hi islands80,

    Here we need to establish that r is +ve or not?.
    Obviously any one of the info given is not sufficient alone. Therefore, answer could be [C] (both sufficient together) or [E] (both not sufficient).

    Lets check for [C]..
    rt = 12
    => t = 12/r

    substituting this in r + t =7
    => r + 12/r = 7
    => r^2 -7r +12 =0

    r = (7 +/- (49 -48)^(1/2))/2
    r = (7 +/- 1)/2
    r = 4 or 3.. since both are +ve [C] is the correct answer.

    Hope it helps!!

    Regards,
    Shantanu

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    Shadow88 Just gettin' started!
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    Post Fri Oct 26, 2012 12:27 pm
    Guys/Girls what do you say about my reasoning to the right answer.
    When putting (1) and (2) together, rt=12 and r+t=12.
    We know that for rt to equal 12, both r and t need to have the same sign, but since r+t=12, both t and r must be positive, otherwise we would have r+t=-12 if r and t were negative. And if r or t were negative in r+t=12, then rt would equal -12, so r and t must be positive. r>0, am i thinking wrong here?

    Just trying to get to a conclusion that take less time. Please correct me if i am wrong.

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    Brent@GMATPrepNow GMAT Instructor
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    Post Sat Oct 27, 2012 6:37 am
    Shadow88 wrote:
    Guys/Girls what do you say about my reasoning to the right answer.
    When putting (1) and (2) together, rt=12 and r+t=12.
    We know that for rt to equal 12, both r and t need to have the same sign, but since r+t=12, both t and r must be positive, otherwise we would have r+t=-12 if r and t were negative. And if r or t were negative in r+t=12, then rt would equal -12, so r and t must be positive. r>0, am i thinking wrong here?

    Just trying to get to a conclusion that take less time. Please correct me if i am wrong.
    Excellent logic, Shadow88

    Since we aren't trying to find the exact value of r here, the method you used to conclude that r must be positive is nice and quick.

    Cheers,
    Brent

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    Shadow88 Just gettin' started!
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    Post Mon Oct 29, 2012 8:02 am
    Thank you Brent and for the quick response.

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