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OG QR 2nd Ed. DS #124

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tofubeans Just gettin' started! Default Avatar
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OG QR 2nd Ed. DS #124 Post Mon Apr 30, 2012 12:58 pm
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  • Lap #[LAPCOUNT] ([LAPTIME])
    124) If rs does not = 0, is 1/r + 1/s = 4?

    1) r + s = 4rs

    2) r = s

    Sorry this may be a silly question or maybe my brain is tired but...

    I'm not sure I understand why A is correct. I understand that the equation in (1) will come out to the be the same equation in the question but isn't that just restating the equation? I'm confused.

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    aneesh.kg GMAT Destroyer!
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    Post Mon Apr 30, 2012 1:11 pm
    You're probably just mentally exhausted and might figure out your mistake if you solve it again after a break. Let me try to help you to save your time.

    The question is whether
    1/r + 1/s = 4 or not.

    Statement (1), as you said, upon manipulation says that
    1/r + 1/s = 4.
    So, is 1/r + 1/s equal to 4 as asked in the question?
    YES!

    So, statement (1) is sufficient.

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    Brent@GMATPrepNow GMAT Instructor
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    Post Mon Apr 30, 2012 3:48 pm
    tofubeans wrote:
    124) If rs does not = 0, is 1/r + 1/s = 4?

    1) r + s = 4rs
    2) r = s

    Target question: Is 1/r + 1/s = 4?

    This one is a great candidate for rephrasing the target question
    Let's add 1/r + 1/s to create one rational expression.
    Find common denominator: s/rs + r/rs
    Add numerators: (s+r)/rs
    So, 1/r + 1/s = (s+r)/rs

    So, rather than ask "Does 1/r + 1/s = 4?" we can ask "Does (s+r)/rs = 4?"

    Even better, we can cross multiply the equation to get: "Does s+r = 4sr?"

    Statement 1: r + s = 4rs
    This is exactly what one of our rephrased target questions asks.
    So, statement 1 is SUFFICIENT

    Statement 2: r = s
    Knowing that r=s does not help us determine whether s+r = 4sr
    So, statement 2 is NOT SUFFICIENT

    Answer: A

    Cheers,
    Brent

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    mido362 Just gettin' started! Default Avatar
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    Post Tue May 01, 2012 10:55 pm
    Hi Guys,
    Please correct me if I am wrong.
    I agree regarding statement 1

    Regarding Statement 2:
    r=s
    1/r +1/s=4
    1/r + 1/r=4
    2/r=4
    r=1/2
    By substituting in the original equation 1/r+1/s=4 so (1/ 1/2) + (1/ 1/2)=4
    Sufficient

    Is that right?

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    Anurag@Gurome GMAT Instructor
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    Post Tue May 01, 2012 11:47 pm
    tofubeans wrote:
    124) If rs does not = 0, is 1/r + 1/s = 4?

    1) r + s = 4rs

    2) r = s

    Sorry this may be a silly question or maybe my brain is tired but...

    I'm not sure I understand why A is correct. I understand that the equation in (1) will come out to the be the same equation in the question but isn't that just restating the equation? I'm confused.
    The question is asking whether (1/r + 1/s) = 4 or not.
    If you replace r = s from the statement 2 into the equation, obviously you'll get a value of r which satisfies the equation. The solutions are in fact r = s = 1/2. But the question is not really asking you to do this! For this particular set of values of r and s the relation satisfies. But not for all r and s that satisfies the relation r = s. For instance, r = s = 1 does not satisfies the equation. Thus statement 2 is not sufficient to answer the question.

    But for statement 1, (r + s) = 4rs => (r + s)/rs = 4 => (1/r + 1/s) = 4.
    Therefore for any set of values of r and s that satisfies the condition given in statement 1, satisfies the equation given in question stem. Hence statement 1 is sufficient.

    The correct answer is A.

    Hope that clears your confusion.

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