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the value of p + q + r?

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sanju09 GMAT Instructor
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the value of p + q + r? Post Thu Feb 16, 2012 3:53 am
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  • Lap #[LAPCOUNT] ([LAPTIME])
    If p:q = (3/7):2 and q:r = 7:(11/2), what is the value of p + q + r?
    I. The value of q is equal to the sum of p and r.
    II. p + 3 q - 2 r = 23.



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    Post Thu Feb 16, 2012 10:24 am
    IMO: D.

    p:q:r::3/14:1:11:14

    Using a ratio and a linear equation you will be able to solve the equation, assume all variables in any one variable.

    What is the OA?

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    neelgandham Community Manager
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    Post Thu Feb 16, 2012 10:24 am
    If p:q = (3/7):2 and q:r = 7:(11/2), what is the value of p + q + r?
    The question can be rephrased to if p:q:r = 3:14:11 then what is the value of p + q + r?
    Quote:
    I.The value of q is equal to the sum of p and r.
    Since p:q:r = 3:14:11, we can represent p,q,r in terms of x(x = a positive integer)
    p = 3x
    q = 14x
    r = 11x
    q = p+q => 14x = 14x. Since, we still are not aware of the value of x, Statement 1 is insufficient to answer the question
    Quote:
    II.p + 3 q - 2 r = 23.
    p + 3 q - 2 r = 3x + (3*14x) - (2*11x) = 23x = 23. Implies x = 1 and p+q+r=3+14+11=28. Statement 1 is sufficient to answer the question

    IMO B

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    Post Fri Feb 17, 2012 1:44 am
    Well very intelligent question but not difficult...

    From simultaneous equations perspective, the answer comes down to be C, as you need 2 equations...

    But B alone can give the answer...

    Statement 1 alone is absolutely insufficient to provide with an answer...

    Statement 2:

    (p:q:r) = (3:14:11)

    let x be the common element between then,

    p = 3x ; q = 14x ; r = 11x

    now putting the values in the second equation, we get

    23x = 23 hence x = 1

    when x =1, the total of (p+q+r) = 28 which is the right answer...


    THa OA is B.

    Please give the OA asap...

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    Post Fri Feb 17, 2012 1:47 am
    Actually statement 1 creates situation like 14x = 14x which is not a valid equation by itself...

    Hence statement 1 is insufficient...

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    Post Sat Feb 18, 2012 6:56 am
    sanju09 wrote:
    If p:q = (3/7):2 and q:r = 7:(11/2), what is the value of p + q + r?
    I. The value of q is equal to the sum of p and r.
    II. p + 3 q - 2 r = 23.

    made up by Sanjeev K Saxena for Avenues Abroad
    I received a PM asking me to comment.

    To combine ratios with a common element, the common element must be represented by the same value in each ratio.

    p:q = (3/7) : 2 = 3:14.
    q:r = 7 : (11/2) = 14:11.
    Combining the ratios:
    p:q:r = 3:14:11.

    Statement 1: q = p+r.
    No new information here.
    In p:q:r = 3:14:11, p+r = 3+11 = 14, which is the value of q.

    Thus, given ANY combination that satisfies p:q:r = 3:14:11, q=p+r.
    If the values in the ratio are doubled so that p=6, q=28, and r=22, q=p+r.
    If the values in the ratio are tripled so that p=9, q=42 and r=33, q=p+r.

    Since an infinite number of combinations are possible, no way to determine p+q+r.
    INSUFFICIENT.

    Statement 2: p + 3q - 2r = 23.
    This equation is satisfied by the values in the ratio.
    If p=3, q=14, and r=11, then p + 3q - 2r3 + 3(14) - 2(11) = 23.
    Thus, this is the ONLY combination that will work here.
    Any MULTIPLE of 3:11:14 will yield a MULTIPLE of 23.
    Thus, p+q+r = 3+14+11 = 28.
    SUFFICIENT.

    The correct answer is B.

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