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Proportion

This topic has 3 expert replies and 0 member replies
marat_isr Newbie | Next Rank: 10 Posts Default Avatar
Joined
06 Mar 2014
Posted:
3 messages

Proportion

Post Thu Mar 02, 2017 10:18 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    In a certain business, production index p is directly proportional to efficiency index e, which in turn directly proportional to investment index i. What is p if i=70?

    1) e=0.5 whenever i=60
    2) p=2.0 whenever i=50

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    Post Thu Mar 02, 2017 2:18 pm
    marat_isr wrote:
    In a certain business, production index p is directly proportional to efficiency index e, which in turn directly proportional to investment index i. What is p if i=70?

    1) e=0.5 whenever i=60
    2) p=2.0 whenever i=50
    When two variables are proportional, we can depict that relationship by multiplying one of the variables by a constant. If x is proportional to y, for example, we can use a constant, 'c,' and write x = c*y.

    We're told that p is proportional to e. So let's say p = c*e. (the constant here is c.) We also know that e is proportional to i, so let's say e = d * i. (the constant here is d. Now we can substitute d * i in place of e in the first equation to get p = c * d * i. We want to know p when i = 70, we want p in the following equation p = c*d*70.

    To summarize, we have the following

    e = d*i
    p = c * d * i

    We want p when p = c*d*70.

    (Note that if we can find c*d, we can find p, so you could rephrase this question as "what is the value of c*d?")

    Statement 1: Not so helpful. If we go to the equation e = d * i, we can substitute to get .5 = d * 60. This allows do solve for d. But we have nothing about c. Not sufficient.

    Statement 2: Initially, we determined that p = c * d * i. Substituting '2' for 'p' and '50' for 'i,' we get 2 = c * d *50; or (1/25) = c*d. c*d is what we want. Remember that we were looking for p, when p = c*d*70. If c*d = 1/25, then p = (1/25)*70. Statement 2 yields a unique value for p when i = 70, so this statement alone is sufficient. The answer is B

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    Post Thu Mar 02, 2017 3:22 pm
    Quote:
    In a certain business, production index p is directly proportional to efficiency index e, which is in turn directly proportional to investment index i. What is p if i=70?


    1) e=0.5 whenever i=60
    2) p=2.0 whenever i=50
    Since all 3 values are directly proportional to one another, p is directly proportional to i.
    Thus:
    p₁/i₁ = p₂/i₂.

    Statement 1:

    No information about p.
    INSUFFICIENT.

    Statement 2:
    If we substitute p₁=2, i₁=50 and i₂=70 into p₁/i₁ = p₂/i₂, we get:
    2/50 = p₂/70.
    Since we can solve for p₂, we can determine the value of p if i=70.
    SUFFICIENT.

    The correct answer is B.

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    Post Thu Mar 02, 2017 8:40 pm
    marat_isr wrote:
    In a certain business, production index p is directly proportional to efficiency index e, which in turn directly proportional to investment index i. What is p if i=70?

    1) e=0.5 whenever i=60
    2) p=2.0 whenever i=50
    We know that p is proportional to e and e is proportional to i.

    Thus, p = ke and e = mi; where k and m are a constant

    From the two, we get = km*i; where km is a constant; we can replace it with a single number say r = km.

    Thus, p = ri.

    If we are able to get the value of the constant 'r', we can answer the question: What is p if i=70?

    Let us take each statement one by one.

    S1: e = 0.5 whenever i = 60

    We cannot get the value of the constant 'r' from the above information, thus statement 1 itself is not sufficient.

    S2: p=2.0 whenever i=50

    Since p = ri, r = p/i = 2/50 = 1/25. We get the unique value of 'r,' thus statement 2 is sufficient.

    To answer the question: p @ (i = 70) = (1/25)*70 = 14/5.

    The correct answer: B

    Hope this helps!

    Relevant book: Manhattan Review GMAT Data Sufficiency Guide

    -Jay
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