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Register now and save up to $200 Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code ## Proportion This topic has 3 expert replies and 0 member replies marat_isr Newbie | Next Rank: 10 Posts Joined 06 Mar 2014 Posted: 3 messages #### Proportion 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 Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums! ### GMAT/MBA Expert DavidG@VeritasPrep Legendary Member Joined 14 Jan 2015 Posted: 2301 messages Followed by: 115 members Thanked: 1074 times GMAT Score: 770 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 _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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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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Jay@ManhattanReview GMAT Instructor
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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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