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Proportion

This topic has 3 expert replies and 0 member replies
marat_isr Newbie | Next Rank: 10 Posts Default Avatar
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Posted:
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Proportion

Post Thu Mar 02, 2017 10:18 am
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 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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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
_________________
Manhattan Review GMAT Prep

Locations: New York | Paris | Shanghai | Munich | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

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