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index ratio relationship

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index ratio relationship

by ithamarsorek » Wed Mar 02, 2011 6:13 pm
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.
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by 4GMAT_Mumbai » Wed Mar 02, 2011 7:56 pm
Hi,

Interesting Q ... Thanks !

Question stem says:

p = <a constant k> * e
e = <a constant m> * i

So, p = k * m * i = <a new constant n> * i

Statement 1:

Gives relationship between e and i. Helps us find m. Great. But, does not take us anywhere as far as either k or p is concerned. Hence, insuff.

Statement 2:

p = n * i

So, 2 = n * 50. n = (2/50)

Going back to the question,

i = 70

p = (2/50) * 70. I will be able to calculate. Hence, suff.

I think the answer is B ... OA please ... Thanks !
Naveenan Ramachandran
4GMAT, Dadar(W) & Ghatkopar(W), Mumbai
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by Anurag@Gurome » Wed Mar 02, 2011 8:33 pm
ithamarsorek wrote: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.


Solution:
Let p = ke where k is a constant.
Let e = ci where c is a constant.
So, p = kci.
If i = 70, e = 70c and p = 70kc.
We need to calculate this p.
Consider first (1) alone.
0.5 = c*60.
Or c = 1/120.
But we need to know k to get the value of p.
Or (1) alone is not sufficient.
Next, consider (2) alone.
It means 2 = kc * 50.
Or kc = 2/50.
Or 70*kc = 14/5.
Or, when i = 70, p is 14/5.
So, (2) alone is sufficient.

The correct answer is (B).
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
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