Data Sufficiency

M7MBA wrote: ↑

Thu Jan 07, 2021 10:33 am

In a certain business, production index \(p\) is directly proportional to efficiency index \(e,\) which is in turn directly proportional to investment \(i.\) What is \(p\) if \(i = 70?\)

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

Answer: B

Source: Official Guide

Solution:

We need to determine the value of p when i = 70. We are told that p is directly proportional to e, which is in turn directly proportional to i. Recall that if x is directly proportional to y, then x = ky for some positive constant k.

Therefore, we have p = ke and e = ji for some positive constants k and j. In other words, p = kji, and if we can determine the values of k and j, or the value of kj, then we can determine the value of p.

Statement One Alone:

Since e = ji, we have:

0.5 = j(60)

j = 0.5/60 = 1/120

However, since we still don’t know the value of k, we can’t determine the value of p. Statement one alone is not sufficient.

Statement Two Alone:

Since p = kji, we have:

2.0 = kj(50)

kj = 2/50 = 1/25

Since kj = 1/25 and p = kji, then, if j = 70, we see that p = 1/25 * 70 = 14/5 = 2.8. Statement two alone is sufficient.


Answer: B