Last Updated on May 10, 2023
GMAT OFFICIAL GUIDE DS
Solution:
We are given that production index p is directly proportional to efficiency index e, which is in turn directly proportional to investment index i. We see that we are being tested on direct variation here. Before jumping into the problem we can discuss direct variation in general.
Given two variables, x and y, if y = kx for some positive constant k, then x and y are said to vary directly with each other, and k is called the constant of variation. In a direct variation, if x increases, y also increases, and if x decreases, y decreases.
We can use this same thought process with the given problem.
Since production index p is directly proportional to efficiency index e, we can create the following equation in which k is a constant.
p = (k)(e)
We are also given that efficiency index e is directly proportional to investment index i. Using this information we can create another equation in which j is a constant.
e = (j)(i)
Thus, p = (k)(j)(i)
We need to determine the value of p when i = 70. Thus, we need to determine the value of 70kj.
Statement One Alone:
e = 0.5 whenever i = 60
Using the information in statement one, we can determine a value for j.
e = (j)(i)
0.5 = j(60)
0.5/60 = j
However, in order to determine 70kj we also need the value of k. Statement one alone is not enough information to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
p = 2.0 whenever i = 50
Using the information in statement two we have enough information to determine the value of 70kj.
p = (k)(j)(i)
2 = (k)(j)(50)
2/50 = kj
We have a value for kj, but we need to evaluate 70kj; therefore, we multiply both sides of the equation by 70.
140/50 = 70kj
Thus, statement two provides enough information to determine the value of 70kj.
Answer: B
