In a Certain Business, Production Index p is directly Proportional GMAT Data Sufficiency

Question: 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

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer:

Solution with Explanation:
Approach Solution (1):

a is directly proportional to b means that as the absolute value of b gets bigger, the absolute value of a gets bigger too, so there is some non-constant x such that a = xb.
So if a is directly proportional to b, then vice versa is also correct.
a is inversely proportional to b means that as the absolute value of b gets bigger, the absolute value of a gets smaller, so there is some non-zero constant y such that a = yb.
So if a is inversely proportional to b, then vice versa is also correct.

Now, look at the question:
Given: p = ex and e = iy (for some constants x and y), so p = ixy

Question: p = 70xy =? So basically we should find the value of xy.

(1) e = 0.5 whenever i = 60 ---> as e = iy then 0.5 = 60y ---> we can find the value of y, but still not sufficient.
(2) p = 2.0 whenever i = 50 ---> as p = ixy then 2 = 50xy ---> we can find the value of xy, hence sufficient.

Correct Option: B

Approach Solution (2):

production index p is directly proportional to the efficiency index e, implies p = ke (k is the constant of proportionality)
e is in turn directly proportional to investment i, implies e = mi (m is the constant of proportionality. Note here that I haven’t taken the constant of proportionality as k here since the constant above and thus constant could be different).
Then, p = kmi (km is the constant of proportionality here. It doesn’t matter that we depict it using two variables. It is still just a number.

e.g. if p = 2e and e = 3i
p = 6i will be the relation. 6 being the constant of proportionality.
So if you have i and need p, you either need this constant directly (as you can find from statement 2) or you need both k and m (statement 1 only gives you m).

Correct Option: B

“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??”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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