Data Sufficiency

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

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

When two variables are proportional, we can depict that relationship by multiplying one of the variables by a constant. If x is proportional to y, for example, we can use a constant, 'c,' and write x = c*y.

We're told that p is proportional to e. So let's say p = c*e. (the constant here is c.) We also know that e is proportional to i, so let's say e = d * i. (the constant here is d. Now we can substitute d * i in place of e in the first equation to get p = c * d * i. We want to know p when i = 70, we want p in the following equation p = c*d*70.

To summarize, we have the following

e = d*i
p = c * d * i

We want p when p = c*d*70.

(Note that if we can find c*d, we can find p, so you could rephrase this question as "what is the value of c*d?")

Statement 1: Not so helpful. If we go to the equation e = d * i, we can substitute to get .5 = d * 60. This allows do solve for d. But we have nothing about c. Not sufficient.

Statement 2: Initially, we determined that p = c * d * i. Substituting '2' for 'p' and '50' for 'i,' we get 2 = c * d *50; or (1/25) = c*d. c*d is what we want. Remember that we were looking for p, when p = c*d*70. If c*d = 1/25, then p = (1/25)*70. Statement 2 yields a unique value for p when i = 70, so this statement alone is sufficient. The answer is B

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:
p�/i� = p₂/i₂.

Statement 1:
No information about p.
INSUFFICIENT.

Statement 2:
If we substitute p�=2, i�=50 and i₂=70 into p�/i� = p₂/i₂, we get:
2/50 = pâ‚‚/70.
Since we can solve for pâ‚‚, we can determine the value of p if i=70.
SUFFICIENT.

The correct answer is B.