Data Sufficiency

A firm increases its revenues by 10% between 2008 and 2009. The firm's costs increase
by 8% during this same time. What is the firm's percent increase in profits over this
period, if profits are defined as revenues minus costs?

(1) The firm's initial profit is $200,000.
(2) The firm's initial revenues are 1.5 times its initial costs.


Considering that the use of 2 or 3 unknowns under tight time constraints can lead to
errors, what is the most efficient way of solving the above question?
SOURCE: GROCKIT.COM
OA B

It took me around 40 seconds to do this, so here goes.

First, let R8, R9 be revenues in 2008 and 2009 respectively.
Second, let C8, C9 be costs in 2008 and 2009 respectively.

Now in the question stem, we have 10% revenue increase, therefore R9/R8 = 1.1 => R9 = 1.1R8
Also, in the question stem, we have 8% cost increase, therefore C9/C8 = 1.08 => C9 = 1.08C8

(I started the formulation just by assuming R as original revenue, and writing 1.1R as increased one, and C as original cost using 1.08C as the new cost. I am writing R8, R9 etc, just for the benefit of understanding)

Then "percentage change in profits" is (R9-C9)/(R8-C8) = (1.1R8 - 1.08C8)/(R8-C8)
So, we see that if we can find ratio of R8 to C8, we will get rid of the variable, we will get the answer.

Now, the first choice only tells us that R8-C8 = 200,000, even if we substituted this, it won't give us the answer as one variable would still remain. Hence, INSUFFICIENT.

For the second choice, we have R8 = 1.5C8, which is exactly what we were looking for, this option will make the "percentage change in profits" a unique number, which is what we wanted. Hence statement by itself is SUFFICIENT. Hence B.

The problem says R becomes 1.1R in 2009 and C becomes 1.08C.

The most efficient way would be to first simplify the question.

The question is:
(P2 - P1)*100/P1 = ?
or
[1 - P2/P1]*100 = ?

where
(P2/P1) = (1.1R - 1.08C)/(R - C) = (1.1(R/C) - 1.08)/((R/C) - 1)

We'll now like to see if any of the options gives us (P2/P1) or (R/C).

Statement(1):
Neither (P2/P1) nor (R/C).
INSUFFICIENT

Statement(2):
We have (R/C)!
SUFFICIENT

[spoiler](B)[/spoiler] is the correct option.

gmatdriller wrote:A firm increases its revenues by 10% between 2008 and 2009. The firm's costs increase
by 8% during this same time. What is the firm's percent increase in profits over this
period, if profits are defined as revenues minus costs?

(1) The firm's initial profit is $200,000.
(2) The firm's initial revenues are 1.5 times its initial costs.


Considering that the use of 2 or 3 unknowns under tight time constraints can lead to
errors, what is the most efficient way of solving the above question?
SOURCE: GROCKIT.COM
OA B

An alternate approach is to plug in values.

Statement 1: The firm's initial profit is $200,000
If the revenues in 1998 = 300,000 and the costs in 1998 = 100,000, then the profit in 1999 = 330,000 - 108,000 = 222,000.
If the revenues in 1998 = 400,000 and the costs in 1998 = 200,000, then the profit in 1999 = 440,000 - 216,000 = 224,000.
Since the change in profit can be different values, INSUFFICIENT.

Statement 2: The firm's initial revenues are 1.5 times its initial costs.
Let the revenues in 1998 = 300 and the costs in 1998 = 200.
Profit in 1998 = 300 - 200 = 100.
Profit in 1999 = 330 - 216 = 114.
Percent increase = 14%.

Let the revenues in 1998 = 600 and the costs in 1998 = 400.
Profit in 1998 = 600 - 400 = 200.
Profit in 1999 = 660 - 432 = 228.
Percent increase = (228-200)/200 * 100 = 14%.

When we increase the initial values by a factor, all of the subsequent values increase by the SAME factor.
Thus, the percent increase in profit will be the same in every case: 14%.
SUFFICIENT.

The correct answer is B.

Thanks to everyone for their great contributions.

I was wondering how to make an efficient choice of number...while, also avoiding the tendency
for errors in multiple variable equations; however, practice, i believe, makes perfect.

IMO: B