Data Sufficiency

Hi, there. I'm happy to help with this.

The Prompt
Firm A operates under the following conditions: for every m% increase in firm A's revenues, its profits increase by n%. Similarly, for every n% increase in firm B's revenues, its profits increase by m%. In 2007, firm A increased its revenues by n% and firm B increased its revenues by m%. Which firm saw a larger percent increase in profit in 2007?

Notice that both conditions are stated as proportions --- that language of "for every" increase of this kind, we get an increase of that kind --- that's the language of proportions. Let's pretend, for a moment, that m = 5 and n = 3. This does not mean that Firm A's revenues definitely increase by 5%. It means if A's revenues increase 5%, profits increase 3%; if revenues increase 10%, profits increase 6%; if revenues increase 15%, profits increase 9%. The only information given in the statement is information about proportions. That's important to remember.

Statement #1: m > n > 0
Substitute m = BIG and n = SMALL. When A has a BIG% increase in revenue, it has a SMALL% increase in profit. Conversely, when B has a SMALL% increase in revenue, it has a BIG% increase in profits. That's interesting, but not sufficient to answer the question --- again, the information in the prompt is only about proportions, and while m > n > 0 establishes something about the relative ratios, it's still possible that A or B had a 0% change in revenue (and hence, a 0% change in profit). Statement #1, by itself, is insufficient.

Statement #2: In 2007, firm A's revenues increased by 3% and firm B's increased by 10%.
These are the actual value of the percent increase in revenue --- knowing this, we still know nothing about m & n, which establish the relative proportions. Because we know nothing about the relative proportions, we can't conclude anything. Statement #2, by itself, is insufficient.

Combined Statements #1 & #2
Now, we know: A's revenue increased by 3%. Call A's percent increase in profits pA. We can set up the proportion m/n = 3/pA ===> pA = (3n/m) ===> A's profits increase by (3n/m)%, which is less than 3%, because m > n > 0.
We also know B's revenue increased by 10%. Call B's percent increase in profits pB. We can set up the proportion n/m = 10/pA ===> pA = (10m/n) ===> B's profits increase by (10m/n)%, which is more than 10%, because m > n > 0.
A's profits increased by less than 3%, and B's profits increased by more than 10%, so B's profits increased by a larger percent. Combined, the statements are sufficient.

Answer = C

Does that make sense? Please let me know if you have any questions on what I've said.

Mike

Dell2, Neelgandham, shekhar.kataria, anandhimanshu85,

My apologies. I realize, going back, that I totally neglected to include the information in the third sentence. If the information in the third sentence is omitted, the answer would be C. BUT, as the question stands, you folks are all correct: the answer should be D.

Sorry for my misreading. Good luck to all of you on the GMAT.

Mike