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
It's Different.
