Tuesday, January 10, 2012

right again!

The official answer to last week's MGRE Math Beast Challenge problem is indeed (E)!

Here is MGRE's explanation:

Interest on debt comprises 2% of total expenses for each division. So if the pharmaceutical division spends 4 times as much as the chemical division does on interest, then total expenses for the pharmaceutical division must be 4 times total expenses for the chemical division. The best thing to do is pick some smart numbers:

Total expenses for pharma = 400
Total expenses for chem= 100

{We might pause here to check our earlier logic. With these numbers, chem would spend 2 for interest on debt and pharma would spend 8. This agrees with what the problem told us about interest on debt.}

Payroll expenses for pharma = 26% of pharma total = (0.26)(400) = 104
Payroll expenses for chem = 38% of chem total = (0.38)(100) = 38

The question asks “What percent of the chemical division's payroll expense is the pharmaceutical division's payroll expense?”
With our numbers, this question is “What percent of 38 is 104?”
Rephrasing a bit: “104 is what percent of 38?”

We can see that 104 is more than 100% of 38, so (A) and (B) can be eliminated.
Actually, 104 is more than twice 38 (i.e. 104 > 76), so (C) and (D) can also be eliminated.

We can solve to prove that (E) is the answer by translating the percent question into an equation:
104 is what percent of 38?
104 = (x/100)(38), where x is the answer.
x = (104)(100)/38
x = 273.6842....

To the nearest whole percent, 104 is 274% of 38.

The correct answer is E.

I like MGRE's explanation, which involves, arguably, a little less math than my own explanation does. Many math problems on both the SAT and the GRE can be solved in this way: through logical deduction instead of hardcore algebra. Remember to eliminate possibilities as you work: by narrowing the number of plausible answers, you increase your chances of guessing correctly-- if you find yourself needing to make a guess. Of course, if you're able to use deduction to eliminate four out of five possibilities, then you're golden!


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