Bunuel wrote:
If \(m\) is three times \(n\), and if \(2n+3\) is 20% of 25, what is the value of \(m\)?
A. 1
B. 2
C. 3
D. 6
E. 12
In single-unknown PS questions, you can always work backwards from the answers, too. I am a big advocate of the (B) or (D) test first, since you could get lucky and either hit the answer or automatically know what the answer had to be. For instance, if you tried 2 and realized it was too high, then only one answer, 1, would work in this question. Trying (C) first means that if it is not the answer, you will likely have to try a second value between the two higher or lower answers, and as we all know, time is a precious commodity on the GMAT™. Anyway, to the problem at hand:
1) For the purpose of illustration, let m = 6. Knowing ahead of time that m = 3n, between 2 or 6 for
m, I know which one makes for an easier time.
2) If m = 6 then n = 2: 6 = 3(2).
3) Check against the known information: 2(2) + 3 is 20% of 25, or 4 + 3 = 0.2 * 25. This leads to an invalid equation, since 7 ≠ 5. Importantly, though, we know that both (D) and (E) must be too high.
4) Try a smaller number. Let m = 2. This is the number in the middle of the remaining answers, so it will either be the answer itself or will point directly to the answer (which will have to be higher or lower). Again, m = 3n .˙. 2 = 3n, and n = 2/3.
5) Check against the known information: 2(2/3) + 3 is 5 (since we figured out 20% of 25 earlier), or (4/3) + 3 = 5, or 4 1/3 = 5. Again, this is not true, but now our answer is too low, and we can rule out both (A) and (B).
The answer must be (C), even without proving it.
Although I solved the question in the same manner as that outlined in the official solution, I like to drop in these alternative methods of approaching the same problem now and then to remind people that
the Quant test measures analytical reasoning as much as it does mathematical prowess. You might think the above method would take a long time, but that is not so. One thing leads to another, and I would imagine that most GMAT™-level test-takers would be able to solve the question within a minute, and there is a certain comfort that comes with knowing you have the correct answer. (I say this to anyone who might have fallen into the n = 1 trap and chosen (A).)
Good luck with your studies.
- Andrew