This Fraction Problem Is Harder Than It Looks
I’ve spoken with multiple students lately who received a disappointing (lower than they were expecting) score on the quant section and who all said that the quant felt relatively easy or straightforward. How is that possible?
First of all, thinking that a test like the GRE is easy is actually a warning sign: unless you are poised to get a perfect score, chances are you’re missing something. Some of the questions are really very challenging and they should feel hard even to someone like me (who did get a perfect score on this test! 🙂 ).
Second, the test writers are phenomenal at writing questions that don’t seem all that complicated but are in fact your worst nightmare. My worst nightmare is not an impossible question “ I know I can’t do it, so I just pick an answer and move on. My worst nightmare is a question that I think I can do, and I spend a decent chunk of time doing it, and then I get it wrong anyway “ even though I’m sure I got it right!
The problem I’ve chosen is actually a GMAT problem; I chose it because it perfectly illustrates the point that I’m trying to make, and it is actually in the same form as GRE problems. Try this GMATPrep problem and you might see what I mean. Set your timer for 2 minutes. and GO!
* Âť Of the 3,600 employees of Company X, 1/3 are clerical. If the clerical staff were to be reduced by 1/3, what percent of the total number of the remaining employees would then be clerical?
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(A) 25%
(B) 22.2%
(C) 20%
(D) 12.5%
(E) 11.1%Âť
What’s hard about this one? It looks completely straightforward!
Hmm so I have 3,600 employees and 1/3 are clerical. That’s easy: 1,200 are clerical. Then I need to take 1/3 of that, so that’s 400. They want the percent of the total, so 400/3600 = 4/36 = 1/9 = ugh. Let’s see, a little quick long division right, 1/9 is 11.1%. Answer E. Done!
Where’s my mistake? Go find it. (Actually, find both of them.) Also note that my wrong answer was right there in the answer choices!!
Oh, I see what I did! I correctly found 1/3 of 1,200, which is 400, but that’s how many are getting laid off. The remaining number is 1,200 “ 400 = 800. Argh! Okay, 800/3600 = 2/9 = 22.2%. The answer is B.
Sigh. Nope. Still wrong. Nightmare!
Okay, let’s try this again, step by painful step. Before I show the correct solution, see if you can figure out how to calculate the other two incorrect solutions. I’ll explain at the end.
Of the 3,600 employees of Company X, 1/3 are clerical.Âť
There are 3,600 employees. 1/3 of the employees are clerical. (3600)(1/3) = 1200. So far so good: there are 1,200 clerical employees.
If the clerical staff were to be reduced by 1/3Âť
Okay, this was one of my mistakes. The clerical staff is reduced byÂť (1200)(1/3) = 400, so the remaining staff equals 800.
what percent of the total number of the remaining employees would then be clerical?Âť
What is the total number of the remaining employees? Oh. The remaining employees. I started with 3,600, but I just laid off 400, so there are only 3,200 remaining. Here’s my second mistake. So the actual calculation should have been 800 / 3200 = 8 / 32 = 1/4. The correct answer (for real this time!) is 25%, or answer A.
Note to those who got this one right: you can see how easy it would be to make any of those other mistakes, right? Imagine the pressure of test day, you know this is the real thing, you’re worried about the timing… and all those things just make these little mistakes even more likely. So, just because you got it right this time doesn’t mean that you’re immune to making these kinds of mistakes in general.
One more note before we talk about the other two wrong answers. When working directly with students, I notice repeatedly that the most common time for careless errors comes towards the end of the problem when the student feels that s/he has already crackedÂť it. I do the same thing: we know now that we’re going to get it right, so we want to finish it off as quickly as possible, and we sort of start to look forward to the next problem already. And then BAM! Careless error. (And, of course, the wrong answer is usually in the mix of answers, because the test writers have done their homework and figured out what errors we’re most likely to make!)
Did you figure out how to get to wrong answers C (20%) or D (12.5%)? Answer D is a result of a mistake we’ve already seen: incorrectly using 400 instead of 800 for the remaining clerical employees. In this case, though, we would use the correct figure of 3,200 for the denominator: 400/3200 = 4/32 = 1/8 = 12.5%.
For C, 20%, I didn’t find a really obvious way to get to that error. In looking at the mix of answers, though, I think it’s possible that the question-writer thought, Hmm, the correct answer is 25% and then the 3 wrong answers are all weird numbers with decimals. So I’d like to have another normalÂť answer in the mix. Then, nobody will pick 25% just because it looks nice, since 20% will also be there. And maybe people will actually think that it must be one of the weird numbers, since there are three of those, so test-takers who have to guess will be less likely to guess 25%. Perfect! I’m done writing this problem.Âť
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Key Takeaways for This looks pretty easy!Âť Problems:
(1) Be alert: there’s a pretty good chance that the problem is not as easy as it looks. The GRE test-writers have mastered the art of making a problem look easier than it is.
(2) Take the problem step-by-step. Write out ALL of your work. (You should be doing this anyway on all quant problems “ it doesn’t take less time to write while you’re thinking, and you will save yourself many careless mistakes if you do actually write out your work.)
(3) Watch out for the I’ve got this / I’m almost done!Âť distraction. When you think you’ve cracked the problem, then focus in even more “ I’m going to get this and I’m not going to make a last-minute mistake! Don’t start thinking about the next problem, or where you are in the section, or whether you might not need to save a little bit of time by speeding up now that you know what you’re doing, or I can’t wait till this stupid test is over!! No. Finish this problem. Then move to the next one.
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* GMATPrep questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.