A few months ago, I wrote a couple of articles targeted toward those students looking for a super-high score (one for quant, one for verbal). I challenged students to answer those questions in much less time than we typically average on test questions.
Well, I’m back with another one in the series. This problem is a bit different though: it’s from our Challenge Problem archive, a question bank consisting of what we call 800+ level problems. (Some might qualify as 750+ but most are harder than anything you’ll ever see on the real test.)
Do you need to be able to answer a question like this in order to score 750+? Absolutely not. (In fact, after my colleague Ron Purewal submitted this question, I tested it out on several of my fellow instructors, all of whom have scored 760+ on the test. Not everyone answered correctly.) Mostly, I’m offering this to stretch your brains, drive you a little crazy, and make one important point (see my second takeaway at the end).
If, however, quant is your strength and you’re hoping to score 51 in that section—you can certainly score 51 without getting this one right, but if you do get this one right in 2 minutes, then you know you’re ready for the quant section.
One more tidbit before we dive in. I chose this question because it is SO very hard. As of right now (as I’m typing this), 254 people have tried this problem and 44 have answered it correctly.
Do a little math here. What percentage of people answered the question correctly?
17%. Random guess position is 20%. Wow.
La la la. I’m just adding words here so that you don’t inadvertently glance down and see the answer while you’re still figuring things out up above. : ) Okay, what are the clues? Integer and remainder tell us that this is likely a number properties problem – this is the “class” I was referring to earlier. I can tell this is number properties from a couple of key words, but it turns out there’s even more going on. The words divided by bring up the idea of divisibility. Finally, the problem begins by talking about the variable n, but also later mentions n – 1 and n + 1. Put those three terms together and what have we got? Consecutive integers!
My appreciation of units first began during college. I was a chemistry major in college, and as part of my major I had to take physics. The topics in physics never came naturally for me so I was always looking for little tricks that would lead me towards a correct answer. One trick I found that was surprisingly effective was to just combine the numbers in the way such that the answer was in the appropriate units. For example if the question asked for an acceleration (the rate at which speed is changing or the second derivative of distance for the calculus-inclined), I knew that acceleration is always in the form of units of distance / units of time^2 (e.g. meters/ seconds^2). So unless I combined the numbers in a way that resulted in these units as the answer – for example by dividing a speed in meters per second by a time in seconds – I knew I had done something wrong.
The last blog post I wrote showed how modifiers can fool people on quant problems – 
For every five hours of studying combinatorics-type questions, the average GMAT student increases their chances of being able to correctly answer a question type that is found only on the very difficult end of the GMAT spectrum. Meanwhile, the same student will have to compute hundreds of basic computations without the aid of a calculator. For students who know how to quickly do these computations, they are rewarded with extra minutes that can be spent double-checking their work and critically thinking about whether their answers make sense. As BenGMAT Franklin might say- a second saved is a second earned on the GMAT… but it doesn’t matter if those extra seconds come from being faster at doing combinatorics questions or quicker at computations. So check out these five math tricks, learn the ones that you like, and practice them daily to give yourself some extra time to finish off that 37th and final quant question.
Wow. I’m glad I don’t have to feed this rabbit. This sounds annoying. : )
