The GMAT is an exam that aims to test how you think about things. Many people have heard this mantra when studying for the GMAT, but it’s not always clear what it means. While there are many formulae and concepts to know ahead of taking the exam, you will be constantly thinking throughout the exam about how to solve the question in front of you. The GMAT specializes in asking questions that require you to think about the solution, not just to plug in numbers mindlessly and return whatever your calculator tells you (including typos and misplaced decimals).
There are many ways the GMAT test makers ensure that you’re thinking logically about the solution of the question. One common example is that the question will give you a story that you have to translate into an equation. Anyone with a calculator can do 15 * 6 * 2 but it’s another skill entirely to translate that a car dealership that’s open every day but Sunday sells 3 SUVs, 5 trucks and 7 sedans per day for a sale that lasts a fortnight (sadly, the word fortnight is somewhat rare on the GMAT). Which skill is more important in business, crunching arbitrary numbers or deciphering which numbers to crunch? (Trick question: they’re both important!) The difference is a computer will calculate numbers much faster than a human ever will, but being able to determine what equation to set up is the more important skill.
This distinction is rather ironic, because the GMAT often provides questions that are simply equations to be solved. If the thought process is so important, why provide questions that are so straight forward? Precisely because you don’t have a calculator to solve them and you still need to use reasoning to get to the correct answer. An arbitrarily difficult question like 987 x 123 is trivial with a calculator and provides no educational benefit, simply an opportunity to exercise your fingers (and they want to look good for summer!) But without a calculator, you can start looking at interesting concepts like unit digits and order of magnitude in order to determine the correct answer. For business students, this is worth much more than a rote calculation or a mindless computation.
Let’s look at an example that’s just an equation but requires some analysis to solve quickly:
(36^3 + 36) / 36 =
This question has no hidden meaning and no interpretation issues. It is as straight forward as 2+2, but much harder because the numbers given are unwieldy. This is, of course, not an accident. A significant number of people will not answer this question correctly, and even more will get it but only after a lengthy process. Let’s see how we can strategically approach a question like this on test day.
Firstly, there’s nothing more to be done here than multiplying a couple of 2-digit numbers, then performing an addition, then performing a division. In theory, each of these operations is completely feasible, so some people will start by trying to solve 36^3 and go from there. However, this is a lengthy process, and at the end, you get an unwieldy number (46,656 to be precise). From there, you need to add 36, and then divide by 36. This will be a very difficult calculation, but if you think of the process we’re doing, you might notice that you just multiplied by 36, and now you’ll have to divide by 36. You can’t exactly shortcut this problem because of the stingy addition, but perhaps we can account for it in some manner.
Multiplying 36 by itself twice will be tedious, but since you’re dividing by 36 afterwards, perhaps you can omit the final multiplication as it will essentially cancel out with the division. The only caveat is that we have to add 36 in between multiplying and dividing, but logically we’re adding 36 and then dividing the sum by 36, which means that this is tantamount to just adding 1. As such, this problem kind of breaks down to just 36 * 36, and then you add 1. If you were willing to multiply 36^3, then 36^2 becomes a much simpler calculation. This operation will yield the correct answer (we’ll see shortly that we don’t even need to execute it), and you can get there entirely by reasoning and logic.
Moreover, you can solve this question using (our friendly neighbour) algebra. When you’re facing a problem with addition of exponents, you always want to turn that problem into multiplication if at all possible. This is because there are no good rules for addition and subtraction with exponents, but the rules for multiplication and division are clear and precise. Taking just the numerator, if you have 36^3 + 36, you can factor out the 36 from both terms. This will leave you with 36 *(36^2 + 1). Considering the denominator again, we end up with (36 *(36^2 + 1)) / 36. This means we can eliminate both the 36 in the numerator and the 36 in the denominator and end up with just (36^2 + 1), which is the same thing we found above.
Now, 36*36 is certainly solvable given a piece of paper and a minute or so, but you can tell a lot from the answer by the answer choices that are given to you. If you square a number with a units digit of 6, the result will always end with 6 as well (this rule applies to all numbers ending in 0, 1, 5 and 6). The result will therefore be some number that ends in 6, to which you must add 1. The final result must thus end with a 7. Perusing the answer choices, only answer choice C satisfies that criterion. The answer must necessarily be C, 1297, even if we don’t spend time confirming that 36^2 is indeed 1,296.
In the quantitative section of the GMAT, you have an average of 2 minutes per question to get the answer. However, this is simply an average over the entire section; you don’t have to spend 2 minutes if you can shortcut the answer in 30 seconds. Similarly, some questions might take you 3 minutes to solve, and as long as you’re making up time on other questions, there’s no problem taking a little longer. However, if you can solve a question in 30 seconds that your peers spend 2 or 3 minutes solving, you just used the secret shortcut that the exam hopes you will use.
Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam. After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.