By Eli Meyer
Timing on the GMAT quantitative section presents a challenge to a majority of students. Between complex formulas, which can be hard to remember and apply, and word problems, which can conceal simple math among layers of text, there are a number of places to lose time—or, if you’ve followed Kaplan’s blogs and other resources, to avoid losing times with clever tricks and strategies.
But the truth is, sometimes you will spend a full minute just decoding a complex word problem. And that’s okay. The GMAT assigns problems adaptively, meaning that every last student will encounter problems that challenge them.
But that extra time needs to come from somewhere. If we’re slowing down to understand complex prompts, we need to speed up somewhere else to save time. And one of the places that you should not be spending a lot of time is arithmetic. The GMAT is designed to be solvable without a calculator, so in today’s blog post, we’ll show you a few of the mental math tricks that will let you quickly do mundane calculation, saving time for the tasks that truly require dedicated attention.
1. Divide before you multiply
The GMAT loves to test complex proportions, cross multiplication, probability, and combinations. It's a sure thing, therefore, that you will at some point encounter arithmetic like this:
21 x 45 x 22
___________
7 x 9 x 11
This task probably won't be given to you directly in the question stem—more likely, this would be an intermediate step after translating a word problem or plugging in numbers for variables. But it's certain you’ll see something like this at some point on some GMAT problem.
In real life, you might plug these straight into a calculator. Doing so would give us this:
Ugly, huh? 5 digit numbers divided by three digit numbers. But the result is a nice even 30. There must be a better way to get there if the division is so neat! The shortcut is to divide. Any time you have numbers over numbers, you should always cancel, cancel, cancel. Dividing first keeps your numbers small and your arithmetic simple. Check out what happens if we cancel first in this problem:
Easy as pie! 7 goes evenly into 21, 9 goes evenly into 45, and 11 goes evenly into 22. Reducing fractions and ratios to their simplest form before multiplying saves you mountains of work.
2. Use nearby easy-to-calculate benchmarks.
Quick, what’s 29 times 4? Okay, with a pencil and paper you can do that multiplication relatively quickly, but it’s not something you can necessarily do in your head.
Quick, what’s 30 times 4? This time, you probably snap-called it. And even if you had to use paper, it should have taken you a fraction of the time to get to the answer of 120.
But there’s a trick to this. 29 is just one away from thirty. So:
Or to put it in plain English, 29 times four is one four less than 30 times four, so we can take that easy to calculate 120, subtract four, and get our answer without so much as a scribble: 29 x 4 = 116. 10s and 5s are very easy to calculate, so for complex multiplication, it can be easier to just round to the nearest 10, then add or subtract.
3. Memorize common arithmetic
Some students really struggle with even the basics of math. If you’re in that category, that’s okay—you can improve those skills by working through basic problems or with lessons such as Kaplan’s Math Refresher course. But some students who are convinced they can’t do math ignore the fact that they do that math on a daily basis! Use your real-life experience to simplify calculations.
For instance, most people know that ¾ is equal to 75%. But every American knows that three quarters make 75 cents, and most currency systems (25 euro-cents, 25 rupee coins) work similarly.
In the same vein, what’s 52 divided by 13? This is slightly less common knowledge, but there are 13 cards in each suit of a 52 card deck. Anyone who knows there are four suits in poker knows the answer to this question.
Clearly you can’t memorize every bit of math you’ll ever see. But the math you use in everyday life, like how many eggs in half-a-dozen or how many products you actually pay for when you buy nine at buy-two-get-one-free, can be applied to more abstract versions of pure math on the GMAT.
Most of the time, you’ll still want scratch work on problems like these. Only do math in your head when you are absolutely confident in the calculation, as a mental misstep can cost you time or even the correct answer. But every single calculation you do represents an opportunity for more efficiency. Don’t go straight for the formal arithmetic grind, because there may be mental shortcut to simplify your work. Try this sample question as an example and stay tuned for the answer which will be posted in the comments section.
~Article provided by the courtesy of Kaplan GMAT
Here is the answer to the question in the above post:
31. E
When we see what appears to be a lengthy arithmetic problem, we should look for ways to simplify the work. When fractions are involved, think about factoring the numerator and denominator, looking for terms that will cancel out.
In this case, 5.005 = 5 × 1.001, and 2.002 = 2 × 1.001. So we can rewrite the original fraction as 5.005/2.002 = 5(1.001)/2(1.001) = 5/2 = 2.5.
Choice (E) is correct.