How to Do Math FAST for the GMAT - Part 2
Welcome to the second installment of our Fast Math series. (Miss part 1? Take a look here.)
Heres the basic premise: Im always on the lookout for ways to get out of doing tedious paper calculations on the GMAT.
The awesome part: the test writers actually set this up for me! They know were not going to have to do a bunch of paper math in b-school or the real world, so they construct problems that allow us to take advantage of all sorts of shortcuts if were paying attention.
Principle #3: Use benchmarks to find percents
Some GMAT problems appear to involve tedious percent calculations, but theyre really not all that tedious if you take a step back and use benchmarks.
What are benchmarks? First, lets start with a numbersay, 140. Now, lets say that the problem calls for 18% of 140. You could set up a couple of fractions and then simplify numerators and denominators but ugh.
Heres how to use benchmarks instead:
The starting number, 140, is 100%.
10% of 140 is 14. Therefore, 20% is twice that, or 28.
Were trying to get to 18%, which is 2% less then 20%.
We already know that 20% = 28. Therefore, 2% = 2.8.
20% - 2% = 18%, so 28 - 2.8 = 25.2.
Thats it! The answer is 25.2
Any percentage can be calculated using some combination of benchmark percentages that are easier to find. The easiest-to-find benchmarks are 100%, 50%, 10%, and 1%. From 50%, you can move the decimal left once to get 5%. Using these 5 benchmarks, you can calculate anything, because you can add up percents.
For example, find 63% of 86.
63% = 50% + 10% + 3(1%)
50% of 86 is 43
10% of 86 is 8.6
1% of 86 is 0.86 (and we need 3%, so its really 3 0.86)
Around about now, Id be glancing at the answer choices to see whether I can estimate from here, because adding that up is annoying. This is the GMAT, so it might just be enough to estimate low 50s. If Im really pressed, I might go as far as, Its 51.6 plus a little less than 3, so around 54. On the GMAT, thatll be enough for me to get to the answer.
Principle #4: Estimate and not just when they tell you to
And that brings us to awesome estimation. Some problems ask you straight up, Approximately how far has the train gone when When they tell you that you can approximate, always do so! But even when they dont, you may be able to estimate.
Train yourself to glance at those Problem Solving answer choices periodically while you work to see how far you really need to go. The correct answer isnt the actual number the correct answer is just A, B, C, D, or E. Who cares how you get there?
In general, if you have numerical answer choices that are decently far apart, you can often estimate at some point in the problempossibly right from the beginning or possibly a little farther in, depending upon the nature of the problem and how far apart the answers are.
Also, how rough can your estimation be? Again, glance at those answers. The farther apart they are, the more loose you can be. Youll need to practice this, like any skill, so that you know how far is too far. As you gain experience, youll start to understand both when and how much you can confidently estimate your way to the answer.
Open up your Official Guide right now and flip to the Problem Solving chapter (chapter 5 in the big book). Start scanning down the answer choices until you find some that look decently far apart, or look for the word approximately in the question. Then see whether (and how) you can estimate.
Some of my favorites from the 2016 edition of the Official Guide (OG2016):
#105 (page 167)
#116 (page 169) (This one tells you that you can estimate)
#169 (page 176) (Can knock out two answers with some general estimation)
As you get better, add some variations into the mix. For instance, one problem might have these five answers:
Now, these guys dont look all that far apart but you may still be able to estimate! Two are negative, two are positive, and one is 0. If you can estimate enough to tell that the answer must be negative, then you have a 50/50 shot at getting this right, even if you dont have enough time or dont know how to do the problem for real.
Take a look at #135 (page 172) in OG2016. Can you tell whether it should be an increase or decrease? What about #136 on the same page: can you figure out whether it should be more or less than half?
Start looking for opportunities to estimatecertainly when the problem asks for an approximate answer, but sometimes even when it doesn't.
I want yours, actually! Have you found any neat ways to reduce tedious calculations? Share them in the comments. And make sure to join us next time for the third installment in the series. Happy studying!