Timing is a big issue for many on the GRE math section. One way in which students could end up saving precious minutes is by using mental math shortcuts, the most powerful of which is known as approximation. What I’ve noticed, however, is some students feel they have to set up some sort of proportion to solve a problem, a step that is both tedious and fraught with the potential for arithmetic errors. So, instead of trying to find the exact answer to a problem by furiously crunching numbers on the paper, learn to approximate and avoid running out of time (as well as a case of hand cramps).

When using approximation to solve a problem, either round numbers up or down so that you get a nice, round number to work with. Rounding numbers to the nearest five or zero usually works well. The key to approximating is to make sure the numbers you round to don’t deviate too much from the original numbers.

For instance, let’s take a look at the problem below:

1. What is 49% of 23?

(A) 10

(B) 11.27

(C) 12.8

(D) 13.7

(E) 15

Many students feel the need to set up an equation and solve for an exact value. For the GRE, you do NOT want to do this. Yes, such an injunction may seem counterintuitive, especially for those who vividly recall their high school math days. Whereas getting an exact value usually led to an A in this context, on the GRE an exact value—and the attendant setting up of an equation or proportion—will only slow you down. That is why you want to approximate, or estimate, wherever possible. The gist is to avoid solving the problem. If the answer choices are really close, then, and only then, set up an equation/proportion to get a more exact number.

So let’s take a look at the question above, and let me re-word it. What is 50% of 23? Easy, right? The answer is half of 23, which is 11.5. Notice I rounded up a little bit. But the answer is going to be very close to 11.5. Again, the essence of approximating is to pick a number that is close to any of the numbers and one that is easy to work with. Rounding 23 to 25 still leaves you with a 49. If you also round the 49 to 50, then you start to deviate a little too much from the original problem. With the spread of the answer choices above, you can still get the correct answer by multiplying .50 x 25 and then choosing the closet answer less than your result.

In the end, either approach will yield (C) 11.27. As long as you are able to do mental math quickly, you can make a 1-minute problem a 15-second one. Savvy students may even solve the problem in less time, if they see that when you multiply .49 x 23, the number has to end in a seven. The only answer choice that has a 7 at the end is (C).

Now, if you’re not used to solving in your head, or approximating/estimating in general, my advice is to start with easy problems. Just as importantly, drop that pen or pencil. That’s right—think of the pen(cil) as a crutch that’s only preventing you from walking, so to speak.

Okay, let’s try another type of problem and one you are very likely to see on the data interpretation (this is the section with those pesky pie/bar/curve graphs). Dispensing with the actual graph and winnowing the problem down to its basics, here is an example. And remember—don’t use your pen!

*14% of a company’s inventory shipped. If the company held on to 170,280 items then approximately how many items did they ship?*

*(A) **21,000*

*(B) **22,500*

*(C) **28,000*

*(D) **30,000*

*(E) **32,500*

This problem is much trickier than the first one. To start, we want to note the difference between the items shipped (14%) and the items not shipped (86%). Next, we want to ask ourselves, what’s a nice round number that’s not too far from 86%? What about 80%? Well, look at the answer choices. Notice that they are actually pretty close together. Using 80% for 86% would significantly change the outcome. So let’s try another number closer to 86%. How about 85%.

Now, let’s return to the information in the problem. 170,280 items can be changed to 170,000 items. We can use the 85% to represent the 170,000 items that did not ship. What is the relation between 170,000 and 85%? Notice that 170 is double 85. So, if we double the percent and multiply by 1,000 we get the total number of items that didn’t ship. So, the total number of items that shipped is double 14%, which is 28, multiplied by 1,000, which equals 28,000 (remember the number of items is in thousands, i.e. 170 thousands or 170,000).

Note that the question asks to approximate. 28,000 is not the exact answer but is very close, and hence an approximation. Had we forgotten that we’d approximated in the beginning by changing 86 percent to 85 percent, and thus 14 percent to 15 percent, we could have mistakenly chosen answer 30,000, choice (D).

The takeaway is to solve problems by approximating. Doing so will save you lots of time, while not taxing your brain scribbling tedious math at the margins of your scratch paper. Remember, approximating well takes practice, but once mastered will pay huge dividends in terms of the time saved on the actual exam.

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@Chris Lele, thanks a lot for your approaches. But I am not very good at mental math. And I am quite sure I will not be able to come up with your solution for 2nd problem. As I am weak I would rather follow different approach,

14% ~ 15% of 170280 ~ 170 * 1000

10% of 170 = 17+

5% of 170 = (half of 10%) 9-

So, 15% = 17+9 = 26

there fore 26*1000 which is closest to 28000.

These steps are very easy, however, emits a little bit obscure result. Should I follow my approach ? or I should somehow follow your approach too.

Thanks in advance

Hi there,

First, I want to highlight that we are not looking for “14% – 15% of 170280”. The question prompt tells us “14% of a company’s inventory shipped. If the company held on to 170,280 items then approximately how many items did they ship?”

This means that 14% was shipped. 86% was held. We are also told that the company held 170,280 items. So, we know that 86% of “x” inventory equals 170,280. In other words:

0.86x = 170,280.

We are looking to solve “0.14x = ???”.

That being said, this calculation process does work as long as you rephrase it to find the right answer. Still, the approach in the explanation may be a more efficient method, but whatever you’re most comfortable with is best! I hope this helps!

help a lot

thanks 🙂

You’re very welcome 😀

Here is another method,

We know that 86%~85% of something is 170280.

Reducing 86% to 85% and 170280 to 170000.

85% –>170000 (Approx)

so, 01% –> 170000/85 = 2000

Now, multiply 2000*14=28000 as the question asks for 14%.

Hi Manu,

That does work–and quite fast. I still think the method above (the one I described) is faster because it bypasses the somewhat cumbersome step of 170,000/85 = 2,000. Still, both methods are excellent and are exactly how the GRE wants you to think :).

It does work for me most of the time if not always.

And By the way, I stopped here to thank Chris and the whole Magoosh team for such wonderful write-up and blogs. The important part is its free and helped me immensely. Appreciate your effort guys. Am done with GRE now and looking forward to my application process. Thanks again.

Hi Manu,

Thanks for the kind words! Hope you did well on the test, and good luck with grad school :).

I was struggling with the prealgebra practice exercises because i was too focused on formulas and fundamentals. I tried these two strategies, and it worked!!!! Thanks!

An easy approach with just addition:

86% = 170280

8.6%= 17028……………………….. (a)

17.2% = 34000 ( approx)

But we need 14%

means we need to deduct 3% from 34000.

from (a)

9 % = 17000 ( approx)

3% = 6000 (approx)

so ans is (34000- 6000) = 28000

That’s an interesting way of doing it :). Quite a few steps, but as long as it worked for you it is effective!

As it contains very easy calculations, its an effective tool for % problems.

Hello Chris,

I don’t quite understand the “why” of the “notice that 170 is double 85” step and the steps that follow. Is there a video lesson on this technique?

Here is how I set up the approximation (to me it seems simpler):

170/.86=196 (original inventory)

197-170=27 closest to answer C.

Hi Len,

The 85 to 170 is more of mental math shortcut that in some ways is obviated by the advent of a calculator (the step that you followed). In this case 170k represented 85%. (which is double). Therefore double 15% is roughly 28k.

Hope that helps!

A simpler approach would be to notice that 14 * 6 = 84 (= approx 86). Therefore, if you divide 170000 by 6, it is equivalent to dividing 86% by 6 to yield approx 14%. Now, 180000 by 6 gives 30000, so the answer is slightly below 30000 i.e 28000.

Prabha,

That’s also a good way! I tried both and think that they take about the same amount of time. Though the multiplying 14 x 6 to 84 not be as readily apparent as doubling 85% to get 170.

Thanks again for your insight :).

I still think there is a lot of extra work going on in your approach. Even at the very end dividing 170280 by 6 is still complicating things. Just divide 170 by 6.

The solution above calls on you to notice that the total number shipped is double the percentage. Therefore, you simply double 14%, add the zeroes, and you get 28, 000. This way you do not even need to set up an equation to cancel out, or for that matter even write anything down. Again, if you were to set up an equation, the key to approximation is to get rid of the cumbersome numbers, i.e. turn 170,280 into 170,000.

Thanks though for sharing your approach – it is always great to see other ways of doing a problem.

a simpler solution while still using approx but only once :

86 are held onto for every 100 in inventory. then how much is in inventory if 170280 are held? (170280*100)/86. Now 14% of this is (14/100)*(170280*100)/86. Cancel the 2 100s, make 86 to 84, eliminate 14 which divides 84 6 times,finally arrive at 28360 by easily dividing 170280 by 6