Conquering Calculations

by on December 29th, 2012

What is the greatest challenge students face on the GMAT?

Timing, anyone?

One of the greatest challenges of the GMAT is the limited time available to do each question. While, pacing oneself during the test is quite a subject in itself, this article focuses on tips that can help you save time when confronted with tedious calculations.

No, this article is not about ballparking. Instead this article is about actual calculations that can help you save time. The idea is not to estimate but to calculate – just that in this case the calculations are simpler.

Let’s try an example:

What is 199*41?

Errr…no way I am ever going to do this multiplication on the exam. I will just approximate!

Sure, you can do that, and do not get me wrong, there is no harm in doing that. However, you can actually do the calculation without scratching your head or pulling out your hair.

Here is how:

199 * 41 can be rewritten as (200 - 1)*(40 + 1) which is

= 200(40 + 1) - 1 (40 + 1)

= 8,000 + 200 - 40 - 1

= 8,200 - 41

= 8,159.

I can almost hear you say, I would rather just multiply the two numbers than follow what you just did. Or you are wondering, why not just do 200 * 40 and choose the closest answer choice. Fair enough but what if you need to find 185 * 37?

In this case, a rough estimate can be tricky.

However, this calculation can be easily broken down into:

185 * 37

= (180 + 5) (40 - 3)

= 180(40 - 3) + 5 (40 - 3)

Now, how on earth am I supposed to know what 18 * 4 equals?

Good question; you don’t!

18 * 4 = (20 - 2) * 4 = 80 - 8 = 72

Likewise, 18 * 3 = (20 - 2) * 3 = 60 - 6 = 54

So, 180(40 - 3) + 5 (40 - 3)

= 7,200 - 540 + 200 - 15

= 7,400 - 555

What do I do now?

The same approach can be easily applied to subtraction.

Try this,

7,400 - 555

= 7,400 - 400 - 155

= 7,000 - 155

= 7,000 - 100 - 55

= 6,900 - 55

= 6,845

The idea is to break down calculations into simpler and smaller steps.

Let’s try that once more.

123 * 45 + 67 - 89

= (120 + 3) (40 + 5) + 67 - 89

= 120(40 + 5) + 3(40 + 5) + 67 - 89

[12 * 4 = (10 + 2) 4 = 40 + 8 = 48]

= 4,800 + 600 + 120 + 15 + 67 - 89

= 4,800 + 600 + 120 + 15 + 70 - 3 - 90 + 1

= 5,400 + 206 - 93

= 5,400 + 206 - 93

= 5,606 - 100 + 7

= 5,506 + 7

= 5,513

For starters, this approach can appear more complicated and daunting than simply multiplying 123 with 45, adding 67 to the product, and finally subtracting 89.

However, with practice, you will realize that not only is the above approach simpler but also a big time saver if you invest time and effort to master it.

Still not convinced?

Try the following calculation both ways and decide for yourself.

789 * 258 + 126 - 14 * 56

6 comments

  • Just a simple suggestion for:
    What is 199*41?

    Instead of approximating both 199 and 41, if only 199 is approximated to 200 the calculation can be done in less then 15 second (figure of speech of course)
    200*41 (simply think of 41*2=82 and then place the 2 two zeros)
    200*41= 8200 (then reduce the one extra 41 place into calculate i.e. 41-200=159)
    =8159

  • I am surprised to read statement such as "Now, how on earth am I supposed to know what 18*4 equals?" Anybody aiming to beat the GMAT should at least have grasp over multiplication tables up to 20. I am sure they can, but such statements do not make the article interesting. But of course this is just my opinion.

  • I expect better from the Economist. Total agreement with Saif and Chintan!

  • Before I use a complicated way like suggested, I'd rather multiply it that way: http://imageshack.us/a/img690/8366/multiplication.png.
    Takes only a few seconds.

  • I agree with Saif, I felt this method just made it more complicated. My instinct was the same as his 200x40= 8200 - 41= 8159. And I also agree with Chintan, my GMAT tutor told me that you need to redrill multiplication up to the twenties plus memorize a certain number of number sequences (prime numbers, etc) ready to go as he says he finds the biggest problem for many people is time. 

  • Sorry meant to say 200 x41! not 200 x 40...

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