How to Do Math FAST for the GMAT – Part 1

by on May 22nd, 2016

speed_upI don’t know about you, but I’m pretty lazy when it comes to doing math on paper. Blame constant access to Excel and the calculator on my phone … but I’m completely over doing math on paper.

If you give me a problem that’s going to require half a page of calculations … well, I’m not going to want to do that problem. But on the GMAT quant section, I don’t get a calculator, so how can I still get a 99th percentile score while staying true to my lazy-math desires?

Let’s do some Fast Math!

Principle #1: Don’t do math till you HAVE to

Sure, write down that equation in the question stem. And, sure, set up the math that you would need to do. BUT. If any of the math looks annoying, don’t do it yet. Be patient. Wait a little longer to see whether you really need to do it.

For instance, I want you to tell me what 5/12 of 81 is. Oh, and then I want you to multiply that result by 240.

5/12 of 81 … hmm. 81 isn’t divisible by 12 … but the two numbers do share 3 as a factor, so I can at least simplify a bit and then maybe I’ll need to do some longhand multiplication and division …

Stop right there. On the GMAT, if I’m doing longhand multiplication or division, I’ve missed something. Back up. Look at the whole problem.

Here’s the full math that I asked you to do:

{5/12} *  {81/1} *  {240/1}

That 81 can’t completely cancel out the 12…but the 240 can! Check it out:

 {5/12} *  {81/1} *  {240/1} =  {5/1} *  {81/1} *  {20/1}

Now, let’s see, 5 times 81

Wait! When multiplying a string of numbers, always look to pair 5’s and 2’s first. Why? 5’s and 2’s create 10’s (or multiples of) and those are a whole lot easier to multiply into the rest of the numbers.

(5)(20) = 100

(100)(81) = 8,100

Done!

Whenever you’ve got a multi-step math problem, try to set up as much as you reasonably can and look to simplify before you even think about solving.

Next, when you can’t simplify any further, don’t just do the remaining math left to right. Take a moment to look at the big picture—see whether you can rearrange or approach the math in a way that makes the calculations easier.

Principle #2: Learn shortcuts for when you do have to do the math

You already saw the first example of this in Principle #1:

Shortcut #1: When multiplying a string of numbers, pair off the 5’s and 2’s and multiply them first.

Let’s say that that problem hadn’t had a 20 in it. If we had to multiply 5 and 81…how would you do that?

You could do long multiplication, of course. But you’re lazy like me, right? So we aren’t going to do that.

There are various shortcuts for multiplication, but here’s my favorite one specifically for multiplying by 5:

Take the non-5 number (in this case, 81) and halve it: 81 → 40.5

Move the decimal one place to the right: 40.5 → 405

Done!

Really. That’s it. Try it again: what is 5*37?

I don’t know about you, but this one’s a bit harder for me to divide by 2. The number 36 divided by 2 is 18 … ah, so 37 divided by 2 must be 18.5.

Finally, move the decimal one place to the right: 18.5 becomes 185.

Shortcut #2: If division involves an annoying number, start from a nearby easier number and then work to the annoying number from there.

Shortcut #3: To multiply by 5, first halve the other number, then make it bigger again by moving the decimal one place to the right.

What if you need to divide by 5 instead? Check it out! Let’s do 81 / 5:

Take the non-5 number (in this case, 81) and double it: 81 → 162

Move the decimal one place to the left: 162 → 16.2

Try it again: what is 896 / 5?

Hmm. 900 * 2 = 1,800, so 896 is 8 less that that, or 1,792.

Then, move the decimal one place to the left to make the number smaller: 1,792 → 179.2.

Shortcut #4: To divide by 5, first double the other number, then make it smaller again by moving the decimal one place to the left.

What do you think so far? We’re just getting started. Take a look at our second installment and start looking for Fast Math opportunities during your studies!

3 comments

  • Gotta admit: this was pretty cool. Thank you for sharing, looking forward to more Fast Math!

  • The math on the equation of 896/5 is incorrect. The method used was for multiplication instead of the division method. Should have been 896*2 = 1792. Move the decimal to the left once to arrive at 179.2. 

    • Totally right - thanks for the catch! That's what I get for deciding to change the number last minute at midnight while trying to hit my deadline... :S

      Article has been updated - did I get it right this time?

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