How to Do Math FAST for the GMAT - Part 1
I dont know about you, but Im pretty lazy when it comes to doing math on paper. Blame constant access to Excel and the calculator on my phone but Im completely over doing math on paper.
If you give me a problem thats going to require half a page of calculations well, Im not going to want to do that problem. But on the GMAT quant section, I dont get a calculator, so how can I still get a 99th percentile score while staying true to my lazy-math desires?
Lets do some Fast Math!
Principle #1: Dont 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, dont 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 [pmath]5/12[/pmath] of [pmath]81[/pmath] is. Oh, and then I want you to multiply that result by 240.
[pmath]5/12[/pmath] of [pmath]81[/pmath] hmm. [pmath]81[/pmath] isnt divisible by [pmath]12[/pmath] but the two numbers do share 3 as a factor, so I can at least simplify a bit and then maybe Ill need to do some longhand multiplication and division
Stop right there. On the GMAT, if Im doing longhand multiplication or division, Ive missed something. Back up. Look at the whole problem.
Heres the full math that I asked you to do:
[pmath]{5/12} * {81/1} * {240/1}[/pmath]
That 81 cant completely cancel out the [pmath]12[/pmath]but the [pmath]240[/pmath] can! Check it out:
[pmath]{5/12} * {81/1} * {240/1} = {5/1} * {81/1} * {20/1}[/pmath]
Now, lets see, [pmath]5[/pmath] times [pmath]81[/pmath]
Wait! When multiplying a string of numbers, always look to pair 5s and 2s first. Why? 5s and 2s create 10s (or multiples of) and those are a whole lot easier to multiply into the rest of the numbers.
[pmath](5)(20) = 100[/pmath]
[pmath](100)(81) = 8,100[/pmath]
Done!
Whenever youve 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 cant simplify any further, dont just do the remaining math left to right. Take a moment to look at the big picturesee 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 5s and 2s and multiply them first.
Lets say that that problem hadnt had a 20 in it. If we had to multiply 5 and 81how would you do that?
You could do long multiplication, of course. But youre lazy like me, right? So we arent going to do that.
There are various shortcuts for multiplication, but heres 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. Thats it. Try it again: what is [pmath]5*37[/pmath]?
I dont know about you, but this ones 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! Lets do [pmath]81 / 5[/pmath]:
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 [pmath]896 / 5[/pmath]?
Hmm. [pmath]900 * 2 = 1,800[/pmath], so [pmath]896[/pmath] 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? Were just getting started.Take a look at our second installmentand start looking for Fast Math opportunities during your studies!