How to Do Math FAST for the GMAT - Part 3
Welcome to the third installment of our Fast Math series. (Miss part 1? Take a look here.)
Make your life easier on the GMAT: do less Math. (Yes, with a capital-M. :)) I use Math-with-a-capital-M to mean formal, textbook math.
Sure, youre going to have to do some textbook math on the GMAT, but its really not a math test. Business schools don't expect you to have to do paper math in b-school or the real world. Rather, theyre testing how you think about math. And thinking about math in the real world is a lot different than textbook, school-based math.
For one thing, the correct answer on the GMAT is never actually a number or a math term. The correct answer is just (A), (B), (C), (D), or (E). How you get to that correct letter doesnt matter in the slightest.
Check out the earlier installments for principles 1 through 4. Lets dive into the 5th one!
Principle #5: Know when to use fractions, or decimals, or percents
Peyman ate 1/5 of the chocolates, Rishi ate 1/4, and Sharmad ate 1/2. What fraction of the chocolates are left over for me?
(These are students in one of my current classes. Hi, guys!)
Theres a reason why fractions, decimals, and percents are always taught together: they are just different forms of the same number. For example, 60% = 6/10 = 0.6.
You already know all that, right? So whats my point?
Different math operations are easier to do with one of these forms than another. Your job is to know which kinds of things are easier to do in which form.
In the problem above, I have to add together three fractions.
But wait! Adding fractions is super annoying because we have to find common denominators. There are three fractions with three different denominators. Ugh!
Its easier to add numbers in percent or decimal form. For example:
Only 5% of the chocolates are left for me. (And I hope you enjoy my beautiful artwork. :D )
Oh, wait, they asked for the fractional amount left. Thats okay; convert back! If you have your common conversions memorized, then you already know that 5% = 1/20. If not, do this:
5% = 5/100 = 1/20
What skills did I need to have to do the above?
(1) I had to recognize that adding (or subtracting) is easier when using percents or decimals.
(2) I had to convert the fractions over. On another problem, this might have been annoying, but this one had nice fractions. This wasnt just luck! Youll find that, on the GMAT, theyre going to set these shortcuts for the people who are trying to find them.
(3) I had to remember to convert back to fractional form. But this was worth it to avoid having to find common denominators!
And, often, you dont even have to do that last step. The answers might be so far apart that I can tell which one must be right. Is 5% equal to 1/20, 1/10, or 1/5? I know its not 1/10 or 1/5, so it must be 1/20.
Alternatively, the answers might actually be in percent form! Glance at them before you solvethat would be a great clue to convert over to percents right away.
Or the problem might be written in such a way that Im calculating the actual number of chocolates left over, so I dont have to convert to fractions again at the end. Lets say they asked how many chocolates were left and they told me that Rishi ate 10 chocolates (along with all of the original info). Rishi ate 25%, so 25% = 10 chocolates. Therefore, 100% = 40 chocolates, and my 5% would amount to 2 whole chocolates. Yum.
(By the way, if you feel comfortable manipulating percentages, you could go straight from 25% = 10 to 5% = 2. Think about how that shortcut works. And remember principle #1: Don't do math till you HAVE to.)
Okay, now that you know that, think for a moment: If the problem requires you to multiply, which form do you want to use? Fractions, decimals, or percents?
In this case, its easier to use fractions for the same reason that we didnt want to use them to add. When you have numerators and denominators, you can simplify before you multiply, making the numbers easier to combine. The same is true for division. For example:
What is 0.25 divided by 0.375?
Ugh. Okay, here we go.
Same as before: (1) Recognize that you want to use the fraction form. (2) Know your conversions. (3) Convert and solve.
As you continue to practice FDP problems, think about where else you can make your life easier by using a different form.
Final Thoughts
What else have you got for me? As you find other principles / good practices for FDP conversions, share them in the comments. Happy studying!