### The GMAT’s Favorite Equation

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After you do even a little bit of studying for the GMAT, you’ll probably start to realize something: the test is as repetitive as a Katy Perry song. You’ll see that the one hard question you’ve never quite understood is actually the same old game, reformulated in some subtle way, but ultimately similar to what you’ve learned before.

This is a good thing, and it’s part of the reason why this test is so learnable (were it not, we’d be out of a job). But the fact is, it’s probably even more repetitive than you’re aware. It’s definitely more repetitive than I was aware until I’d done a few years of teaching. But the more I teach the test, the more I realize certain high-level principles permeate the GMAT.

For example, you probably realize that a bunch of problems about distance and rate are similar. But maybe you haven’t fully connected these to questions about revenue.

“What? What does revenue have to do with distance?”

Well, as it turns out, they’re both a form of “the GMAT’s favorite equation.” This is a secret formula that underlies a great deal of GMAT word problems. It deserves a dramatic unveiling, but since this is a blog, a cool GIF is about all we got:

#### THE GMAT’S FAVORITE EQUATION IS…

(Total # of Thing A) = (# of Thing A’s per Thing B) x (Total # of Thing B)

Seriously. The GMAT gets off to this equation so much my company is letting me use a turn of phrase as crass as ‘gets off to.’

Let’s start with the form you’re most familiar with. You know the old equation, D=RxT. Using units of ‘miles’ and hours,’ all that amounts to is:

(Total Miles) = (# of Miles per Hour) x (Total Hours)

You might have realized already that this is very similar to the work equation, W=RxT. Well, that’s just:

(Total jobs done) = (# jobs per time unit) x (Total time units)

But now let’s think about revenue. Revenue for selling some item is the price of the item times the number of items sold. But what is a ‘price?’ It’s just the number of dollars for one unit. So:

(Total Dollars) = (# of Dollars per Unit) x (Total Units)

Exact same equation. How about averages? Those are different, yeah?

Nope.

Take a school with an average number of students in each classroom:

(Total students) = (Average number of students in each classroom) x (Total Classrooms)

An average, if you think about it, is just a rate.

Even something like ‘there are twice as many boys as girls’ turns into:

(Total Boys) = (2 boys per girl) * (Total Girls)  or B=2G

The number of people grew by 30%:

(Total ‘New’ People) = (130 New People per 100 ‘Old’ People) x (Total ‘Old’ People) or N = 1.3O

Jill has 20% fewer coffee cups than Darryl has:

(Jill’s total coffee cups) = (80 of Jill’s coffee cups per 100 of Darryl’s coffee cups) x (Darryl’s total coffee cups) or J = (4/5) * D

Have you figured out what’s going on here?

In the end, it’s all about ratios. That’s all it ever is. Even the word ‘rate,’ you might see now, sounds like ‘ratio.’ The GMAT is obsessed with this.

A percent change is just a ratio of the amount of items now to the amount of items before. An average is just the ratio of the amount of some ‘stuff’ to the amount of another ‘stuff.’ A ‘percent’ is just a ratio of the amount of a ‘thing’ to 100 units of another ‘thing.’  Price is just a ratio of the number of dollars to a single item.

The GMAT is obsessed with ‘parts’ and ‘wholes,’ and with the distinction and relationship between relative values (ratios) and actual values (totals). Hence, the favorite equation.

This shows up on both Quant and Verbal. Take a look at #655 in your 2017 OG. After you’ve done it, see if you can specify the form of the favorite equation that is used in this problem.

*Jeopardy music*

(Total Ash) = (Amount of Ash per Truckload burnt) x (Total # Truckloads burnt)

The problem says the city will reduce the Total Ash by half reducing the Total Truckloads by half, but what about that ratio in the middle? That’s where we’re playing here. You’ll find this same game in several other CR questions—keep your eyes peeled for it. Parts and wholes, rates and totals.

Think about how else they could use this relationship for this ash situation. What if—instead of burning half the total truckloads from last year—their plan to lower total ash was to recycle enough from each truck such that each truck of refuse makes less ash? What must be assumed then?

That the ‘# of truckloads’ doesn’t increase enough to offset this decrease in the rate of ash per truck. Parts and wholes.

Take a look at page 534. See if you can identify which of these questions also use(s) the favorite equation.

“Okay, this is all interesting… I guess… But so what? How does this help me?”

In a few ways:

1) It specifies one of the ‘hidden gears’ of the test. Understanding and recognizing it will help you understand the test better.

2) When in doubt on a word problem, look for a chance to set up a form of this ‘favorite equation.’ How could you express the values for the two totals and the ratio in between? A number? A variable? An expression? See how you can set up this relationship.

3) It shows how your improvement on a question can permeate throughout the test, even across the Quant/Verbal sections, so long as you review that question deeply, correctly, and frequently.

Now go out and find this thing all over the test. 📝

Want some more GMAT tips from Reed? Attend the first session of one of his upcoming GMAT courses absolutely free, no strings attached. Seriously.

Reed Arnold is a Manhattan Prep instructor based in New York, NY. He has a B.A. in economics, philosophy, and mathematics and an M.S. in commerce, both from the University of Virginia. He enjoys writing, acting, Chipotle burritos, and teaching the GMAT. Check out Reed’s upcoming GMAT courses here.

1. Rahul Sehgal January 12, 2018 at 5:02 am

An excellent write up. Thanks for sharing !