# GRE Math Techniques: Plugging in and reverse plugging in

Hello, GRE students, and welcome back to our series on the specifics of GRE math. (As I like to remind folks, the testmakers want to call it Quantitative Reasoning, but you and I can just call it math.)

So far, we've covered the basics of arithmetic and algebra on the GRE. Next week, we'll discuss geometry, but I wanted to pause and cover two of the most important techniques you can use to get the GRE score you deserve. They are Plugging In and Reverse Plugging In.

## Remember: the GRE isn't a math test

When your tenth grade math teacher gave you a quiz, the reason behind it was to assess how well you had learned the material. This is why you had to—everyone say it with me—*show your work*. The GRE, on the other hand, only cares about the answer.

Is there a place for the "right" way to do a math question? Sure, if it's the most efficient, but most of the time you'll want to approach the math from a different angle.

Let's see what Plugging In can do for us.

## Plugging in

We'll start off with a very simple question just so we can get the gist of the technique:

Jerry is X years old. Bobby is 5 years younger than Jerry. In terms of X, how old will Bobby be in Y years?

1. Y(X - 5)

2. X(Y - 5)

3. X + Y - 5

4. X + Y

5. Y/5 + Y

As I said: this is not a tough question, and you could most likely do it algebraically, but why? *If I can use arithmetic instead of algebra, then I should do that every time.*

Let's employ the Plugging In technique.

Instead of "X" and "Y" we can substitute integers and—as long as we follow the rules of the question—make our lives easier. We'll make X = 10 and Y = 20, and just trust that we'll remember that. Right?

No! We write our numbers down! Don't ever leave things in your head on the GRE.

Now, once we've written down our numbers, we need to solve the problem using those numbers. Here's the new question:

Jerry is 10 years old. Bobby is 5 years younger. How old will Bobby be in 20 years?

Well, if Jerry is 10 and Bobby is 5 years younger, then Bobby is currently 5 years old. And in 20 years, Bobby will be 25 years old. Remember where you wrote down what your X and Y was? Right under that, you're going to write 25 and you'll circle it or put it in a box or a star: something that will remind you that "25" is your answer.

So, we have our question, “How old will Bobby be in 20 years?” and we will go through the answer choices substituting X = 10 and Y = 20, seeking a goal value of 25.

*20(10 - 5) would equal 100, so this is not our answer.**10(20 - 5) is equal to 150, which is also wrong.**10 + 20 - 5 equals 25, which is our answer.*

Should we stop there? On this type of question, one where there's no possibility of the variables standing for negative, fractional, or exponential numbers, then you should choose answer choice C and move on.

## Reverse plugging in

All tests have a fatal flaw, and the fatal flaw of any standardized test--including the GRE--is this: the correct answer is written down in front of you. Now, it's hidden within four wrong answers, but it's still there. An analogy I often use with my students is the toy that teaches shapes, the one where the baby has to put the triangular block through the triangular hole. The block can only go through one hole.

Let's try this technique, and again we will use an easier question that you'll probably see on the GRE.

Phil spent 1/4 of his paycheck to repair his motorcycle, and then paid the registration and insurance, which each cost 1/3 of the remainder of his paycheck. Phil had $0 before he received his check. He now has $231 left. How much was his check for?

A. $2772

B. $1622

C. $924

D. $870

E. $693

Always start with choice C for Reverse Plugging In. Why? Because our answers go from smallest to largest! By starting in the middle, we can be most efficient. If C is too small, then we go the next bigger answer, and vice versa. By starting in the middle, we can limit the amount of times we'll need to work through the problem to twice. If C is too small, and so is "D," then we choose E and move on. Had we started at A, we would have needed to do the work four times.

Let's do the math, starting with answer choice C: Phil’s paycheck was $924, and he spent 1/4 on the repair. One-quarter of $924 is $231. We subtract that from our original number, leaving us with $693. One-third of $693 is $231, so we subtract that for the registration, and again for the insurance. (693 - 231 - 231). This leaves us with $231, which is what the problem was asking for. As such, C is our answer.

Obviously, there's more to these techniques, and they both require practice, but with The Economist's GRE program and a proper study schedule, you'll be Plugging In and Reverse Plugging In in no time!

Next up: Geometry!