We all make mistakes. That being said, you should strive to never make the same mistake twice. If you understand some of the most common math mistakes, you can use your awareness to actively avoid falling into these traps.

## Mistake #1: Not reading the problem carefully

Under timed conditions, you may feel compelled to rush. But remember, by misreading a word (or not reading it entirely), you can make a relatively straightforward problem seem intractable. You may flail about the answer choices, picking one—usually the incorrect one—that happens to be somewhat close to your answer.

Worse yet, you may get a numeric entry question and blithely enter in the wrong answer—something you could easily have avoided doing had you read the question carefully.

Before you begin attempting a solution, you need to know *exactly* what the question is asking you to solve. Sometimes, students will see that a variable like ‘x’ is involved, and they will immediately start solving for ‘x’. They hastily input an answer, only to realize later that the prompt was actually asking for the value of ‘1/x’.

Never start blindly solving a problem. Always acknowledge what you are specifically seeking.

## Mistake #2: Flubbing the math

Many common math mistakes result from forgetting something as minor as writing a negative sign. Other times, simple mathematical errors—like thinking that 16 x 5 = 90—can be very costly. Math is about precision, so use your prep time to become an efficient and unerring human calculator.

## Mistake #3: Making unwarranted assumptions

When presented with geometric diagrams, students often erroneously assume the figure accurately represents the information given by the prompt. However, there’s no guarantee that a figure will be drawn to scale on the GRE. If we see the following on the GRE:

Beware—although this figure *looks* like a square, there’s no information to prove it. We need to have data that irrefutably shows ∠P = ∠Q = ∠R = ∠S = 90º, and that PQ = QR = RS = PS to confirm this shape is a square. Otherwise, the shape above could actually be a rhombus, or a rectangle, or even an irregular quadrilateral. So be wary of diagrams—all assumptions need to be backed up by geometrical reasoning.

## Mistake #4: Confusing the units

It’s important to keep your units straight, especially when handling work rate problems. For example:

- If a problem is asking you
*how long*a machine takes to make an order, make sure your answer reflects hours, or seconds, or some metric of time. - Or if a problem is asking about a
*rate*, then your answer needs to be in a form like widgets per hour, or widgets per second. - Sometimes, tricky problems will ask you to find the
*inverse rate*, which reverses the above: seconds per widget, or hours per widget.

In any case, you’ll want to read the question carefully and know exactly what you’re solving for.

## Mistake #5: Forgetting 0 and 1

This is one of the common math mistakes that can trip you up on the GRE test. Especially in Quantitative Comparison, you always want to make sure to plug in 0 and 1 if the constraints permit doing so. Oftentimes plugging in a 0 or 1 will prove the exception, thus making the answer (D).

Since this is a common GRE mistake, we’ve provided a practice problem so you can try this technique for yourself.

#### Practice Problem:

*x* is a non-negative integer.

Column A | Column B |
---|---|

2x^{2} | 3x^{3} |

A) The quantity in Column A is greater.

B) The quantity in Column B is greater.

C) The two quantities are equal.

D) The relationship cannot be determined from the information given.

### Answer and Explanation:

Remember to plug in 0 and 1. If you don’t, you will choose the obvious—but actually incorrect—answer (B). However, if *x* is zero the two columns are equal. Because of this one instance, we cannot say for sure which side is bigger. Thus (D) is the correct answer.

## Mistake #6: Forgetting the smallest prime number

Remember, 2 is the smallest prime number. It is the only *even* prime. 1 is NOT a prime.

## Mistake #7: Mixing up “must be” and “could be”

There is a subtle, but important difference here. If a question is phrased “must be,” then the answer you choose must always hold true for the conditions stated in the problem. “Could be” means that the answer only holds true in certain instances (i.e., for certain numbers).

All of this makes a lot more sense when in the context of the problem. So, let’s take a look!

#### Practice Problem:

*c* and *d* are prime numbers. If *c – d* is an odd prime, then which of the following must be true?

A) *c*is even

B) *d* is odd

C) *c x d* is odd

D) *d* is even

E) *c x d – c* is even

### Answer and Explanation:

First off, don’t let the variables throw you. There is an answer, so there must be some pattern that you have to discern.

If you remember, I mentioned that 2 is the only even prime. Thus, the rest are all odd. The question says that *c – d* is an odd prime. The only way to get an odd number when we subtract two numbers is that one number must be odd, and one must be even.

Since 2 is the only even prime, we know that 2 must be *d*. (*c* cannot equal ‘2’ because *c – d* would end up being a negative number, and primes can’t be negative.)

We don’t have to know what exact number *c* equals, as long as *c – d* equals an odd prime. *c = 5* is perfect. We plug in those values into the question.

Only (D) works as the correct answer. And we know that *d* must be even, because *d* must equal 2, an even number.

## Final Thoughts on Common Math Mistakes

You’ll definitely make some common math mistakes as you study, and that’s okay. Any time an error comes up, treat it as an opportunity to correct a misguided approach. Keep an error log, and make it your goal to never repeat a mistake.

*Editor’s Note: This post was originally published in February 2012 and has been updated for freshness, accuracy, and comprehensiveness.*

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