Math Ability questions are multiple-choice math questions that give you five possible answer choices. You are required to select the best answer. Problem Solving questions test your ability to solve mathematical problems involving arithmetic, algebra, and geometry, as well as word problems, by using problem-solving insight, logic, and the application of basic skills.

The basic skills necessary to do well on this section include high school arithmetic, algebra, and intuitive geometry - no formal trigonometry or calculus is necessary. These skills, along with logical insight into problem-solving situations, are covered by the examination.

Directions: Solve each problem in this section by using the information given and your own mathematical calculations. Select the correct answer of the five choices given. Use the scratch paper given for any necessary calculations.

All scratchwork is to be done on the paper given at the test; get used to referring back to the screen as you do your calculations and drawings. You are looking for the one correct answer; therefore, although other answers may be close, there is never more than one right answer.

Here are just a few samples of what you can expect in the Math Ability portion of the GRE General Test.

Tip: Always carefully focus on what you are looking for to ensure that you are answering the right question.

Sample 1

If x + 6 = 9, then 3x + 1 =

  1. 3

  2. 9

  3. 10

  4. 34

  5. 46

You should first focus on 3x + 1, because this is what you are solving for. Solving for x leaves x = 3, and then substituting into 3x + 1 gives 3(3) + 1, or 10. The most common mistake is to solve for x, which is 3, and mistakenly choose A as your answer. But remember, you are solving for 3x + 1, not just x. You should also notice that most of the other choices would all be possible answers if you made common or simple mistakes. The correct answer is C. Make sure that you're answering the right question.

Sample 2

An employee's annual salary was increased $15,000. If her new annual salary now equals $90,000, what was the percent increase?

  1. 15%

  2. 16-2/3%

  3. 20%

  4. 22%

  5. 24%

Focus on what you are looking for. In this case, percent increase.

Percent increase = change/starting point. If the employee's salary was increased $15,000 to $90,000, then the starting salary was 90,000 - 15,000 = 75,000. Therefore,

percent increase = 15,000/75,000 = 1/5 = 20%

The correct answer is C.

Tip: "Pulling" information out of the word problem structure can often give you a better look at what you are working with, and therefore, you gain additional insight into the problem. Organize this information on your scratch paper.

Sample 3

Which of the following is equal to 1/5 of 0.02 percent?

  1. 0.4

  2. 0.04

  3. 0.004

  4. 0.0004

  5. 0.00004

Simplifying this problem first means changing 1/5 to .2. Next change 0.02 percent to 0.0002 (that is, .02 X .01 = 0.0002).

Now that you have simplified the problem, multiply .2 X 0.0002, which gives 0.00004. The correct answer is E. Notice that simplifying can make a problem much easier to solve.

Tip: If you immediately recognize the method or proper formula to solve the problem, go ahead and do the work. Work forward.

Sample 4

What is the greatest common factor of the numbers 18, 24, and 30?

  1. 2

  2. 3

  3. 4

  4. 6

  5. 12

The largest number that divides evenly into 18, 24, and 30 is 6. You could've worked from the answers, but here you should start with the largest answer choice, because you're looking for the greatest common factor.

The correct answer is D.

Tip: If you don't immediately recognize a method or formula to solve the problem, you may want to try a reasonable approach and then work from the answer choices. Try to be reasonable.

Pop Quiz!

Which of the following could be a description of how to begin solving the following system of equations using the substitution method?


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