 # The ABCs of the Quantitative Reasoning Section of the GRE

Not a math whiz? Consider yourself a poet instead of a quant?

Not to worry. You don’t have to be a walking calculator to score well on the quant reasoning section of the GRE revised general test. But it will certainly help you to know exactly what to expect when you sit down for the exam and how best to get ready for it.

This section tests your basic math skills, your understanding of elementary mathematical concepts, and your ability to reason quantitatively and to model and solve problems with quantitative methods.

You’re given this part of the test in two 35-minute sections, with about 20 questions in each. So the total time to complete the quant part of the revised GRE general test is 70 minutes.

Some of the questions in the measure are posed in real-life settings, while others are posed in purely mathematical settings. The skills, concepts and abilities are tested in the four content areas: arithmetic, algebra, geometry, and data analysis. The latter includes basic descriptive statistics, such as mean, median, mode, range, standard deviation, quartiles and percentiles; interpretation of data in tables and graphs, among other things.

The content in these areas includes high school mathematics and statistics at a level that is generally no higher than a second course in algebra. Lucky for poets, it does not include trigonometry, calculus or other higher-level mathematics.

You’ll face four types of questions in the Quantitative Reasoning section: quantitative comparison questions; multiple-choice questions in which you’ll select one answer; multiple-choice questions in which you can select one or more answers, and finally, numeric entry questions.

Each question appears either independently as a discrete question or as part of a set of questions called a data interpretation set. All of the questions in a set are based on the same data presented in tables, graphs or other displays of data. You’re allowed to use a basic calculator for this section, and for the computer-based test, the calculator is provided on-screen. For the paper-based test, a handheld calculator is provided at the test center.

EXAMPLES OF QUANTITATIVE COMPARISON QUESTIONS.

Questions of this type ask you to compare two quantities – Quantity A and Quantity B – and then determine which of the following statements describes the comparison. It could be that quantity A is greater or B, or that the two quantities are equal. Yet another possibility: the relationship cannot be determined from the provided information.

Sample 1:

Quantity A   (2) (6)

Quantity B    2 + 6

(A) Quantity A is greater. (B) Quantity B is greater. (C) The two quantities are equal. (D) The relationship cannot be determined from the information given. Explanation Since 12 is greater than 8, Quantity A is greater than Quantity B. Thus, the correct answer is choice A, Quantity A is greater.

Sample 2:

Lionel is younger than Maria.

Quantity A – Twice Lionel’s age.

Quantity B – Maria’s age.

A) Quantity A is greater. (B) Quantity B is greater. (C) The two quantities are equal. (D) The relationship cannot be determined from the information given. Explanation If Lionel’s age is 6 years and Maria’s age is 10 years, then Quantity A is greater, but if Lionel’s age is 4 years and Maria’s age is 10 years, then Quantity B is greater. Thus, the relationship cannot be determined. The correct answer is choice D, the relationship cannot be determined from the information given.

Sample 3:

Quantity A – 54% of 360

Quantity B – 150

(A) Quantity A is greater. (B) Quantity B is greater. (C) The two quantities are equal. (D) The relationship cannot be determined from the information given. Explanation: Without doing the exact computation, you can see that 54 percent of 360 is greater than  of 360, which is 180, and 180 is greater than Quantity B, 150. Thus, the correct answer is choice A, Quantity A is greater.

SIMPLE TEST-TAKING STRATEGIES FOR QUANT COMPARISONS.

Become familiar with the answer choices. Quantitative Comparison questions always have the same answer choices, so get to know them, especially the last answer choice, “The relationship cannot be determined from the information given.” Never select this last choice if it is clear that the values of the two quantities can be determined by computation. Also, if you determine that one quantity is greater than the other, make sure you carefully select the corresponding answer choice so as not to reverse the first two answer choices.

Avoid unnecessary computations. Don’t waste time performing needless computations in order to compare the two quantities. Simplify, transform or estimate one or both of the given quantities only as much as is necessary to compare them.

Remember that geometric figures are not necessarily drawn to scale. If any aspect of a given geometric figure is not fully determined, try to redraw the figure, keeping those aspects that are completely determined by the given information fixed but changing the aspects of the figure that are not determined. Examine the results. What variations are possible in the relative lengths of line segments or measures of angles?

Plug in numbers. If one or both of the quantities are algebraic expressions, you can substitute easy numbers for the variables and compare the resulting quantities in your analysis. Consider all kinds of appropriate numbers before you give an answer: e.g., zero, positive and negative numbers, small and large numbers, fractions and decimals. If you see that Quantity A is greater than Quantity B in one case and Quantity B is greater than Quantity A in another case, choose “The relationship cannot be determined from the information given.”

Simplify the comparison. If both quantities are algebraic or arithmetic expressions and you cannot easily see a relationship between them, you can try to simplify the comparison. Try a step-by-step simplification that is similar to the steps involved when you solve the equation for x, or that is similar to the steps involved when you determine that the inequality  is equivalent to the simpler inequality  Begin by setting up a comparison involving the two quantities, as follows: where is a “placeholder” that could represent the relationship greater than (>), less than (<) or equal to (=) or could represent the fact that the relationship cannot be determined from the information given. Then try to simplify the comparison, step-by-step, until you can determine a relationship between simplified quantities. For example, you may conclude after the last step that represents equal to (=). Based on this conclusion, you may be able to compare Quantities A and B. To understand this strategy more fully, see sample questions 6–9.

EXAMPLES OF MULTIPLE-CHOICE QUESTIONS.

These questions are multiple-choice questions that ask the examinee to select only one answer choice from a list of five choices. You’ll also have some questions that will ask you to answer with one or more choices.

Sample 1:

The figure above shows a circle with center C and radius 6. What is the sum of the areas of the two shaded regions?

A)

B)

C)

D)

E)

Sample 2:

The figure above shows the graph of a function f, defined by  for all numbers x. For which of the following functions g defined for all numbers x does the graph of g intersect the graph of f ?

A)  g (x) = x – 2

B)  g (x) = x +3

C)  g (x) = 2x – 2

D)  g (x) = 2x + 3

E)  g (x) = 3x – 2

SIMPLE TEST-TAKING STRATEGIES FOR MULTIPLE-CHOICE QUESTIONS.

Examine the answer choices. In some questions you are asked explicitly which of the choices has a certain property. You may have to consider each choice separately or you may be able to see a relationship between the choices that will help you find the answer more quickly. In other questions, it may be helpful to work backward from the choices, say, by substituting the choices in an equation or inequality to see which one works. However, be careful, as that method may take more time than using reasoning.

For questions that require approximations, scan the answer choices to see how close an approximation is needed. In other questions, too, it may be helpful to scan the choices briefly before solving the problem to get a better sense of what the question is asking. If computations are involved in the solution, it may be necessary to carry out all computations exactly and round only your final answer in order to get the required degree of accuracy. In other questions, you may find that estimation is sufficient and will help you avoid spending time on long computations.

EXAMPLES OF NUMERIC-ENTRY QUESTIONS.

Sample 1:

One pen costs \$0.25 and one marker costs \$0.35. At those prices, what is the total cost of 18 pens and 100 markers?

\$

Explanation

Multiplying \$0.25 by 18 yields \$4.50, which is the cost of the 18 pens; and multiplying \$0.35 by 100 yields \$35.00, which is the cost of the 100 markers. The total cost is therefore Equivalent decimals, such as \$39.5 or \$39.500, are considered correct. Thus, the correct answer is \$39.50 (or equivalent).

Note that the dollar symbol is in front of the answer box, so the symbol \$ does not need to be entered in the box. In fact, only numbers, a decimal point and a negative sign can be entered in the answer box.

Sample 2:

A merchant made a profit of \$5 on the sale of a sweater that cost the merchant \$15. What is the profit expressed as a percent of the merchant’s cost?

Explanation

The percent profit is percent, which is 33% to the nearest whole percent. Thus, the correct answer is 33% (or equivalent).

If you use the calculator and the Transfer Display button, the number that will be transferred to the answer box is 33.333333, which is incorrect since it is not given to the nearest whole percent. You will need to adjust the number in the answer box by deleting all of the digits to the right of the decimal point (using the Backspace key).

Also, since you are asked to give the answer as a percent, the decimal equivalent of 33 percent, which is 0.33, is incorrect. The percent symbol next to the answer box indicates that the form of the answer must be a percent. Entering 0.33 in the box would erroneously give the answer 0.33%.

SIMPLE TEST-TAKING STRATEGIES FOR NUMERIC-ENTRY QUESTIONS.

Make sure you answer the question that is asked. Since there are no answer choices to guide you, read the question carefully and make sure you provide the type of answer required. Sometimes there will be labels before or after the answer box to indicate the appropriate type of answer. Pay special attention to units such as feet or miles, to orders of magnitude such as millions or billions, and to percents as compared with decimals.

If you are asked to round your answer, make sure you round to the required degree of accuracy. For example, if an answer of 46.7 is to be rounded to the nearest integer, you need to enter the number 47. If your solution strategy involves intermediate computations, you should carry out all computations exactly and round only your final answer in order to get the required degree of accuracy. If no rounding instructions are given, enter the exact answer.

Examine your answer to see if it is reasonable with respect to the information given. You may want to use estimation or another solution path to double-check your answer. 