# Quantitative Reasoning

The main objective of the GRE quantitative segment is to assess the test-taker’s grasp of the basic math concepts.Candidates taking the computer-based test are provided with on-screen calculators, and those taking the paper-based test are provided handheld calculators. However, the ETS GRE website contains some guidelines that advise against the use of the calculator for some type of questions.On your GRE, you will see all the Quantitative Comparison questions first, then Problem Solving questions. Near the end of the Problem Solving questions, you’ll encounter the Data Interpretation questions, presented as a set.

Some of the Quantitative Reasoning questions are posed in real-life settings, while others are posed in purely mathematical settings. Many of the questions are “* word problems,”* which must be translated and modeled mathematically.The most common Problem Solving questions are standard multiple-choice questions with 5 choices and one correct answer. Variants include questions that ask you to select 1 or more answer choices from a list (all-that-apply) and questions that ask you to enter your answer in a box (numeric entry).

The * Quantitative Reasoning section* of the GRE

^{®}General Test contains four types of questions:

Comparison Questions**Quantitative**- Multiple-choice Questions — Select One Answer Choice
- Multiple-choice Questions — Select One or More Answer Choices
- Numeric Entry Questions

**Concepts In** **Quantitative Reasoning section**

**Concepts In**

**Quantitative Reasoning section**

- Algebra
- Arithmetic
- Geometry
- Data Analysis

## Sample questions

### Algebra

The review of algebra begins with algebraic expressions, equations, inequalities, and functions and then progresses to several examples of applying them to solve real-life word problems. The review of algebra ends with coordinate geometry and graphs of functions as other important algebraic tools for solving problems.

**1.**Find an algebraic expression to represent each of the following.

(a)The square of *y *is subtracted from 5, and the result is multiplied by

(b)Three times *x *is squared, and the result is divided by

(c)The product of *x *+ 4 and *y *is added to 18

**Correct answer **

(a)37 (5 –*y*^{2} ),or 185 – 37 *y*^{2}

(b)(3*x*)^{2 }/7 , or 9*x*^{2}/7

(c) 18 + ( *x *+ 4)( *y *), or 18 + *xy *+ 4 *y*

*2. *For a given two-digit positive integer, the tens digit is 5 more than the units digit. The sum of the digits is 11. Find the integer.

*2.*

**Correct answer 83**

**3.**What is the value of *f *( *x*) = 3*x*^{2} – 7*x *+ 23, when *x *= -2?

**Correct answer – ****49**

*4. *If the ratio of 2*x *to 5*y *is 3 to 4, what is the ratio of *x *to *y *?

*4.*

**Correct answer- 15 to 8**

*5.*. Kathleen’s weekly salary was increased by 8 percent to $712.80. What was her weekly salary before the increase?

*5.*

**Correct answer – $660**

*6. *A theater sells children’s tickets for half the adult ticket price. If 5 adult tickets and 8 children’s tickets cost a total of $81, what is the cost of an adult ticket?

*6.*

**Correct answer – $9**

**Arithmetic**

The review of arithmetic begins with integers, fractions, and decimals and progresses to the set of real numbers. The basic arithmetic operations of addition, subtraction, multiplication, and division are discussed, along with exponents and roots. The review of arithmetic ends with the concepts of ratio and percent.

*1. *Which of the integers 2, 9, 19, 29, 30, 37, 45, 49, 51, 83, 90, and 91 are prime numbers?

*1.*

**Correct answer – 2, 19, 29, 37, and 83**

*2. *If a person’s salary increases from $200 per week to $234 per week, what is the percent increase in the person’s salary?

*2.*

**Correct answer- 17% **

*3. *If an athlete’s weight decreases from 160 pounds to 152 pounds, what is the percent decrease in the athlete’s weight?

*3.*

**Correct answer – 5%**

*4. *A particular stock is valued at $40 per share. If the value increases by 20 percent and then decreases by 25 percent, what will be the value of the stock per share after the decrease?

*4.*

**Correct answer $36 per share**

*5. *There are a total of 20 dogs and cats at a kennel. If the ratio of the number of dogs to the number of cats at the kennel is 3 to 2, how many cats are at the kennel?

*5.*

**Correct answer- 8 cats**

**Geometry**

The review of geometry begins with lines and angles and progresses to other plane figures, such as polygons, triangles, quadrilaterals, and circles. The review of geometry ends with some basic three-dimensional figures. Coordinate geometry is covered in the Algebra part.

*1. *What is the sum of the measures of the interior angles of a decagon (10-sided polygon) ?

*1.*

** Correct answer – **1, 440°

*2. *If the polygon in exercise 4 is regular, what is the measure of each interior angle?

*2.*

**Correct answer – 144°**

*3. *The lengths of two sides of an isosceles triangle are 15 and 22. What are the possible values of the perimeter?

*3.*

**Correct answer- 52 and 59**

*4. *Triangles *PQR *and *XYZ *are similar. If *PQ *= 6, *PR *= 4, and *XY *= 9, what is the length of side *XZ *?

*4.*

**Correct answer- 6**

**Data Analysis**

The review of data analysis begins with methods for presenting data, followed by counting methods and probability, and then progresses to distributions of data, random variables, and probability distributions. The review of data analysis ends with examples of data interpretation

*1. *Martha invited 4 friends to go with her to the movies. There are 120 different ways in which they can sit together in a row of 5 seats, one person per seat. In how many of those ways is Martha sitting in the middle seat?

*1.*

** Correct answer – **24

*2. *How many 3-digit positive integers are odd and do not contain the digit 5 ?

*2.*

** Correct answer – **288

*3. *From a box of 10 lightbulbs, you are to remove 4. How many different sets of 4 lightbulbs could you remove?

*3.*

** Correct answer – **210

*4. *A talent contest has 8 contestants. Judges must award prizes for first, second, and third places, with no ties.

*4.*

###### (a) In how many different ways can the judges award the 3 prizes?

###### (b)How many different groups of 3 people can get prizes?

** Correct answer – **(a) 336

(b) 56

*5. *If an integer is randomly selected from all positive 2-digit integers, what is the probability that the integer chosen has

*5.*

###### (a) a 4 in the tens place?

###### (b)at least one 4 in the tens place or the units place?

###### (c)no 4 in either place?

*Correct answer – (a) *__1__9

__(b)1__5

__(c)4__5

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