All About GRE Quantitative Reasoning

The Quantitative Reasoning section tests the candidate’s competency in Maths. The questions involved are taken from topics like – Algebra, Geometry, Arithmetic and Data Analysis. The candidates needn’t worry about tougher Maths topics like Calculus, Trigonometry, etc. The GRE Quantitative segment has two sections each having 20 questions each and the candidate has 35 minutes per section.

Quantitative Reasoning Question Types

There are four types of questions that are asked in the GRE Quantitative Reasoning section. They are:

• Quantitative Comparison
• Multiple Choice- Select one answer
• Multiple Choice- Select one or more answers
• Numeric Entry

All four types of questions can be bundled together for a single question. A Data Interpretation question gives data and then a set of questions are asked based on it. This set can consist of all the types of questions that are mentioned above.

Quantitative Comparison

Question of this type asks the candidate to compare two given mathematical statements, A & B, and choose one of the FIVE options.

A. Quantity A is greater

B. Quantity B is greater

C. Quantity A and B are the same

D. The two quantities are equal

E. The relation cannot be determined

Multiple Choice – Select one

This is a regular multiple-choice question, with just one correct answer. The test taker is asked to choose only one answer

Multiple Choice – Select one or more

This question is a slight variation of the traditional multiple-choice questions. There will be more than one correct answer, and the test taker is expected to select all the correct answers. Choosing partial answers doesn’t give the candidate any marks, instead, marks are awarded only if all correct answers are selected.

Numeric Entry

Questions of this type ask the candidate to type in the correct answer using the keyboard. If the answer contains a numerator and a denominator, then there are two separate boxes for them. Both can be filled in using the keyboard.

GRE Quant Sections

The quantitative reasoning aims to find out the understanding, interpreting and analyzing the ability of a candidate, through the presented quantitative information. The questions are of the high-school level. This section can be further divided into 4 major sections: Arithmetic, Algebra, Geometry, Data Analysis. 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. It points out that the powers of reasoning and estimating may be more effective and less time-consuming in these cases. The detailed syllabus for GRE quant is as follows:

Arithmetic-

Arithmetic bags 29% of the Quantitative Reasoning questions. Percentage and number properties are the most tested topics of this section as they have the highest question ratio. It lies in the midsection of the spectrum as per the experts, which means it is neither too tough nor too easy questions are given in the exam. Following topics fall under arithmetic:-

1. Integers
2. Fractions
3. Exponents and Roots
4. Decimals
5. Real Numbers
6. Ratio
7. Percentages

Let’s have a look at the examples, portraying how a different approach towards solving a question can help you to save your precious time.

1. A Shopkeeper sells a good at a Certain Price and makes a loss of 8%. If he would have increased the selling Price by Rs 900 he could have gained 7% from the transaction. Find the Actual Cost of the Article?

Options:

A. 5000

B. 7200

C. 6850

D. 6000

E. 8100

Explanation:

Let us Assume the Cost Price be Rs 100

So while Selling the Person Makes a Loss of 8 %

Loss of 8% on Rs 100 = Rs 8.

So the Selling Price = Cost Price – Loss

Selling Price = 100 – 8 = Rs 92

Now,

If he adds Rs X with the Current Selling Price he Gains 7% i.e. 7% Profit on Cost Price.

I.e. profit = Rs 7 on Cost Price of Rs 100.

Therefore Selling Price + Rs X = 107

Selling Price = 92 Rs

Therefore Rs X = 15

But we Rs X was Rs 900 (given in Question)

So we assumed CP is 100 which corresponds to 100% of the Value

So if 15% Corresponds to Rs 900

Then 100% Corresponds to?

900 x 100/15 = Rs 6000(Cross Multiplication)

Hence Option D) 6000 is the Answer i.e. The Cost Price of the Article.

Alternative Approach (Required for GRE):

If the Shopkeeper is selling the Good at a Certain Price and making 8% loss and If he adds Rs 900 and now goes into 7% Profit. That means Earlier he was in 8 % Loss now he is in 7% Profit after addition of Rs 900.

So he Covered the Distance or the Gap: 8% + 7% = 15% by Adding Rs 900.

As the profit & loss is always calculated on Cost Price

15% of Cost Price = 900

So 100% of Cost Price =?

900×100/15 = Rs 6000

Now, look at another question portraying how a change in approach can simplify the solution.

1. At her current job, Mary gets a 1.5% raise twice per year. Which of the following choices represents Mary’s current income y years after starting the job at a starting salary of s?

Options:

A. s (1.5)2y

B. s y

C. s

D. s (1.5) y/2

E. s (1.015) y/2

Explanation:

‘S’ is the current Salary for Mary.

Now every year she gets a raise Twice i.e. of 1.5% of Salary.

In terms of Value or it would (100% +1.5%) S = (101.5%) S

So it’s happening twice a year for ‘y’

Therefore, as it is done twice a year,

The only equation which satisfies the above condition is equation 3:

As by seeing the option it is twice for how many years ’y’ hence it should be a successive multiplication twice for y years hence the above equation is our answer.

Option C)

Geometry-

Geometry comprises just 14% of the questions that are asked in the GRE quant section. But they are considered to be the toughest questions of all, by many students. The most difficult Geometry questions are generally related to topics like triangles and quadrilaterals. Following are the geometrical concepts asked in the GRE exam::

1. Lines and Angles
2. Polygons
3. Triangles
4. Quadrilaterals
5. Circles
6. 3-D Figures

1. A rectangular box is 10 inches Wide, 10 inches long & 5 inches high. What can be the greatest possible distance, in inches, between any two points?

Options:

A. 5

B. 10

C. 20

D. 15

E. 5

Explanation:

There can ‘n’ no. of Points on the body and as it’s a Rectangular Box which is also called a Cuboid.

So which 2 points are the Farthest or at the maximum Distance?

Best way to answer such a question is to Draw the Diagram or visualize.

Let a, b and c be the 3 measurements of the box as already given in the question

Hence the points which are the body diagonal would be the furthest.

So from one topmost Corner to the bottom-most corner is called a Body Diagonal and on one face is called a Face Diagonal.

So, what would be the Length of Body Diagonal?

Length of Face Diagonal (Pythagoras Theorem): 10^2+ 10^2+ 5^2.

So Again Body Diagonal would be =15

Hence Option D is the Answer.

Alternative Approach (Required for GRE):

The space diagonal can also be calculated using the formula= (diagonal^2 = length^2 + width^2 + height^2)

Body Diagonal Direct Formula Approach derived from Above method:

=d^2=a^2+b^2+c^2

= 10^2+10^2+5^2 = √225= 15

Hence, option D is the answer

Algebra-

Almost 29% questions in the GRE Quant syllabus are from this part of maths. On the spectrum of easy and tough, as per the experts, algebra lies more on the easier side. But most of the time, one or two questions in algebra always turn out to be the toughest questions, which majority of GRE aspirants answer incorrectly. Following are the topics, which fall under algebra:

1. Operations with Algebraic Expressions
2. Rules of Exponents
3. Solving Linear Equations
4. Solving Quadratic Equations
5. Solving Linear Inequalities
6. Functions
7. Applications
8. Coordinate Geometry
9. Graphs of Functions

What is the number of real solutions of the equation – 7|x| – 18 = 0?

Options:

A. 2

B. 4

C. 3

D. 1

E. 5

Explanations:

– 7|x| – 18 = 0

Here |x| is always positive,

But if we want to remove Modulus we have 2 Conditions.

Condition 1:

X > 1

In this case the Modulus opens Positive hence,

The Equation becomes,

– 7x – 18 = 0

By solving this equation we get,

– 9x + 2x – 18 = 0,

(x+2)(x-9) =0

As x > 1,

We have X = 9, as X cannot be -2

Condition 2:

X < 1

In this case the Modulus opens negative hence,

The Equation becomes,

+7x – 18 = 0

By solving this equation we get,

+9x – 2x – 18 = 0,

(x-2)(x+9) =0

As x < 1,

We have X = -9, as X cannot be 2,

Therefore we have two real solutions for the equations

Option A) 2.

Data Analysis

Data analysis questions have the reputation of challenging the examinees at each step. It comprises 28% questions of the GRE quantitative section. Following topics fall under data analysis section:-

1. Graphical Methods for Describing Data
2. Numerical Methods for Describing Data
3. Counting Methods
4. Probability
5. Distributions of Data, Random Variables, and Probability Distributions
6. Data Interpretation Examples

Important Assumptions

• All numbers are real numbers
• All Geometric figures like triangles, circles, quadrilaterals are not necessarily drawn to scale. The candidate should not assume quantities like the length of line or angle measures unless specified.
• Coordinate systems like diagrams drawn on an x-y plane are drawn to scale.
• Graphical representations like the bar, pie graphs, etc. are drawn to scale. Candidates can use these diagrams to read, estimate values.

ETS GRE provides a calculator for both online and offline examinations. Students taking the online examinations will have the calculator on the test screen.

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