Σ Official GRE Curriculum

GRE Quantitative Reasoning Practice

Master GRE Quant with 990+ calibrated problems across Arithmetic, Algebra, Geometry, and Data Analysis. Includes step-by-step KaTeX mathematical proofs and trap explanations.

Launch 10-Question Quantitative Reasoning Drill → Take Daily 20-Question Challenge

Topic Modules

Quantitative Reasoning Syllabus Breakdown

Select an individual topic module below to view detailed strategies, formulas, and verified sample questions.

Arithmetic & Number Properties

249 Qs

Master integers, prime numbers, divisibility rules, fractions, decimals, exponents, and roots on the GRE Quantitative section.

View Arithmetic & Number Properties Guide & Sample Problems →

Algebra & Functions

245 Qs

Conquer linear equations, quadratic inequalities, systems of equations, absolute value functions, and algebraic word problems.

View Algebra & Functions Guide & Sample Problems →

Geometry & Coordinate Planes

248 Qs

Understand triangles, circles, quadrilaterals, 3D solids, and coordinate geometry formulas with KaTeX diagrams and proofs.

View Geometry & Coordinate Planes Guide & Sample Problems →

Data Analysis & Statistics

268 Qs

Analyze charts, graphs, normal distribution, permutations, combinations, and probability under timed GRE conditions.

View Data Analysis & Statistics Guide & Sample Problems →

Verified Examples

Representative Quantitative Reasoning Problems

Question 1 Quantitative algebra

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3x - 7 = 2(x + 4)

, what is the value of

x^2 - 10

Show Official Answer & Step-by-Step Rationale

Correct Answer:

215

Step-by-Step Proof:

1. Solve for

x

3x - 7 = 2x + 8

3x - 2x = 8 + 7 \implies x = 15

2. Calculate

x^2 - 10

15^2 - 10 = 225 - 10 = 215

Thus, the correct answer is

215

🎯 Key Rule:

Always read the prompt carefully: ETS often asks for an expression like

x^2 - 10

rather than

x

itself.

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Question 2 Quantitative algebra

Click an answer to check

In the

xy

-coordinate plane, line

L_1

passes through the points

(2, 3)

and

(6, 11)

. Line

L_2

is perpendicular to

L_1

and passes through the point

(4, -1)

. What is the

y

-intercept of line

L_2

Show Official Answer & Step-by-Step Rationale

Correct Answer:

1

Step-by-Step Proof:

1. Find the slope of line

L_1

m_1 = \frac{11 - 3}{6 - 2} = \frac{8}{4} = 2

2. Since

L_2 \perp L_1

, its slope

m_2

is the negative reciprocal:

m_2 = -\frac{1}{m_1} = -\frac{1}{2}

3. Use point-slope form with

(4, -1)

y - (-1) = -\frac{1}{2}(x - 4)

y + 1 = -\frac{1}{2}x + 2 \implies y = -\frac{1}{2}x + 1

4. The

y

-intercept (

b

) is

1

🎯 Key Rule:

Perpendicular lines have negative reciprocal slopes:

m_1 \cdot m_2 = -1

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Question 3 Quantitative algebra

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Given Condition:

x

is a nonzero real number.

Quantity A

(x + 1)^2

Quantity B

(x - 1)^2

Compare Quantity A and Quantity B based on the given condition.

Show Official Answer & Step-by-Step Rationale

Correct Answer: The relationship cannot be determined from the information given.

Step-by-Step Proof:

1. Expand both quantities: - Quantity A:

x^2 + 2x + 1

- Quantity B:

x^2 - 2x + 1

2. Subtract

x^2 + 1

from both quantities: - Quantity A becomes

2x

- Quantity B becomes

-2x

3. Test cases based on sign: - If

x = 2

(positive): Quantity A

= 4

, Quantity B

= -4 \implies \text{Quantity A} > \text{Quantity B}

. - If

x = -2

(negative): Quantity A

= -4

, Quantity B

= 4 \implies \text{Quantity B} > \text{Quantity A}

. Because the relative order flips when

x

switches signs, the relationship cannot be determined.

Common ETS Trap Warning:

Standard ETS trap: examinees unconsciously test only positive integers (

x = 1, 2

), where Quantity A is larger, and fail to test negative values where the inequality inverts.

🎯 Key Rule:

Always test numbers from the "ZONE F" framework: Zero, One, Negatives, Extremes, and Fractions.

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