GRE Verbal & Quantitative Reasoning
Mastery v2.0: A Rigorous 150-Question
Advanced Practice Exam Featuring High-
Difficulty Quantitative Problem-Solving,
Nuanced Textual Analysis, and Critical
Reasoning for Competitive Candidates. a well
detailed exam 2025/2026 graded A+
upgraded !!!
Part I: Quantitative Reasoning (75 Questions)
Subtopics: Arithmetic, Algebra, Geometry, Data Analysis, Word Problems, Number
Theory
,1. Arithmetic: Divisibility
If integer 𝑛 is divisible by 6 and 10, then it must also be divisible by which of the
following?
A) 12
B) 15
C) 20
D) 25
E) 30
Correct Answer: E
Rationale: If n is divisible by 6 (2×3) and 10 (2×5), it must contain factors 2, 3, and 5.
The LCM of 6 and 10 is 30, so n must be divisible by 30.
2. Algebra: Simultaneous Equations
If 2𝑥 + 3𝑦 = 14 and 3𝑥 + 2𝑦 = 16, what is the value of 𝑥 − 𝑦?
A) -2
B) 0
C) 2
D) 4
E) 6
Correct Answer: C
Rationale: Subtract the first equation from the second: (3x+2y) - (2x+3y) = 16 - 14 → x -
y = 2.
3. Geometry: Triangles & Angles
In triangle ABC, angle A is twice angle B, and angle C is 30° more than angle B. What is
,the measure of angle A?
A) 30°
B) 45°
C) 60°
D) 75°
E) 90°
Correct Answer: C
Rationale: Let B = x. Then A = 2x, C = x+30. Sum: 2x + x + (x+30) = 180 → 4x = 150 → x
= 37.5. A = 2x = 75°. Wait, 2*37.5 = 75. Yes.
4. Data Analysis: Probability (Dependent Events)
A bag contains 5 red and 7 blue marbles. Two marbles are drawn without replacement.
What is the probability that the second marble is red, given that the first marble was
blue?
A) 5/11
B) 5/12
C) 7/12
D) 7/11
E) 1/2
Correct Answer: A
Rationale: After drawing one blue marble, there are 5 red marbles and 11 total marbles
left. Probability = 5/11.
5. Arithmetic: Exponents & Roots
Simplify √64𝑥 6 .
3
, A) 4x^2
B) 4x^3
C) 8x^2
D) 8x^3
E) 16x^2
Correct Answer: A
Rationale: √64 = 4 and √𝑥 6 = 𝑥 6/3 = 𝑥 2 . So the result is 4𝑥 2 .
3 3
6. Algebra: Quadratic Equations (Discriminant)
For what value of 𝑘 does the equation 𝑥 2 + 𝑘𝑥 + 9 = 0 have exactly one real solution?
A) 3
B) 6
C) -6
D) ±6
E) ±3
Correct Answer: D
Rationale: One real solution means discriminant = 0: 𝑘 2 − 4(1)(9) = 0 → 𝑘 2 = 36 → 𝑘 =
±6.
7. Word Problem: Rates (Combined Work)
Machine A can produce 100 widgets in 4 hours. Machine B can produce 100 widgets in
6 hours. How long will it take both machines working together to produce 100 widgets?
A) 2.0 hours
B) 2.4 hours
C) 2.6 hours
Mastery v2.0: A Rigorous 150-Question
Advanced Practice Exam Featuring High-
Difficulty Quantitative Problem-Solving,
Nuanced Textual Analysis, and Critical
Reasoning for Competitive Candidates. a well
detailed exam 2025/2026 graded A+
upgraded !!!
Part I: Quantitative Reasoning (75 Questions)
Subtopics: Arithmetic, Algebra, Geometry, Data Analysis, Word Problems, Number
Theory
,1. Arithmetic: Divisibility
If integer 𝑛 is divisible by 6 and 10, then it must also be divisible by which of the
following?
A) 12
B) 15
C) 20
D) 25
E) 30
Correct Answer: E
Rationale: If n is divisible by 6 (2×3) and 10 (2×5), it must contain factors 2, 3, and 5.
The LCM of 6 and 10 is 30, so n must be divisible by 30.
2. Algebra: Simultaneous Equations
If 2𝑥 + 3𝑦 = 14 and 3𝑥 + 2𝑦 = 16, what is the value of 𝑥 − 𝑦?
A) -2
B) 0
C) 2
D) 4
E) 6
Correct Answer: C
Rationale: Subtract the first equation from the second: (3x+2y) - (2x+3y) = 16 - 14 → x -
y = 2.
3. Geometry: Triangles & Angles
In triangle ABC, angle A is twice angle B, and angle C is 30° more than angle B. What is
,the measure of angle A?
A) 30°
B) 45°
C) 60°
D) 75°
E) 90°
Correct Answer: C
Rationale: Let B = x. Then A = 2x, C = x+30. Sum: 2x + x + (x+30) = 180 → 4x = 150 → x
= 37.5. A = 2x = 75°. Wait, 2*37.5 = 75. Yes.
4. Data Analysis: Probability (Dependent Events)
A bag contains 5 red and 7 blue marbles. Two marbles are drawn without replacement.
What is the probability that the second marble is red, given that the first marble was
blue?
A) 5/11
B) 5/12
C) 7/12
D) 7/11
E) 1/2
Correct Answer: A
Rationale: After drawing one blue marble, there are 5 red marbles and 11 total marbles
left. Probability = 5/11.
5. Arithmetic: Exponents & Roots
Simplify √64𝑥 6 .
3
, A) 4x^2
B) 4x^3
C) 8x^2
D) 8x^3
E) 16x^2
Correct Answer: A
Rationale: √64 = 4 and √𝑥 6 = 𝑥 6/3 = 𝑥 2 . So the result is 4𝑥 2 .
3 3
6. Algebra: Quadratic Equations (Discriminant)
For what value of 𝑘 does the equation 𝑥 2 + 𝑘𝑥 + 9 = 0 have exactly one real solution?
A) 3
B) 6
C) -6
D) ±6
E) ±3
Correct Answer: D
Rationale: One real solution means discriminant = 0: 𝑘 2 − 4(1)(9) = 0 → 𝑘 2 = 36 → 𝑘 =
±6.
7. Word Problem: Rates (Combined Work)
Machine A can produce 100 widgets in 4 hours. Machine B can produce 100 widgets in
6 hours. How long will it take both machines working together to produce 100 widgets?
A) 2.0 hours
B) 2.4 hours
C) 2.6 hours
