GRE Quantitative Reasoning Set 2 Practice Questions with Answers

Forty percent of the GRE score is determined by the Quantitative Reasoning section, making it essential to master arithmetic, algebra, geometry, and data analysis. Whether you are aiming for a high-percentile score in engineering or social sciences, consistent exposure to diverse problem types is the most effective way to build mathematical stamina. This GRE Quantitative Reasoning Set 2 Practice Questions with Answers guide provides a targeted look at intermediate and advanced concepts to help you sharpen your mental math and logical deduction skills. By working through these problems, you will familiarize yourself with the specific trickery that the Educational Testing Service (ETS) often employs to distract test-takers.

Concept Explanation

GRE Quantitative Reasoning Set 2 focuses on the application of algebraic properties, geometric relationships, and statistical distributions to solve complex word problems. Success in this section requires more than just memorizing formulas; it demands an understanding of how to manipulate equations and interpret data sets under time pressure. The exam evaluates your ability to reason quantitatively and to model and solve problems using quantitative methods. Key areas include number properties (such as prime factorization and remainders), coordinate geometry, and counting methods like permutations and combinations. You can further refine your study plan using a personalized AI MasterPlan to ensure you cover these high-yield topics before test day.

Solved Examples

Review these worked examples to understand the logical steps required for common GRE problem types.

1. Algebraic Manipulation: If $x^2 - y^2 = 24$ and $x + y = 6$, what is the value of $x - y$?
   1. Recall the difference of squares identity: $x^2 - y^2 = (x + y)(x - y)$.
   2. Substitute the given values into the identity: $24 = (6)(x - y)$.
   3. Divide both sides by 6 to isolate the term: $x - y = 4$.
   4. The answer is 4.
2. Geometry (Circles): A circle is inscribed in a square with a side length of 10. What is the area of the region inside the square but outside the circle?
   1. Calculate the area of the square: $10 \times 10 = 100$.
   2. Determine the radius of the circle. Since it is inscribed, the diameter equals the side of the square (10), so the radius $r = 5$.
   3. Calculate the area of the circle: $\text{Area} = \pi r^2 = \pi(5^2) = 25\pi$.
   4. Subtract the circle's area from the square's area: $100 - 25\pi$.
3. Probability: A bag contains 4 red marbles and 6 blue marbles. If two marbles are drawn at random without replacement, what is the probability that both are red?
   1. Find the probability of the first marble being red: $\frac{4}{10} = \frac{2}{5}$.
   2. Find the probability of the second marble being red, given the first was red: $\frac{3}{9} = \frac{1}{3}$.
   3. Multiply the two probabilities: $\frac{2}{5} \times \frac{1}{3} = \frac{2}{15}$.
   4. The probability is $\frac{2}{15}$.

Practice Questions

Test your knowledge with these GRE Quantitative Reasoning Set 2 Practice Questions. Remember to use the Khan Academy GRE prep resources if you need to brush up on specific mathematical foundations.

1. If $3^x = 81$, what is the value of $(x-1)^2$?

2. Quantity A: The average (arithmetic mean) of $n, n+1, n+2$.
Quantity B: $n+1$.
Compare the two quantities.

3. A rectangular tank has a length of 5 meters, a width of 4 meters, and a height of 3 meters. If the tank is half full of water, what is the volume of the water in cubic meters?

4. Solve for $z$: $\frac{2z}{3} - 4 = 10$.

5. A set of numbers consists of {2, 4, 6, 8, 10}. If the number 12 is added to the set, how does the median change?

6. Quantity A: The number of distinct prime factors of 60.
Quantity B: The number of distinct prime factors of 90.

7. If the ratio of the interior angles of a triangle is 2:3:5, what is the measure of the largest angle in degrees?

8. A shopper bought a jacket for $120 after a 20% discount. What was the original price of the jacket?

9. If $f(x) = x^2 - 3x + 2$, find $f(-2)$.

10. A line in the xy-plane passes through the points (0, 0) and (4, 8). What is the slope of the line?

Answers & Explanations

1. Answer: 9. First, solve for $x$. Since $3^4 = 81$, $x = 4$. Then, substitute $x$ into the expression: $(4 - 1)^2 = 3^2 = 9$.

2. Answer: The two quantities are equal. The mean of three consecutive integers is the middle integer. Summing them gives $3n + 3$. Dividing by 3 yields $n + 1$, which is identical to Quantity B.

3. Answer: 30. The total volume of the tank is $5 \times 4 \times 3 = 60$ cubic meters. Since the tank is half full, the water volume is $60 / 2 = 30$.

4. Answer: 21. Add 4 to both sides: $\frac{2z}{3} = 14$. Multiply by 3: $2z = 42$. Divide by 2: $z = 21$.

5. Answer: It increases from 6 to 7. The original median of {2, 4, 6, 8, 10} is 6. The new set is {2, 4, 6, 8, 10, 12}. The median is the average of the two middle terms: $(6+8)/2 = 7$.

6. Answer: The two quantities are equal. The prime factors of 60 are 2, 3, and 5. The prime factors of 90 are 2, 3, and 5. Both have exactly 3 distinct prime factors.

7. Answer: 90. Let the angles be $2x, 3x,$ and $5x$. Their sum is 180: $2x + 3x + 5x = 180 \rightarrow 10x = 180 \rightarrow x = 18$. The largest angle is $5(18) = 90$.

8. Answer: $150. If the discount is 20%, the $120 represents 80% of the original price ($P$). So, $0.8P = 120$. Dividing 120 by 0.8 gives $P = 150$.

9. Answer: 12. Substitute -2 for $x$: $(-2)^2 - 3(-2) + 2 = 4 + 6 + 2 = 12$.

10. Answer: 2. The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Here, $m = \frac{8 - 0}{4 - 0} = \frac{8}{4} = 2$.

1. If a circle has a circumference of \( 10\pi \), what is its area?

• A\( 10\pi \)
• B\( 20\pi \)
• C\( 25\pi \)
• D\( 100\pi \)

Frequently Asked Questions

What is the best way to handle Quantitative Comparison questions?

The most effective strategy is to simplify both quantities to their most basic forms or plug in numbers like 0, 1, and negatives to see if the relationship changes. If the relationship varies based on the numbers chosen, the answer is always "the relationship cannot be determined."

How much geometry is on the GRE?

Geometry typically accounts for about 15% of the Quantitative Reasoning section, focusing on basic shapes like circles, triangles, and quadrilaterals. You do not need to know complex trigonometry or calculus, but you must be comfortable with the Pythagorean theorem and area formulas.

Can I use a calculator during the GRE?

Yes, an on-screen calculator is provided during the computer-based GRE for basic arithmetic. However, it is limited in function, so you should prioritize mental math for simple calculations to save time for more complex reasoning.

What are the most common algebraic errors to avoid?

Common mistakes include incorrectly distributing negative signs across parentheses and forgetting to perform the same operation on both sides of an inequality. To avoid these, practice with an AI Question Generator that highlights step-by-step errors in your logic.

How does the GRE score data analysis questions?

Data analysis questions, which include interpreting graphs and tables, are scored the same as other math questions but often require multiple steps. They test your ability to synthesize information and identify trends rather than just performing raw calculation.