ETS announced the roll out of the new shorter GRE General Test and the internet is buzzing with questions from the anticipated test-takers. Well, here’s some relief! This blog comes packed with the latest GRE quantitative reasoning questions and much more.

## What topics do the GRE Quantitative Reasoning questions cover?

The GRE Quantitative Reasoning section covers a broad range of topics, including arithmetic, algebra, geometry, and data analysis. Within these topics, you can expect questions involving number properties, equations, inequalities, functions, coordinate geometry, and statistics. By practicing questions from each of these areas, you develop a well-rounded understanding of the concepts and enhance your problem-solving abilities across various domains.

## How can I effectively utilize the free GRE Quant practice questions?

To make the most of your practice sessions, it’s important to approach the free GRE Quant practice questions strategically. Here are a few tips to help you maximize your learning:

1. Create a study schedule: Allocate dedicated time slots for practicing GRE Quant questions. Consistency is key when it comes to skill development.
2. Focus on weak areas: Identify the topics or question types that you find challenging and prioritize them during your practice sessions. By targeting your weaknesses, you can gradually improve and build confidence.
3. Review solutions carefully: After attempting a question, compare your solution with the provided solution. Understand the underlying concepts and strategies used to solve the problem. This will help you gain insights and learn alternative approaches.
4. Track your progress: Keep a record of the questions you have attempted, the ones you struggled with, and the ones you answered correctly. This tracking will allow you to gauge your progress over time and identify areas that require further attention.
5. Simulate exam conditions: Occasionally, simulate the actual exam conditions by timing yourself and solving questions in a distraction-free environment. This will help you develop your pacing skills and build confidence for the real test.

## Free GRE Quant Practice Questions with Solutions

To help you kickstart your GRE Quantitative Reasoning preparation, we have compiled a selection of free practice questions with detailed solutions. Solve each question to the best of your ability and refer to the explanations provided for further clarity. Remember, practice makes perfect, so embrace these questions as valuable learning opportunities on your journey to GRE success. Each question is followed by a detailed solution to guide you through the problem-solving process.

Question 1:
Problem: Solve the equation: √(x – 3) + 2 = 5.

Solution: To isolate the square root term, we subtract 2 from both sides: √(x – 3) = 3. To eliminate the square root, we square both sides: (x – 3) = 9. Adding 3 to both sides, we get x = 12.

Question 2:
Problem: Find the value of x that satisfies the equation: 4^x = 64.

Solution: Rewrite 64 as a power of 4: 64 = 4^3. Equating the exponents, we have x = 3.

Question 3:
Problem: Calculate the area of a triangle with sides measuring 10 units, 12 units, and 15 units.

Solution: Using Heron’s formula, we find the semi-perimeter (s) of the triangle by adding the three sides and dividing by 2: s = (10 + 12 + 15)/2 = 37/2. Applying the formula for the area (A) of a triangle: A = √(s(s-a)(s-b)(s-c)), where a, b, and c are the side lengths, we get A = √((37/2)(37/2-10)(37/2-12)(37/2-15)). Simplifying further, A = √(37/2 * 17/2 * 13/2 * 11/2) = 65/2 square units.

Question 4:
Problem: Solve the inequality: 3x – 8 > 2x + 3.

Solution: To isolate the variable, we subtract 2x from both sides: x – 8 > 3. Adding 8 to both sides, we find x > 11.

Question 5:
Problem: A shop offers a 25% discount on an item originally priced at \$80. What is the sale price of the item?

Solution: To calculate the discount amount, we multiply the original price by the discount rate: \$80 * 0.25 = \$20. Subtracting the discount from the original price, we find the sale price: \$80 – \$20 = \$60.

Question 6:
Problem: Solve the equation system:
2x + 3y = 10
4x – 2y = 8.

Solution: We can use the method of substitution to solve the system. From the first equation, we can isolate x: x = (10 – 3y)/2. Substituting this value of x into the second equation, we get: 4((10 – 3y)/2) – 2y = 8. Simplifying, we have: (20 – 6y) – 2y = 8. Combining like terms, we get: 20 – 8y = 8. Solving for y, we have: -8y = 8 – 20, which gives -8y = -12. Dividing both sides by -8, we find y = 3/2. Substituting this value of y into the first equation, we can solve for x: 2x + 3(3/2) = 10. Simplifying, we get: 2x + 9/2 = 10. Subtracting 9/2 from both sides, we have: 2x = 10 – 9/2, which simplifies to 2x = 11/2. Dividing both sides by 2, we find x = 11/4.

Question 7:
Problem: A jar contains 6 red balls, 8 blue balls, and 10 green balls. If one ball is selected at random, what is the probability of selecting a red ball or a green ball?

Solution: To find the probability, we divide the number of favorable outcomes (red or green balls) by the total number of possible outcomes (all balls). The number of favorable outcomes is 6 (red balls) + 10 (green balls) = 16. The total number of balls is 6 (red balls) + 8 (blue balls) + 10 (green balls) = 24. Therefore, the probability of selecting a red ball or a green ball is 16/24, which simplifies to 2/3 or approximately 0.667.

Question 8:
Problem: If the radius of a circle is doubled, by what factor does its circumference increase?

Solution: The circumference of a circle is given by the formula C = 2πr, where r is the radius. If the radius is doubled, the new radius becomes 2r. Substituting this value into the formula, we have: C = 2π(2r) = 4πr. Therefore, the circumference increases by a factor of 4.

Question 9:
Problem: A train travels at a constant speed of 80 kilometers per hour. How long will it take to travel a distance of 200 kilometers?

Solution: To find the time taken, we divide the distance by the speed: 200 km / 80 km/h = 2.5 hours.

Question 10:
Problem: Solve the quadratic equation: x^2 + 5x + 6 = 0.

Solution: To factor the quadratic equation, we look for two numbers whose sum is 5 (the coefficient of the x term) and whose product is 6 (the constant term). The numbers 2 and 3 satisfy these conditions. Therefore, the equation can be factored as: (x + 2)(x + 3) = 0. Setting each factor equal to zero, we have: x + 2 = 0 and x + 3 = 0. Solving for x, we find x = -2 and x = -3.

These sample GRE Quant practice questions with detailed explanations and increased difficulty level will help you enhance your problem-solving skills and prepare effectively for the GRE exam.

#### 1. What is the GRE?

The GRE, or Graduate Record Examination, is a standardized test commonly required for admission to graduate programs in various disciplines. It assesses the verbal, quantitative, and analytical writing skills of candidates.

#### 2. How long is the GRE Quantitative Reasoning section?

The new shorter GRE Quantitative Reasoning section consists of 27 questions to be answered in 47 minutes.

#### 3. Can I use a calculator during the GRE Quantitative Reasoning section?

Yes, you are allowed to use an on-screen calculator provided by the testing center for the GRE Quantitative Reasoning section. However, keep in mind that the calculator is basic, so it’s essential to practice mental math and perform calculations efficiently.

#### 4. Are the practice questions in this article representative of the actual GRE Quantitative Reasoning questions?

While the practice questions in this article are designed to reflect the nature of GRE Quantitative Reasoning questions, they may not be identical to the questions you will encounter on the exam. Nevertheless, practicing these questions will help you develop the necessary skills and familiarity with the test format.

#### 5. What should I do if I’m struggling with a particular question or topic?

If you’re struggling with a specific question or topic, don’t get discouraged. Review the solution provided, seek additional explanations from reliable sources, and consult GRE preparation resources or tutors for further guidance. Consistent practice and targeted learning will help you overcome difficulties and improve your performance.

### Bottom Line

Practicing GRE Quantitative Reasoning questions is crucial for several reasons. First and foremost, it familiarizes you with the question format and helps you understand the types of problems you’ll encounter on the actual GRE. By solving a variety of questions, you develop essential skills such as critical thinking, analytical reasoning, and mathematical problem-solving. Additionally, regular practice enhances your speed and accuracy, allowing you to manage your time effectively during the exam.

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