# GRE® Algebra Question Bank

#### What is tested in the GRE from Algebra? GRE Syllabus

The following concepts are tested as part of algebra in the GRE General Test - Quantitative Reasoning Section. Algebra concepts in the GRE quant section could appear in any of the 4 question types viz., problem solving, quantitative comparison, numeric entry, or more than one answer correct. The questionbank provides questions from algebra in all of these variants.

• Solutions to pair of linear equations in 2 variables
• Types of solutions to pair of linear equations in 2 variables
• Word problems in linear equations
• Solution to quadratic equations by factorizing the equation and by using the quadratic formula
• Nature of roots of a quadratic equations
• Word problems in quadratic equations
• Solution to Linear inequalities
• Solution to Inequalities of quadratic expressions
• Inequalities and absolute values
• Inequalities and exponents
• Word problems in inequalities
• Elementary questions in algebraic functions

Sample GRE practice questions from Algebra are given below in this questionbank. Attempt these questions and check whether you have got the correct answer. If you face difficulty finding the answer to any question, go to the explanatory answer or the video explanations (provided for all questions) to learn how to crack the GRE sample question in this question bank.

The concepts covered in this GRE questionbank include framing and solving linear equations in two variables, linear equations in one variable, simultaneous equations solution, finding the roots of a quadratic equation, determining nature of roots of a quadratic equation, finding curve that a quadratic equation represents, and word problems in quadratic equations.

1. GRE Problem Solving Question

When four is added to six times a number and the result squared, the result obtained is four times the square of the sum of the number and its next multiple. What is the number?

1. $$frac{1}{3}$ 2. $\frac{-1}{3}$ 3. 3 4. -3 5. 1 Approach to solve this Algebra Word Problem Step 1: Assign a variable to represent the number. Step 2: Convert "When four is added to six times a number and the result squared" into a mathematical expression. This expression will be the left hand side of the equation. Step 3: Frame a mathematical expression for "four times the square of the sum of the number and its next multiple". This expression is the right hand side of the equation. Step 4: Equate expressions obtained in steps 2 and 3 and solve for the unknown. 2. GRE Quantitative Comparison Question $\frac{x}{y}$ < 0 Quantity A Quantity B$4x + 3y)(x – 6y) 4x2 + 16xy – 18y2

1. Quantity A is greater
2. Quantity B is greater
3. The two quantities are equal
4. Cannot be determined
Approach to solve this GRE Quantitative Comparison Question

Step 1: Rewrite the expression given in Quantity A as a standard quadratic expression.
Step 2: Compare it with quadratic expression in Quantity B by cancelling like terms in both quantities.
Step 3: Use the information that $$frac{x}{y}$ < 0 when evaluating what is left on both sides after cancelling like terms to arrive at the answer to this GRE quantitative comparison question. 3. GRE Quantitative Comparison Question x, y ≠ 0 and x > y Quantity A Quantity B $\frac{1}{\frac{x}{y} + \frac{y}{x}}$ $\frac{1}{\frac{x}{y} - \frac{y}{x}}$ 1. Quantity A is greater 2. Quantity B is greater 3. The two quantities are equal 4. Cannot be determined Approach to solve this GRE Polynomials Quantitative Comparison Question Step 1: Rewrite the expression given in Quantity A in the form of a fraction $\frac{p}{q}$. Step 2: Rewrite the expression given in Quantity B in the form of a fraction $\frac{p}{q}$. Step 3: Look for a counter example. One example in which Quantity A is greater than B and another in which Quantity B is greater than A. Step 4: If you are able to find a counter example, then the answer is evident. 4. GRE Select One or More Answers Question If f$x) = x2 + 4, which of the following is equal to f(9)?

1. f(13)
2. f(-3)
3. f(-9)
4. f(f(√5))
5. f(f(√13))
6. f(f(-√5))
Approach to solve this GRE Functions Question

Step 1: Evaluate the value of f(9).
Step 2: Evaluate values of fucntion for all the 6 answer options.
Step 3: Select options whose values are equal to the value of f(9).

5. GRE Problem Solving Question

What is the least positive integer that will satisfy the inequality x2 + 17x – 84 > 0?

1. 1
2. 21
3. 4
4. 22
5. 5
Approach to solve this GRE Inequalities Question

Step 1: Factorise the given quadratic expression.
Step 2: Compute the turning points. Essentially, the roots of the quadratic equation.
Step 3: Divide the number line into 3 intervals based on the values of the two roots of the quadratic equation.
Step 4: Find the intervals in which the inequality holds good.
Step 5: Find the smallest positive integer in the first interval in which the inequality holds good when the intervals are arranged in ascending order.

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