# GRE Math : Algebra

## Example Questions

### Example Question #5 : How To Find A Rational Number From An Exponent

Simplify

Explanation:

Whenever you see lots of multiplication (e.g. exponents, which are notation for repetitive multiplication) separated by addition or subtraction, a common way to transform the expression is to factor out common terms on either side of the + or - sign. That allows you to create more multiplication, which is helpful in reducing fractions or in reducing the addition/subtraction to numbers you can quickly calculate by hand as you'll see here.

So let's factor a .

We have .

And you'll see that the addition inside parentheses becomes quite manageable, leading to the final answer of

### Example Question #1 : How To Find Out When An Equation Has No Solution

Quantity A:

Quantity B:

Quantity B is greater.

The two quantities are equal.

Quantity A is greater.

The relationship cannot be determined from the information given.

The relationship cannot be determined from the information given.

Explanation:

We are given that y = 32.  Plug this value of y into the second equation.

32 = x2 – 4

36 = x2

x = +/– 6.

Next find a value for Quantity A:

y/7 = 32/7

This number is less than +6, but more than –6. Thus, the relationship cannot be determined from the information given.

### Example Question #41 : Gre Quantitative Reasoning

Column A:

Column B:

The values are equal.

The relationship cannot be determined.

Column B is greater.

Column A is greater.

The relationship cannot be determined.

Explanation:

Column B is greater for positive numbers.

The columns are equal for 0.

Column A is greater for negative numbers.

Because our answer changes depending on the value inserted, we cannot determine the relationship.

### Example Question #1 : Linear / Rational / Variable Equations

Find the solution to the following equation if x = 3:

y = (4x2 - 2)/(9 - x2)

6

0

no possible solution

3

no possible solution

Explanation:

Substituting 3 in for x, you will get 0 in the denominator of the fraction. It is not possible to have 0 be the denominator for a fraction so there is no possible solution to this equation.

I.  x = 0

II. x = –1

III. x = 1

I only

III only

I, II, and III

II only

II and III only

I only

Explanation:

### Example Question #1 : How To Find Out When An Equation Has No Solution

1

–1/2

–3

3

There is no solution

There is no solution

Explanation:

### Example Question #1 : Equations / Inequalities

Explanation:

A fraction is considered undefined when the denominator equals 0. Set the denominator equal to zero and solve for the variable.

### Example Question #10 : How To Find Out When An Equation Has No Solution

Solve:

Explanation:

First, distribute, making sure to watch for negatives.

Combine like terms.

Subtract 7x from both sides.

### Example Question #3 : How To Find Out When An Equation Has No Solution

Solve:

Infinitely Many Solutions

No Solution

No Solution

Explanation:

First, distribute the  to the terms inside the parentheses.

This is false for any value of . Thus, there is no solution.

Solve .

No solutions