# GRE Math : Linear / Rational / Variable Equations

## Example Questions

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### Example Question #1 : Equations / Inequalities

Quantity A:

Quantity B:

The two quantities are equal.

Quantity A is greater.

The relationship cannot be determined from the information given.

Quantity B is greater.

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 #2 : How To Find Out When An Equation Has No Solution

Column A:

Column B:

The relationship cannot be determined.

Column B is greater.

The values are equal.

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

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

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

no possible solution

3

0

6

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

III only

II only

I only

I, II, and III

II and III only

I only

Explanation:

### Example Question #5 : 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 #6 : How To Find Out When An Equation Has No Solution

Explanation:

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

### Example Question #7 : 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 #8 : 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.

### Example Question #1 : Equations / Inequalities

Solve .

No solutions

No solutions

Explanation:

By definition, the absolute value of an expression can never be less than 0. Therefore, there are no solutions to the above expression.

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

Quantity A:

Quantity B: 11

The relationship cannot be determined.

Quantity B is greater

Quantity A is greater

The two quantities are equal.

Quantity B is greater

Explanation:

Expand  out into .

Since , it can be seen that

so Quantity B is greater.

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