### All GRE Math Resources

## Example Questions

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

Quantity A:

Quantity B:

**Possible Answers:**

Quantity A is greater.

Quantity B is greater.

The relationship cannot be determined from the information given.

The two quantities are equal.

**Correct answer:**

The relationship cannot be determined from the information given.

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

32 = x^{2} – 4

36 = x^{2}

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

Column A:

Column B:

**Possible Answers:**

Column B is greater.

The relationship cannot be determined.

Column A is greater.

The values are equal.

**Correct answer:**

The relationship cannot be determined.

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 : How To Find Out When An Equation Has No Solution

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

y = (4x^{2} - 2)/(9 - x^{2})

**Possible Answers:**

0

no possible solution

3

6

**Correct answer:**

no possible solution

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.

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

I. *x* = 0

II. *x* = –1

III. *x* = 1

**Possible Answers:**

II only

I only

II and III only

I, II, and III

III only

**Correct answer:**

I only

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

**Possible Answers:**

–3

1

3

–1/2

There is no solution

**Correct answer:**

There is no solution

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

**Possible Answers:**

None of the other answers

**Correct answer:**

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:

**Possible Answers:**

**Correct answer:**

First, distribute, making sure to watch for negatives.

Combine like terms.

Subtract 7x from both sides.

Add 18 on both sides and be careful adding integers.

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

Solve:

**Possible Answers:**

Infinitely Many Solutions

No Solution

**Correct answer:**

No Solution

First, distribute the to the terms inside the parentheses.

Add 6x to both sides.

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

### Example Question #6 : Linear / Rational / Variable Equations

Solve .

**Possible Answers:**

No solutions

**Correct answer:**

No solutions

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 #1 : Linear / Rational / Variable Equations

Quantity A:

Quantity B: 11

**Possible Answers:**

The two quantities are equal.

Quantity B is greater

Quantity A is greater

The relationship cannot be determined.

**Correct answer:**

Quantity B is greater

Expand out into .

Since , it can be seen that

so Quantity B is greater.