### All GMAT Math Resources

## Example Questions

### Example Question #331 : Algebra

Give the solution set of the equation:

**Possible Answers:**

**Correct answer:**

Case 1:

Then , and the equation becomes

Case 2:

Then , and the equation becomes

However, this conflicts with the fact that , so this is a false solution.

The only solution is therefore .

### Example Question #22 : Solving Equations

Give the solution set of the equation:

**Possible Answers:**

**Correct answer:**

Case 1: is nonnegative - that is, .

The equation becomes

Either , in which case ,

or , in which case , which is impossible, as we are assuming that is nonnegative.

case 2: is negative - that is,

The equation becomes

Either , in which case , which is impossible since we are assuming that is negative,

or , in which case .

and can both be confirmed as solutions.

### Example Question #21 : Solving Equations

What is the equation of the line that goes through and is parallel to ?

**Possible Answers:**

**Correct answer:**

First, we have to find the slope from using the general form Therefore

Parallel lines have the same slope, so the new line has a slope of and point .

Use the point-slope equation:

### Example Question #21 : Solving Equations

What is the -intercept of ?

**Possible Answers:**

**Correct answer:**

To solve for the -intercept, you set the to zero and solve for :

-intercept:

### Example Question #21 : Equations

What is the y-intercept of ?

**Possible Answers:**

**Correct answer:**

To solve for the y-intercept, you set to zero and solve for :

Therefore, the y-intercept is:

### Example Question #23 : Solving Equations

What is the -intercept of ?

**Possible Answers:**

**Correct answer:**

To solve for the -inter, you set to zero and solve for :

**x-intercept:**

### Example Question #24 : Solving Equations

What is the y-intercept of ?

**Possible Answers:**

**Correct answer:**

To solve for the y-intercept of , you set to zero and solve for :

y-intercept:

### Example Question #25 : Solving Equations

To convert Fahrenheit temperature to the equivalent in Celsius , use the formula

To the nearest tenth of a degree, convert to degrees Celsius.

**Possible Answers:**

**Correct answer:**

### Example Question #21 : Solving Equations

Solve for :

**Possible Answers:**

The equation has no solution.

**Correct answer:**

Rewrite as a compound equation, then solve each equation individually:

or

### Example Question #30 : Solving Equations

Solve for :

**Possible Answers:**

The equation has no solution.

**Correct answer:**

Eliminate the denominators by multiplying by , then solve the resulting equation:

Solve using the method:

or