### All GMAT Math Resources

## Example Questions

### Example Question #1 : Linear Equations, One Unknown

For what value of would the following equation have no solution?

**Possible Answers:**

The equation must always have at least one solution regardless of the value of .

**Correct answer:**

Simplify both sides of the equation as much as possible, and solve for in the equation in terms of :

has exactly one solution unless the denominator is 0 - that is, . We make sure that this value renders no solution by substituting:

The equation has no solution, and is the correct answer.

### Example Question #2 : Linear Equations, One Unknown

Solve for :

**Possible Answers:**

**Correct answer:**

### Example Question #3 : Linear Equations, One Unknown

Solve for :

**Possible Answers:**

**Correct answer:**

### Example Question #4 : Linear Equations, One Unknown

Solve for :

**Possible Answers:**

**Correct answer:**

### Example Question #5 : Linear Equations, One Unknown

What is the midpoint coordinate of and ?

**Possible Answers:**

**Correct answer:**

Midpoint formula:

### Example Question #6 : Linear Equations, One Unknown

What is the midpoint coordinate of and ?

**Possible Answers:**

**Correct answer:**

Midpoint formula:

### Example Question #7 : Linear Equations, One Unknown

What is the midpoint coordinate of and ?

**Possible Answers:**

**Correct answer:**

Midpoint formula:

### Example Question #8 : Linear Equations, One Unknown

Solve the following equation:

.

**Possible Answers:**

**Correct answer:**

We start by isolating the absolute value expression:

This gives us two cases when we remove the absolute value:

and

Then we solve for each case:

### Example Question #9 : Linear Equations, One Unknown

Solve for :

**Possible Answers:**

The equation has no solution.

**Correct answer:**

### Example Question #10 : Linear Equations, One Unknown

Solve for :

**Possible Answers:**

The equation has no solution.

**Correct answer:**