### All GMAT Math Resources

## Example Questions

### Example Question #31 : Understanding Functions

The first two terms of an arithmetic sequence are

What is the tenth term of this sequence?

**Possible Answers:**

**Correct answer:**

The common difference of this arithmetic sequence is , so the tenth term is

### Example Question #31 : Understanding Functions

The first two terms of a geometric sequence are

What is the sum of the fourth and fifth terms?

**Possible Answers:**

**Correct answer:**

The common ratio of the sequence is

The fourth and fifth terms can be found by repeated multiplication:

, the fourth term

, the fifth term

Add the fourth and fifth terms:

### Example Question #31 : Functions/Series

The first six terms of a sequence are:

What is the next term?

**Possible Answers:**

**Correct answer:**

The numbers are generated by addition as follows:

Each entry is generated by adding the next perfect square to the previous entry. Therefore, the next entry will be generated as follows:

### Example Question #32 : Understanding Functions

The first six terms of a sequence are:

What is the eight term?

**Possible Answers:**

**Correct answer:**

The terms are generated by adding an increment that increases by 2 with every term:

81 is the eighth term.

### Example Question #33 : Understanding Functions

Define an operation on the set of real numbers as follows:

For all real numbers , if and only if and , and otherwise.

Evaluate:

**Possible Answers:**

**Correct answer:**

can be evaluated by using the second part of the definition, since both numbers are positive:

can be evaluated by using the first part of the definition, since both numbers are negative:

### Example Question #31 : Functions/Series

Define an operation on two real numbers as follows:

For all real numbers ,

if and only if , and otherwise.

Evaluate:

**Possible Answers:**

**Correct answer:**

We can evaluate both and using the first part of the definition, since the second number is nonzero in both cases.

### Example Question #35 : Understanding Functions

Define an operation on the real numbers as follows:

for all real .

Evaluate:

**Possible Answers:**

**Correct answer:**

### Example Question #31 : Understanding Functions

Define .

What is ?

**Possible Answers:**

**Correct answer:**

Replace with .

Now exchange and and solve for in the new expression:

### Example Question #181 : Algebra

Define

What is ?

**Possible Answers:**

**Correct answer:**

Replace with .

Now exchange and and solve for in the new expression:

### Example Question #182 : Algebra

Define an operation on two real numbers as follows:

for all real numbers

Solve for :

**Possible Answers:**

**Correct answer:**

Substitute into the definition and solve: