### All GMAT Math Resources

## Example Questions

### Example Question #41 : Functions/Series

Define .

What is ?

**Possible Answers:**

**Correct answer:**

Replace with .

Now exchange and and solve for in the new expression:

### Example Question #42 : Functions/Series

Define an operation on the set of positive integers as follows:

if and are both odd or both even; otherwise, .

Evaluate:

**Possible Answers:**

**Correct answer:**

Both and can be defined using the first part of the definition of , as in the first case, both numbers are odd, and in the second case, both are even.

Add:

### Example Question #41 : Understanding Functions

Define .

What is ?

**Possible Answers:**

**Correct answer:**

Replace with .

Now exchange and , and solve for in the new expression:

### Example Question #43 : Functions/Series

Define .

What is ?

**Possible Answers:**

**Correct answer:**

Replace with .

Now exchange and and solve for in the new expression:

Therefore,

.

### Example Question #41 : Functions/Series

Define an operation on two real numbers as follows:

For all real ,

.

Evaluate:

**Possible Answers:**

**Correct answer:**

### Example Question #1271 : Gmat Quantitative Reasoning

is defined to be the greatest integer less than or equal to .

Define

Evaluate

**Possible Answers:**

**Correct answer:**

### Example Question #44 : Functions/Series

Evaluate .

**Possible Answers:**

**Correct answer:**

### Example Question #41 : Functions/Series

For any real , define .

For what value or values of would ?

**Possible Answers:**

No such value of exists.

**Correct answer:**

For such an to exist, it must hold that .

Take the square root of both sides:

or

Case 1:

Case 2:

### Example Question #191 : Algebra

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

Evaluate .

**Possible Answers:**

**Correct answer:**

First, evaluate by substituting :

Second, evaluate in the same way.

### Example Question #1275 : Gmat Quantitative Reasoning

Define an operation as follows:

For any real , .

For what value or values of is it true that ?

**Possible Answers:**

No such value of exists.

**Correct answer:**

Substitute into the definition, and then set the expression equal to 0 to solve for :