GMAT Math : Functions/Series

Study concepts, example questions & explanations for GMAT Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #41 : Functions/Series

Define .

What is  ?

Possible Answers:

Correct answer:

Explanation:

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:

Explanation:

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:

Explanation:

Replace  with .

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

 

Example Question #43 : Functions/Series

Define .

What is  ?

Possible Answers:

Correct answer:

Explanation:

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:

Explanation:

Example Question #1271 : Gmat Quantitative Reasoning

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

Define 

Evaluate 

Possible Answers:

Correct answer:

Explanation:

Example Question #44 : Functions/Series

Evaluate .

Possible Answers:

Correct answer:

Explanation:

 

 

 

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:

Explanation:

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:

Explanation:

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:

Explanation:

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

 

Learning Tools by Varsity Tutors