GMAT Math : Functions/Series

Study concepts, example questions & explanations for GMAT Math

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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:

Explanation:

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:

Explanation:

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:

Explanation:

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:

Explanation:

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:

Explanation:

 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:

Explanation:

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:

Explanation:

Example Question #31 : Understanding Functions

Define .

What is   ?

Possible Answers:

Correct answer:

Explanation:

Replace  with .

Now exchange  and  and solve for  in the new expression:

Example Question #181 : Algebra

Define 

What is  ?

Possible Answers:

Correct answer:

Explanation:

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:

Explanation:

Substitute  into the definition and solve:

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