GMAT Math : Functions/Series

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #71 : Functions/Series

What is the sum of all odd numbers from 0 to 59 inclusive? 

Possible Answers:

Correct answer:

Explanation:

We can manipulate summations to make them easier to work with. Here, we are asked for the sum of odd terms from 1 to 59. We can calculate this by subtracting the summation of the even terms from the summation of all numbers from 1 to 59, using the formula  to sum all terms from 1 to .

 

In other words, we have to calculate , since the even numbers are given by  or .

We obtain the final answer 900.

Example Question #72 : Functions/Series

Define  . Which of the following would be a valid alternative way of expressing the definition of ?

Possible Answers:

Correct answer:

Explanation:

By definition:

If , then  ,and subsequently, 

If , then  ,and subsequently, 

Example Question #73 : Functions/Series

Piecewise

Let  be the piecewise-defined function graphed above. Define the function .

Evaluate .

Possible Answers:

Correct answer:

Explanation:

As seen in the diagram below, the graph of  includes the point .

Piecewise 1

Therefore, , and

.

, so 

.

Therefore, , the correct choice.

Example Question #74 : Functions/Series

Piecewise

Let  be the piecewise-defined function graphed above. Define the function .

Evaluate .

Possible Answers:

Correct answer:

Explanation:

, so

, so

As seen in the diagram below, the graph of  includes the point .

Piecewise 1

Therefore, , and , the correct choice.

Example Question #75 : Understanding Functions

Piecewise

Let  be the piecewise-defined function graphed above. Define function .

Evaluate .

Possible Answers:

4 is not in the domain of 

Correct answer:

Explanation:

 such that .As seen in the diagram below, the graph of  includes the point , so .

Piecewise 1

, so

, the correct choice.

Example Question #72 : Functions/Series

Piecewise

Let  be the piecewise-defined function graphed above. Define function .

Evaluate .

Possible Answers:

4 is not in the domain of .

Correct answer:

4 is not in the domain of .

Explanation:

, so

Therefore, 

, which is equal to  such that .

However, the range of the function , as can be seen from the diagram, is  - 5 lies outside the range of , and, consequently, outside the domain of . Therefore, the expression  is undefined, and, equivalently, 4 is not in the domain of .

Example Question #71 : Understanding Functions

Piecewise

Let  be the piecewise-defined function graphed above. Define a function .

Evaluate .

Possible Answers:

6 is not in the domain of .

Correct answer:

Explanation:

From the diagram below, it can be seen that the point  is on the graph of 

Therefore, , and

 if , so, since

,

and 

Therefore, .

Example Question #74 : Functions/Series

Piecewise

Let  be the piecewise-defined function graphed above. Define a function .

Evaluate 

Possible Answers:

.

Correct answer:

.

Explanation:

 

 if , so, since

Therefore, , and 

As can be seen from the diagram, however, the domain of  is . 10 is not in the domain of . Therefore,  is not in the domain of .

Example Question #75 : Functions/Series

Give the third term of a sequence .

Statement 1: The first and second terms are 10 and 20, respectively.

Statement 2: The fourth and fifth terms are 40 and 50, respectively.

Possible Answers:

STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.

BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.

BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.

STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.

EITHER STATEMENT ALONE provides sufficient information to answer the question.

Correct answer:

BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.

Explanation:

The two statements are insuffcient to determine the third term. Between them, only four of the terms are given. While the sequence seems to be arithmetic with common difference 10, this is not explicitly stated; no specific rule is given for the sequence.

Example Question #71 : Functions/Series

Piecewise

Let  be the piecewise-defined function graphed above. Define function

.

Give the domain of the function .

Possible Answers:

Correct answer:

Explanation:

 is a polynomial function, so its own domain is the set of all real numbers. This does not restrict the domain of . However, since , it follows that  must fall within the domain of , which is .

Therefore,

The domain of  is the set .

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