GMAT Math : Functions/Series

Study concepts, example questions & explanations for GMAT Math

Create An Account

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Functions/Series

Define f (x) = 4x - 9 .

Evaluate $(f \circ g) (9)$ .

Statement 1: g (9) = 8

Statement 2: g (12) = 9

Possible Answers:

BOTH statements TOGETHER are insufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Correct answer:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Explanation:

If you know that g (9) = 8 , then you can calculate:

$(f \circ g) (9) = f (\; g(9)\; ) = f(8) = 4\cdot8 -9 = 23$

Knowing the -values of that are paired with -value 9, however, is neither necessary nor useful here.

Report an Error

Example Question #2 : Functions/Series

The first term of an arithmetic sequence is 100. What is the second term?

Statement 1: The sum of the third and fourth terms is 320.

Statement 2: The tenth term subtracted from the twelfth term yields a difference of 48.

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

Let be the common difference of the sequence. Then the third and fourth terms are, respectively, 100 + 2d and 100+3d . If their sum is 320, then

(100+2d) + (100+3d) =320

200+5d = 320

5d = 120

d = 24

If the difference between the twelfth term 100+11d and tenth term 100+9d is 24, then

(100+11d) - (100+9d) = 48

2d= 48

d = 24

From either statement, the common difference can be calculated, then added to 100 to get the second term, 124.

Report an Error

Example Question #1 : Functions/Series

What is the first term of a geometric sequence?

Statement 1: The product of the second and third terms is 4,096.

Statement 2: The product of the first and fourth terms is 4,096.

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

Let be the first term and be the common ratio. Then the first four terms are:

$A,AR,AR^{2},AR^{3}$

The two statements are equivalent to the equations $AR \cdot AR^{2} = 4.096$ and $A \cdot AR^{3} = 4,096$ . But they turn out to be equivalent as can be seen here:

$AR \cdot AR^{2} = 4096$

$A \cdot A \cdot R \cdot R^{2} = 4096$

$A^{2}R^{3} = 4.096$

$A \cdot AR^{3} = 4,096$

$A^{2}R^{3} = 4,096$

This (common) statement alone is not enough to allow us to calculate .

Report an Error

Example Question #2 : Functions/Series

This relation has five different ordered pairs: is it a function?

$\begin{matrix} \underline{x}&\underline{y}\\ 1& A\\ 2& A\\ 3& A\\ B&A + 1 \\ 5& A + 2 \end{matrix}$

Statement 1: A = 3

Statement 2: B = 5

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Correct answer:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Explanation:

To prove that a relation is a function, you must prove that no -coordinate is matched with more than one -coordinate. Statement 2 proves that this is false, since 5 is now matched with both and A + 1 , which are different numbers regardless of . Statement 1 is irrelevant, since it does not prove or disprove this condition.

Report an Error

Example Question #3 : Functions/Series

$f ^{-1} (A) = 40$

Evaluate .

Statement 1: The graph of includes the point (40, 19) .

Statement 2: f(19) = 40

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Explanation:

If $f ^{-1} (A) = 40$ , then f(40) = A , so this question is equivalent to evaluating f(40) .

If the ordered pair (40, 19) is on the graph of , then f(40) = 19 , so A = 19 .

Knowing that f(19) = 40 is of no help, as this just tells us $f ^{-1} (40) = 19$ .

Report an Error

Example Question #4 : Functions/Series

What is the first term of the geometric sequence?

Statement 1: The sum of the second and third terms is 90.

Statement 2: The sum of the third and fourth terms is 450.

Possible Answers:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Explanation:

Let be the first term and be the common ratio. Then the first four terms are:

$A,AR,AR^{2},AR^{3}$ .

The two statements below are equivalent to $AR+ AR^{2} = 90$ and $AR^{2}+AR^{3} = 450$ , respectively. Neither, alone, will help you figure out or . If you know both, you can use algebra to deduce their values:

$AR^{2}(1+R) = 450$

AR (1 + R) = 90

Divide both sides of the first equation by both sides of the second:

R = 5

Substitute this value into either equation. We'll use the 2nd equation:

$A \cdot 5 \cdot (1 + 5) = 90$

$A \cdot 30 = 90$

A = 3

Report an Error

Example Question #5 : Functions/Series

$\left \lfloor x\right \rfloor$ is defined to be the greatest integer less than or equal to .

Evaluate $\left \lfloor \frac{A}{B} \right \rfloor$

Statement 1: A + 4 = B

Statement 2: B = 2A

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Explanation:

Statement 1 is not enough to answer this question.

Case 1: A = 1,B= 5

Then $\left \lfloor \frac{A}{B} \right \rfloor = \left \lfloor \frac{1}{5} \right \rfloor = 0$

Case 2: A = -1,B= 3

Then $\left \lfloor \frac{A}{B} \right \rfloor = \left \lfloor \frac{-1}{3} \right \rfloor = \left \lfloor - \frac{1}{3} \right \rfloor = -1$

If Statement 2 is true, however:

$\left \lfloor \frac{A}{B} \right \rfloor = \left \lfloor \frac{A}{2A} \right \rfloor = \left \lfloor \frac{1}{2} \right \rfloor =0$

Report an Error

Example Question #6 : Functions/Series

This relation has the following five ordered pairs: is it a function?

$\begin{matrix} \underline{x}&\underline{y}\\ 1& 6\\ 2& 4\\ 3& 7\\ 4&B \\ A& 9 \end{matrix}$

Statement 1: A = 5

Statement 2: B = 4

Possible Answers:

BOTH statements TOGETHER are insufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Explanation:

To prove that a relation is a function, you must prove that no -coordinate is matched with more than one -coordinate. Statement 1 proves that this is true. Statement 2 is irrelevant; it is possible for more than one -coordinate to be matched with the same -coordinate in a function.

Report an Error

Example Question #6 : Dsq: Understanding Functions

This relation has five different ordered pairs: is it a function?

$\begin{matrix} \underline{x}&\underline{y}\\ 1& 6\\ 2& 4\\ 3& 7\\ 4&B \\ A& 9 \end{matrix}$

Statement 1: A = 3

Statement 2: B = 5

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Explanation:

To prove that a relation is a function, you must prove that no -coordinate is matched with more than one -coordinate. Statement 1 proves that this is false, since 3 is now matched with both 7 and 9. Statement 2 is irrelevant, since it does not prove or disprove this condition.

Report an Error

Example Question #7 : Dsq: Understanding Functions

Define an operation $\diamond$ as follows:

For any real numbers A,B ,

$A \diamond B = A^{2}-B$

Evaluate $5 \diamond 0 + 0 \diamond 5$

Possible Answers:

Undefined

Correct answer:

Explanation:

$5 \diamond 0 = 5^{2}-0 = 25$

$0\diamond 5 = 0^{2}-5 = -5$

$5 \diamond 0 + 0 \diamond 5 = 25 + (-5) = 20$

Report an Error

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ISEE Tutors in Denver, Algebra Tutors in Seattle, SAT Tutors in Washington DC, English Tutors in San Diego, French Tutors in San Francisco-Bay Area, Algebra Tutors in Los Angeles, French Tutors in Denver, Calculus Tutors in Los Angeles, English Tutors in Phoenix, Biology Tutors in Washington DC

Popular Courses & Classes

ACT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Chicago, Spanish Courses & Classes in San Diego, GMAT Courses & Classes in Boston, Spanish Courses & Classes in Chicago, Spanish Courses & Classes in Los Angeles, GMAT Courses & Classes in Washington DC, ACT Courses & Classes in Denver, LSAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Miami

Popular Test Prep

ACT Test Prep in Phoenix, GMAT Test Prep in Boston, ISEE Test Prep in Denver, MCAT Test Prep in Atlanta, SAT Test Prep in Atlanta, GRE Test Prep in San Diego, ACT Test Prep in San Francisco-Bay Area, ACT Test Prep in Miami, ACT Test Prep in Denver, MCAT Test Prep in Chicago

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

Email address:
Your name:
Feedback:

GMAT Math : Functions/Series

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Functions/Series

Example Question #2 : Functions/Series

Example Question #1 : Functions/Series

Example Question #2 : Functions/Series

Example Question #3 : Functions/Series

Example Question #4 : Functions/Series

Example Question #5 : Functions/Series

Example Question #6 : Functions/Series

Example Question #6 : Dsq: Understanding Functions

Example Question #7 : Dsq: Understanding Functions

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details