GMAT Math : GMAT Quantitative Reasoning

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 #31 : Functions/Series

Define an operation $\triangleright$ on two real numbers as follows:

For all real numbers a,b ,

$a \triangleright b = \frac{a}{b}$ if and only if $b \neq 0$ , and $a \triangleright b = a ^{2}$ otherwise.

Evaluate:

$\left (5 \triangleright 2 \right )-\left ( 2 \triangleright 5 \right )$

Possible Answers:

2.1

- 2.1

Correct answer:

2.1

Explanation:

We can evaluate both $5 \triangleright 2 \right$ and $2 \triangleright 5$ using the first part of the definition, since the second number is nonzero in both cases.

$a \triangleright b = \frac{a}{b}$

$5\triangleright 2 = \frac{5}{2} = 2.5$

$2\triangleright 5 = \frac{2}{5} = 0.4$

$\left (5 \triangleright 2 \right )-\left ( 2 \triangleright 5 \right ) = 2.5 - 0.4 = 2.1$

Report an Error

Example Question #171 : Algebra

Define an operation $\bullet$ on the real numbers as follows:

$a \bullet b = a ^{2} (b- 10)$ for all real a,b .

Evaluate:

$10 \bullet 5$

Possible Answers:

500

Correct answer:

Explanation:

$a \bullet b = a ^{2} (b- 10)$

$10 \bullet 5 = 10 ^{2} (5- 10) = 100 \cdot (-5) = -500$

Report an Error

Example Question #33 : Functions/Series

Define f (x) = 5x + 9 .

What is $f ^{-1}$ ?

Possible Answers:

$f ^{-1} (x)=- \frac{1}{5}x + \frac{9}{5}$

$f ^{-1} (x)=- \frac{1}{5}x - \frac{9}{5}$

$f ^{-1} (x)= \frac{1}{5}x - \frac{9}{5}$

$f ^{-1} (x)=-5x -9$

$f ^{-1} (x)= \frac{1}{5}x - 9$

Correct answer:

$f ^{-1} (x)= \frac{1}{5}x - \frac{9}{5}$

Explanation:

Replace f(x) with .

y = 5x + 9

Now exchange and and solve for in the new expression:

x = 5y + 9

x - 9 = 5y + 9 - 9

x - 9 = 5y

$\left (x - 9 \right ) \div 5 = 5y \div 5$

$\frac{1}{5}x - \frac{9}{5} = y$

$f ^{-1} (x)= \frac{1}{5}x - \frac{9}{5}$

Report an Error

Example Question #34 : Understanding Functions

Define $f (x) = x ^{3}$

What is $f ^{-1}$ ?

Possible Answers:

$f ^{-1} (x) = - \sqrt[3]{x}$

$f (x) = \frac{1}{x ^{3}}$

$f (x) = - x ^{3}$

$f (x) = - \frac{1}{x ^{3}}$

$f ^{-1} (x) = \sqrt[3]{x}$

Correct answer:

$f ^{-1} (x) = \sqrt[3]{x}$

Explanation:

Replace f(x) with .

$y= x ^{3}$

Now exchange and and solve for in the new expression:

$x= y^{3}$

$\sqrt[3]{x}= \sqrt[3]{y^{3}}$

$\sqrt[3]{x}=y$

$f^{-1}(x)= \sqrt[3]{x}$

Report an Error

Example Question #181 : Algebra

Define an operation $\bigstar$ on two real numbers as follows:

$a \bigstar b = 100-ab$ for all real numbers a,b

Solve for :

$y \bigstar 7 = 44$

Possible Answers:

y=8

$y = 10 \frac{4}{7}$

y=137

y = 49

y = 7

Correct answer:

y=8

Explanation:

Substitute a=y,b=7 into the definition and solve:

$a \bigstar b = 100-ab$

$y \bigstar 7 = 44$

$100- y \cdot 7 = 44$

100- 7 y = 44

100- 7 y -100 = 44-100

- 7 y = -56

$- 7 y\div (-7) = -56 \div (-7)$

y=8

Report an Error

Example Question #41 : Functions/Series

Define $f(x)= x ^{3} - 125$ .

What is $f ^{-1}$ ?

Possible Answers:

$f ^{-1} (x)= \sqrt[3]{x}+5$

$f ^{-1} (x)= \sqrt[3]{x}+125$

$f ^{-1} (x)= \sqrt[3]{x+125}$

$f ^{-1} (x)= \sqrt[3]{x+5}$

$f ^{-1} (x)=\frac{1}{x ^{3} - 125}$

Correct answer:

$f ^{-1} (x)= \sqrt[3]{x+125}$

Explanation:

Replace f(x) with .

$y= x ^{3} - 125$

Now exchange and and solve for in the new expression:

$x= y^{3} - 125$

$x + 125= y^{3} - 125 + 125$

$x + 125= y^{3}$

$\sqrt[3]{x + 125 }= y$

$f ^{-1} (x)= \sqrt[3]{x+125}$

Report an Error

Example Question #41 : Functions/Series

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

$a \oplus b = ab$ if and are both odd or both even; otherwise, $a \oplus b = 0$ .

Evaluate:

$\left ( 5 \oplus 5\right ) + \left ( 6 \oplus 6\right )$

Possible Answers:

6 1

Correct answer:

6 1

Explanation:

Both $5 \oplus 5$ and $6 \oplus 6$ can be defined using the first part of the definition of $a \oplus b$ , as in the first case, both numbers are odd, and in the second case, both are even.

$a \oplus b = ab$

$5 \oplus 5 = 5 \times 5 = 25$

$6 \oplus 6 =6 \times 6 = 36$

Add:

$\left ( 5 \oplus 5\right ) + \left ( 6 \oplus 6\right ) = 25 + 36 = 61$

Report an Error

Example Question #1261 : Problem Solving Questions

Define $f (x) = \frac{5}{4-x}$ .

What is $f ^{-1}$ ?

Possible Answers:

$f^{-1}(x)=\frac{5-x }{4}$

$f^{-1}(x)=\frac{ 5x -4 }{x }$

$f^{-1}(x)=\frac{ 4x -5 }{x }$

$f^{-1}(x)=\frac{ 4x -1 }{5x }$

$f^{-1}(x)=\frac{ 4-x }{5}$

Correct answer:

$f^{-1}(x)=\frac{ 4x -5 }{x }$

Explanation:

Replace f(x) with .

$y = \frac{5}{4-x}$

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

$x = \frac{5}{4-y}$

$x \left ( 4-y \right ) = \frac{5}{4-y} \left ( 4-y \right )$

$x \left ( 4-y \right ) = 5$

$\frac{x \left ( 4-y \right ) }{x }=\frac{ 5 }{x }$

$4-y=\frac{ 5 }{x }$

$4-y +y -\frac{ 5 }{x } =\frac{ 5 }{x }+y -\frac{ 5 }{x }$

$4-\frac{ 5 }{x } =y$

$f^{-1}(x)= 4-\frac{ 5 }{x } =\frac{ 4x }{x } -\frac{ 5 }{x } = \frac{ 4x -5 }{x }$

Report an Error

Example Question #1261 : Problem Solving Questions

Define $f (x) = \frac{1}{7} x- 13$ .

What is $f ^{-1}$ ?

Possible Answers:

$f ^{-1} (x) = 7 x + 13$

$f ^{-1} (x) = - 7 x + 91$

$f ^{-1} (x) = -\frac{1}{7} x + 13$

$f ^{-1} (x) = -\frac{1}{7} x + 91$

$f ^{-1} (x) = 7 x + 91$

Correct answer:

$f ^{-1} (x) = 7 x + 91$

Explanation:

Replace f(x) with .

$y = \frac{1}{7} x- 13$

Now exchange and and solve for in the new expression:

$x= \frac{1}{7} y- 13$

$x + 13 = \frac{1}{7} y- 13 + 13$

$x + 13 = \frac{1}{7} y$

$\left ( x + 13 \right ) \cdot 7 = \frac{1}{7} y \cdot 7$

7 x + 91 = y

Therefore,

$f ^{-1} (x) = 7 x + 91$ .

Report an Error

Example Question #41 : Understanding Functions

Define an operation $\bigstar$ on two real numbers as follows:

For all real a,b ,

$a \bigstar b = a+ \sqrt{\left |b \right |}$ .

Evaluate:

$49 \bigstar (-64)$

Possible Answers:

Correct answer:

Explanation:

$a \bigstar b = a+ \sqrt{\left |b \right |}$

$49 \bigstar (-64) = 49 + \sqrt{\left | -64 \right |} = 49 + \sqrt{64 } = 49 + 8 = 57$

Report an Error

All GMAT Math Resources

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

Popular Subjects

Algebra Tutors in Houston, GRE Tutors in Philadelphia, LSAT Tutors in Denver, LSAT Tutors in Atlanta, Calculus Tutors in Phoenix, Reading Tutors in Philadelphia, GRE Tutors in San Francisco-Bay Area, MCAT Tutors in Los Angeles, English Tutors in Miami, GMAT Tutors in Boston

Popular Courses & Classes

LSAT Courses & Classes in Seattle, ISEE Courses & Classes in Houston, ACT Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Phoenix, SSAT Courses & Classes in New York City, MCAT Courses & Classes in Atlanta, SAT Courses & Classes in Los Angeles, GMAT Courses & Classes in San Diego, SAT Courses & Classes in Denver, LSAT Courses & Classes in Washington DC

Popular Test Prep

SAT Test Prep in Seattle, LSAT Test Prep in Phoenix, SAT Test Prep in Miami, LSAT Test Prep in Seattle, SAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Miami, ISEE Test Prep in San Diego, ISEE Test Prep in Phoenix, ISEE Test Prep in Chicago, GRE 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 : GMAT Quantitative Reasoning

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #31 : Functions/Series

Example Question #171 : Algebra

Example Question #33 : Functions/Series

Example Question #34 : Understanding Functions

Example Question #181 : Algebra

Example Question #41 : Functions/Series

Example Question #41 : Functions/Series

Example Question #1261 : Problem Solving Questions

Example Question #1261 : Problem Solving Questions

Example Question #41 : Understanding Functions

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details