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 #17 : Algebra

Given 5x-7y=-2 and 8y-x=7 , find the values of and .

Possible Answers:

x=1, y=1

x=-1, y=1

x=2, y=-1

x=4, y=-1

Correct answer:

x=1, y=1

Explanation:

We can solve this problem by setting up a system of equations and using elimination:

5x-7y=-2

8y-x=7

We can eliminate the and solve for by multiplying the bottom equation by and adding the equations:

5x-7y=-2

-5x+40y=35

___________________

33y=33

y=1

We can now find by substituting our into any equation:

8(1)-x=7

8-7=x

x=1

Report an Error

Example Question #1101 : Gmat Quantitative Reasoning

The product of two positive numbers, and , yields . If their sum is , what is the value of ?

Possible Answers:

$\textup{More information is required to solve this problem.}$

Correct answer:

$\textup{More information is required to solve this problem.}$

Explanation:

We have enough information to write out two equations:

$n\cdot p=24$

n+p=11

Using the first equation, we can narrow our potential values to: $\textup{ 1 and 24, 2 and 12, 3 and 8, and 4 and 6}$ .

Using the second equation, we can narrow down our values even further to $\textup{3 and 8}$ . We are, however, being asked specifically for the value of . Since we cannot state if the or the represents and which represents , we cannot answer this question. Additional data, such as is less than , would be required.

Report an Error

Example Question #14 : Algebra

Solve for .

3x-2y=16

-2x+3y=-4

Possible Answers:

10.5

Correct answer:

Explanation:

We can solve this problem in the same way we would solve a system of equations using elimination. Since we are solving for we can manipulate the system to cancel out the values: 3(3x-2y=16) 9x-6y=48

2(-2x+3y=-4) -4x+6y=-8

We then add the equations. Notice how the values cancel out 5x=40

leaving us with x=8

Report an Error

Example Question #1101 : Gmat Quantitative Reasoning

Solve the following system of equations:

x+y=7

x-y=3

Possible Answers:

x=2,y=5

x=4,y=3

x=3,y=4

x=5,y=2

Correct answer:

x=5,y=2

Explanation:

To solve, I used the elimination method by adding the tqo equations together. That eliminates y and leaves you with:

$2x=10\Rightarrow x=5$

Therefore,

$(5)+y=7\Rightarrow y=2$

Report an Error

Example Question #22 : Algebra

Which of the following equations is parallel to the line given by the equation:

$y = \frac{-4}{3}x + 15$

Possible Answers:

$y = \frac{3}{4}x +15$

-3y = 45 - 4x

-6y = 8x + 18

3y = -8x + 15

-4y = 3x + 15

Correct answer:

-6y = 8x + 18

Explanation:

For lines to be parallel, their equations must have equal slopes. Therefore, we are looking for another line with a slope of -4/3. If we convert the equation:

-6y = 8x + 18

into slope - intercept form, we get:

$\frac{-6y}{-6} = \frac{8x}{-6} + \frac{18}{-6}$

$y = \frac{-8}{6}x - 3 = y = \frac{-4}{3}x - 3$

It has the same slope, and therefore is parallel to the original line.

Report an Error

Example Question #22 : Algebra

The equations -6y = 3x + 18 and 4y = -8x + 12 intersect at the point (4, y) . What is y?

Possible Answers:

$\frac{1}{5}$

$\frac{-1}{5}$

Correct answer:

Explanation:

The easiest way to solve the problem is to solve for y in one of the equations and then plug it into the other equation:

$\frac{4y}{4} = \frac{-8x}{4} + \frac{12}{4} = y = -2x + 3$

-6(-2x + 3) = 3x + 18 12x - 3x - 18 + 18 = 3x -3x + 18 + 18

9x = 36

x = 4

We can then plug that x-value into one of the original equations:

4y = -8(4) + 12

$\frac{4y}{4} = \frac{-32 + 12}{4} = y= \frac{-20}{4} = -5$

Report an Error

Example Question #1 : Understanding Exponents

$\frac{6^{3}}{36} + \frac{3^{68}}{3^{67}}=$

Possible Answers:

$\dpi{100} \small 6$

cannot be determined

$\dpi{100} \small 9$

$\dpi{100} \small 36$

$\dpi{100} \small 18$

Correct answer:

$\dpi{100} \small 9$

Explanation:

$\frac{6^{3}}{36} = \frac{6^{3}}{6^{2}} = 6$

$\frac{3^{68}}{3^{67}} = 3^{68-67} = 3$

Putting these together,

$\frac{6^{3}}{36} + \frac{3^{68}}{3^{67}}= 6 + 3 = 9$

Report an Error

Example Question #1 : Exponents

$\dpi{100} \small 3x^{4}\times x^{2}+x^{2}-x =$

Possible Answers:

$x(3x^{5}-x+1)$

$x(3x^{5}+x-1)$

$3x^{9}$

$3x^{5}+x-1$

$3x^{7}$

Correct answer:

$x(3x^{5}+x-1)$

Explanation:

$\dpi{100} \small 3x^{4}\times x^{2} =3x^{6}$

Then, $\dpi{100} \small 3x^{4}\times x^{2}+x^{2}-x = 3x^{6}+x^{2}-x = x(3x^{5}+x-1)$

Report an Error

Example Question #1 : Exponents

$4^{\frac{3}{2}} + 27^{\frac{2}{3}} =$

Possible Answers:

$\dpi{100} \small 8$

$\dpi{100} \small 16$

$\dpi{100} \small 27$

$\dpi{100} \small 17$

$\dpi{100} \small 9$

Correct answer:

$\dpi{100} \small 17$

Explanation:

$4^{\frac{3}{2}}=(4^{\frac{1}{2}})^{3} = 2^{3} = 8$

$27^{\frac{2}{3}}=(27^{\frac{1}{3}})^{2} = 3^{2} = 9$

Then putting them together, $4^{\frac{3}{2}} + 27^{\frac{2}{3}} = 8 + 9 = 17$

Report an Error

Example Question #2 : Understanding Exponents

Which of the following expressions is equivalent to this expression?

$\small \frac{x^{-\frac{1}{2}}}{x^{\frac{1}{3}}}$

You may assume that $\small x > 0$ .

Possible Answers:

$\small \small \frac{\sqrt[6]{x^{5}}}{x}$

$\small x\sqrt{x}$

$\small \small \small \frac{\sqrt[5]{x^{6}}}{x}$

$\small \frac{\sqrt[6]{x}}{x}$

$\small \sqrt[3]{x^{2}}$

Correct answer:

$\small \frac{\sqrt[6]{x}}{x}$

Explanation:

$\small \small \small \small \small \small \small \small \small \frac{x^{-\frac{1}{2}}}{x^{\frac{1}{3}}} = x^{-\frac{1}{2} -{\frac{1}{3}} } = x^{-\frac{2}{6} -{\frac{3}{6}} }= x^{-\frac{5}{6} }= \frac{1}{ x^{\frac{5}{6}}}$

$\small \small \small = \frac{1}{\sqrt[6]{x^{5}}}= \frac{\sqrt[6]{x}}{\sqrt[6]{x^{5}}\cdot \sqrt[6]{x}}= \frac{\sqrt[6]{x}}{x}$

Report an Error

All GMAT Math Resources

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

Popular Subjects

Math Tutors in Atlanta, Biology Tutors in Phoenix, ACT Tutors in Dallas Fort Worth, LSAT Tutors in San Diego, French Tutors in San Diego, SAT Tutors in Denver, Biology Tutors in Dallas Fort Worth, ISEE Tutors in Boston, Math Tutors in San Francisco-Bay Area, French Tutors in Washington DC

Popular Courses & Classes

ACT Courses & Classes in Atlanta, Spanish Courses & Classes in New York City, SSAT Courses & Classes in Atlanta, ACT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Boston, SSAT Courses & Classes in Chicago, LSAT Courses & Classes in Washington DC, MCAT Courses & Classes in Philadelphia, MCAT Courses & Classes in Los Angeles

Popular Test Prep

ACT Test Prep in Atlanta, ACT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Dallas Fort Worth, ACT Test Prep in Dallas Fort Worth, SSAT Test Prep in Phoenix, SAT Test Prep in Washington DC, SSAT Test Prep in Los Angeles, GRE Test Prep in San Diego, LSAT Test Prep in Miami, SSAT Test Prep in San Diego

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 #17 : Algebra

Example Question #1101 : Gmat Quantitative Reasoning

Example Question #14 : Algebra

Example Question #1101 : Gmat Quantitative Reasoning

Example Question #22 : Algebra

Example Question #22 : Algebra

Example Question #1 : Understanding Exponents

Example Question #1 : Exponents

Example Question #1 : Exponents

Example Question #2 : Understanding Exponents

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details