GMAT Math : Algebra

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

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

Example Questions

Example Question #34 : Solving Equations

A factory makes barrels of the same shape but different sizes; the amount of water they hold varies directly as the cube of their height. The four-foot-high barrel holds 20 gallons of water; how much water would the six-foot-high barrel hold?

Possible Answers:

$67 \frac{1}{2}\textrm{ gal}$

$30\textrm{ gal}$

$80\textrm{ gal}$

$45\textrm{ gal}$

$64\textrm{ gal}$

Correct answer:

$67 \frac{1}{2}\textrm{ gal}$

Explanation:

Let be the height of a barrel and be its volume. Since varies directly as the cube of , the variation equation is

$V = k h^{3}$

for some constant of variation .

We find by substituting V = 20, h= 4 from the smaller barrels:

$20 = k \cdot 4^{3}$

$20 = k \cdot 64$

$k = \frac{20 }{64}= \frac{5 }{16}$

Then the variation equation is:

$V = \frac{5 }{16} h^{3}$

Now we can substitute h = 6 to find the volume of the larger barrel:

$V = \frac{5 }{16} \cdot 6^{3} = \frac{5 }{16} \cdot 216 = \frac{5 }{16} \cdot \frac{216}{1} = \frac{5 }{2} \cdot \frac{27}{1} = \frac{135 }{2}= 67 \frac{1 }{2}$

The larger barrel holds $67 \frac{1 }{2}$ gallons.

Report an Error

Example Question #35 : Solving Equations

Solve for .

-x-3xy+4>0

Possible Answers:

$x>\frac{4}{1+3y}$

$x<\frac{-4}{1+3y}$

$x>\frac{-4}{1+3y}$

$x<\frac{4}{1+3y}$

Correct answer:

$x<\frac{4}{1+3y}$

Explanation:

$-x-3xy+4>0\Rightarrow 4>x+3xy$

$4>x(1+3y) \Rightarrow \frac{4}{1+3y}>x$

Report an Error

Example Question #32 : Equations

To convert Celsius temperature to the equivalent in Fahrenheit temperature , use the formula

$F = \frac{9}{5}C + 32$

To the nearest tenth of a degree, convert $70^{\circ } C$ to degrees Fahrenheit.

Possible Answers:

$183.6 ^{\circ } F$

$68.4 ^{\circ } F$

$158.0 ^{\circ } F$

$94.0 ^{\circ } F$

$21.1 ^{\circ } F$

Correct answer:

$158.0 ^{\circ } F$

Explanation:

$F = \frac{9}{5}C + 32 = \frac{9}{5} \cdot 70 + 32 = 126 + 32 = 158$

Report an Error

Example Question #351 : Algebra

Solve for :

13+X-Y=2Y

Possible Answers:

X=-16Y

X=10

X=-13+3Y

X=13+-3Y

X=16Y

Correct answer:

X=-13+3Y

Explanation:

13+X-Y=2Y

We need to isolate . Move all other terms to the right hand side of the equation:

13+X-Y-13+Y=2Y-13+Y

Combine like terms:

X=-13+3Y

Report an Error

Example Question #354 : Algebra

Solve for the value of :

|x-4|=-3x+5

Possible Answers:

$(\frac{9}{4},\frac{1}{2})$

$(\frac{4}{9},\frac{1}{2})$

$(-\frac{9}{4},\frac{1}{2})$

$(\frac{5}{4},\frac{3}{2})$

$(-\frac{1}{2}, \frac{9}{4})$

Correct answer:

$(\frac{9}{4},\frac{1}{2})$

Explanation:

|x-4|=-3x+5

To solve this absolute value equation, we need to set the right side of the equation equal to a positive and negative version in order to calculate the two options for absolute value.

x-4=-3x+5 OR x-4=-(-3x+5)=3x-5

x+3x=5+4 OR x-3x=-5+4

4x=9 OR -2x=-1

$x=\frac{9}{4}$ OR $x=\frac{1}{2}$

Report an Error

Example Question #41 : Solving Equations

4-n=5

5m-8=12+3m

You are given the equations above. What is m-n ?

Possible Answers:

Correct answer:

Explanation:

We first solve each of the equations to find and :

4-n=5

-n=5-4

n=-1

5m-8=12+3m

5m-3m=12+8

2m=20

m=10

m-n=10-(-1)=10+1=11

Therefore, m-n=11 .

Report an Error

Example Question #41 : Equations

You are given the following equation:

$x=\frac{x-6}{3+x}$

What is the value of $x^{2}+2x+3$ ?

Possible Answers:

Correct answer:

Explanation:

First, we need to solve the provided equation for .

$x=\frac{x-6}{3+x}$

x(3+x)=x-6

$3x+x^{2}=x-6$

$3x+x^{2}-x=-6$

$x^{2}+2x+6=0$

We want to find the value of $x^{2}+2x+3$ . We can put the equation in this form by subtracting from each side:

$x^{2}+2x+6-3=-3$

$x^{2}+2x+3=-3$

Report an Error

Example Question #353 : Algebra

Solve $\left | 2x+12\right |=20$ .

Possible Answers:

x=8 or x=-16

x=4 or x=-16

x=-16

x=4

x=8

Correct answer:

x=4 or x=-16

Explanation:

Since we are solving an absolute value equation, $\left | 2x+12\right |=20$ , we must solve for both potential values of the equation:

1.) 2x+12=20

2.) 2x+12=-20

Solving Equation 1:

2x+12=20

2x=8

x=4

Solving Equation 2:

2x+12=-20

2x=-32

x=-16

Therefore, for $\left | 2x+12\right |=20$ , x=4 or x=-16 .

Report an Error

Example Question #1441 : Gmat Quantitative Reasoning

Solve for : 3y-4x=7x+33

Possible Answers:

$y=\frac{3}{11}x+11$

$y=\frac{11}{3}x+11$

Not enough information provided

$y=-\frac{3}{11}x+11$

$y=-\frac{11}{3}x+11$

Correct answer:

$y=\frac{11}{3}x+11$

Explanation:

In order to solve 3y-4x=7x+33 for , we need to isolate on one side of the equation:

3y-4x=7x+33

3y=11x+33

$y=\frac{11}{3}x+11$

Report an Error

Example Question #354 : Algebra

Which of the following is a solution to the equation 7x+3y=22 ?

Possible Answers:

x=1, y=5

Two of the other answers are correct.

x=5, y=1

x=4, y=2

x=2, y=3

Correct answer:

x=1, y=5

Explanation:

In order to find values of and for which 7x+3y=22 , we need to plug the values into the equation:

1.) x=1, y=5 : 7(1)+3(5)=7+15=22 Correct

2.) x=5, y=1 : 7(5)+3(1)=35+3=38 Incorrect

3.) x=2, y=3 : 7(2)+3(3)=14+9=23 Incorrect

4.) x=4, y=2 : 7(4)+3(2)=28+6=34 Incorrect

Therefore, the only correct answer is x=1, y=5 .

Report an Error

All GMAT Math Resources

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

Popular Subjects

English Tutors in Washington DC, SAT Tutors in San Francisco-Bay Area, French Tutors in San Diego, ACT Tutors in Houston, Spanish Tutors in New York City, SAT Tutors in Miami, GRE Tutors in Denver, Computer Science Tutors in Philadelphia, GMAT Tutors in Phoenix, GRE Tutors in San Francisco-Bay Area

Popular Courses & Classes

Spanish Courses & Classes in Boston, SSAT Courses & Classes in Chicago, GMAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Seattle, GMAT Courses & Classes in Miami, LSAT Courses & Classes in Washington DC, ISEE Courses & Classes in Houston, MCAT Courses & Classes in Boston, GRE Courses & Classes in Miami, LSAT Courses & Classes in Boston

Popular Test Prep

SSAT Test Prep in Philadelphia, ACT Test Prep in San Diego, GMAT Test Prep in Denver, LSAT Test Prep in Phoenix, ACT Test Prep in Seattle, GMAT Test Prep in Seattle, LSAT Test Prep in Miami, ACT Test Prep in Denver, SAT Test Prep in Houston, ISEE Test Prep in Dallas Fort Worth

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 : Algebra

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #34 : Solving Equations

Example Question #35 : Solving Equations

Example Question #32 : Equations

Example Question #351 : Algebra

Example Question #354 : Algebra

Example Question #41 : Solving Equations

Example Question #41 : Equations

Example Question #353 : Algebra

Example Question #1441 : Gmat Quantitative Reasoning

Example Question #354 : Algebra

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details