GMAT Math : Solving equations

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 #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 #355 : Algebra

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 #42 : Equations

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

Possible Answers:

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

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

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

Not enough information provided

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

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

Example Question #361 : Algebra

Solve for : $\frac{1}{3}x+\frac{2}{3}y=\frac{7}{9}$

Possible Answers:

$y=\frac{7}{3}-2x$

$x=\frac{7}{3}-2y$

$x=\frac{2}{3}-7y$

$x=\frac{3}{7}-2y$

Not enough information provided

Correct answer:

$x=\frac{7}{3}-2y$

Explanation:

In order to solve the equation for , we need to isolate on one side of the equation:

$\frac{1}{3}x+\frac{2}{3}y=\frac{7}{9}$

$\frac{1}{3}x=\frac{7}{9}-\frac{2}{3}y$

$x=\frac{21}{9}-2y$

Reducing the fraction,

$x=\frac{7}{3}-2y$

Report an Error

Example Question #361 : Algebra

Solve for in the equation

3d + ad + y = 10

Possible Answers:

$d= \frac{10 - y }{3+a}$

$d= \frac{10 + y }{3+a}$

$d= \frac{10 - y+a }{3 }$

$d= \frac{10 - y-a }{3 }$

$d= \frac{y-10 }{3+a}$

Correct answer:

$d= \frac{10 - y }{3+a}$

Explanation:

3d + ad + y = 10

3d + ad + y - y= 10 - y

3d + ad = 10 - y

$\left (3 + a \right )d = 10 - y$

$\frac{\left (3 + a \right )d }{3+a}= \frac{10 - y }{3+a}$

$d= \frac{10 - y }{3+a}$

Report an Error

Example Question #363 : Algebra

Solve for in the equation:

$v = 1+ \sqrt[3]{w-7}$

Possible Answers:

$w = v^{3} -3v^{2}+3v+6$

$w = v^{3} +6$

$w = v^{3} +3v^{2}+3v-6$

$w = v^{3} +3v^{2}+3v+8$

$w = v^{3} -3v^{2}+3v-8$

Correct answer:

$w = v^{3} -3v^{2}+3v+6$

Explanation:

$v = 1+ \sqrt[3]{w-7}$

$v- 1 = 1+ \sqrt[3]{w-7} - 1$

$\sqrt[3]{w-7} = v- 1$

$\left (\sqrt[3]{w-7}\right )^{3} = \left (v- 1 \right )^{3}$

$w-7= v^{3} -3v^{2}+3v-1$

$w-7+ 7= v^{3} -3v^{2}+3v-1 + 7$

$w = v^{3} -3v^{2}+3v+6$

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 Phoenix, Reading Tutors in Miami, SSAT Tutors in Boston, Spanish Tutors in Washington DC, Algebra Tutors in Philadelphia, SSAT Tutors in New York City, Computer Science Tutors in Dallas Fort Worth, SAT Tutors in Chicago, GRE Tutors in Houston, Algebra Tutors in Houston

Popular Courses & Classes

ISEE Courses & Classes in Washington DC, SSAT Courses & Classes in Miami, GRE Courses & Classes in Phoenix, GMAT Courses & Classes in Seattle, Spanish Courses & Classes in Washington DC, MCAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in New York City, GRE Courses & Classes in Boston, GMAT Courses & Classes in Phoenix

Popular Test Prep

ISEE Test Prep in Miami, ISEE Test Prep in New York City, SAT Test Prep in Atlanta, SSAT Test Prep in Denver, GMAT Test Prep in Phoenix, GRE Test Prep in San Diego, GRE Test Prep in Chicago, SAT Test Prep in Phoenix, GRE Test Prep in Phoenix, MCAT Test Prep in Washington DC

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 : Solving equations

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #351 : Algebra

Example Question #354 : Algebra

Example Question #355 : Algebra

Example Question #41 : Equations

Example Question #353 : Algebra

Example Question #42 : Equations

Example Question #354 : Algebra

Example Question #361 : Algebra

Example Question #361 : Algebra

Example Question #363 : Algebra

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details