GMAT Math : Algebra

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 #331 : Algebra

Solve for :

| 4x - 18 | + 18 = 57

Possible Answers:

$x=-5.25 \textrm{ or }x=14.25$

$x=-14.25\textrm{ or }x=14.25$

$x=-5.25 \textrm{ or }x=5.25$

x=14.25

x=-14.25

Correct answer:

$x=-5.25 \textrm{ or }x=14.25$

Explanation:

First, isolate the absolute value expression on one side:

| 4x - 18 | + 18 = 57

| 4x - 18 | + 18 -18 = 57-18

| 4x - 18 | = 39

Rewrite as a compound sentence:

$4x - 18 = - 39 \textrm{ or } 4x - 18 = 39$

Solve each separately:

4x - 18 = - 39

4x - 18+18 = - 39+18

4x= - 21

$4x \div 4= - 21 \div 4$

x= - 5.25

4x - 18 = 39

4x - 18+18 = 39+18

4x= 57

$4x \div 4=57 \div 4$

x = 14.25

The solution set is $\left \{ -5.25, 14.25\right \}$ .

Report an Error

Example Question #1415 : Gmat Quantitative Reasoning

Give the solution set of the equation:

$\left | x ^{2} - 2x \right | = 3x -6$

Possible Answers:

$x \in \left \{ -3, 3\right \}$

The equation has no solution.

$x \in \left \{ -3, 2\right \}$

$x \in \left \{ 2, 3\right \}$

$x \in \left \{ -3, 2, 3\right \}$

Correct answer:

$x \in \left \{ 2, 3\right \}$

Explanation:

Write this as a compound equation and solve each separately.

$\left | x ^{2} - 2x \right | = 3x -6$

$x ^{2} - 2x = 3x -6 \textrm{ or }x ^{2} - 2x = -\left ( 3x -6 \right )$

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

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

$x ^{2} - 5x + 6 =0$

(x-3) (x-2) =0

$x - 3 = 0 \Rightarrow x = 3$

$x - 2 = 0 \Rightarrow x =2$

$x ^{2} - 2x = -\left ( 3x -6 \right )$

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

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

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

(x + 3) (x - 2)= 0

$x + 3 = 0 \Rightarrow x = -3$

$x - 2 = 0 \Rightarrow x =2$

This gives us three possible solutions - $\left \{ -3, 2, 3\right \}$ . We check all three.

x = -3

$\left | x ^{2} - 2x \right | = 3x -6$

$\left | \left ( -3\right ) ^{2} - 2 (-3) \right | = 3 (-3) -6$

$\left | \left9 - (-6) \right | = -9-6$

$\left |15| = -15$

15 = -15

This is a false statement so we can eliminate as a false "solution".

x = 2

$\left | x ^{2} - 2x \right | = 3x -6$

$\left |2^{2} - 2 \cdot 2 \right | = 2 \cdot 3 -6$

$\left | \left 4-4 \right | = 6-6$

|0| = 0

0=0

2 is a solution.

x = 3

$\left | x ^{2} - 2x \right | = 3x -6$

$\left | 3 ^{2} - 2 \cdot 3 \right | = 3 \cdot 3 -6$

$\left | \left 9 - 6\right | = 9-6$

$\left |3 | = 3$

3= 3

3 is a solution.

The solution set is $x \in \left \{ 2, 3\right \}$ .

Report an Error

Example Question #12 : Equations

Solve for :

$4 ^{5x - 7} = 8 ^{2x -1}$

Possible Answers:

x = 4.25

x = -1.0625

The equation has no solution

x = 0.6875

x = 2.75

Correct answer:

x = 2.75

Explanation:

Since $2 ^{2} = 4$ and $2^{3} = 8$ , replace, and use the exponent rules:

$4 ^{5x - 7} = 8 ^{2x -1}$

$\left ( 2 ^{2} \right ) ^{5x - 7} = \left ( 2^{3} \right ) ^{2x -1}$

$2 ^{2 \left ( 5x - 7 \right )}=2 ^{3 \left ( 2x - 1 \right )}$

Set the exponents equal to each other and solve for :

$2 \left ( 5x - 7 \right )=3 \left ( 2x - 1 \right )$

10x -14=6x - 3

10x-6x -14+14=6x -6x - 3+14

4x = 11

$4x \div 4 = 11 \div 4$

x = 2.75

Report an Error

Example Question #1414 : Gmat Quantitative Reasoning

Give the solution set of the equation:

$2x + \left | x\right | = 60$

Possible Answers:

x = 20

$x = 20 \textrm{ or }x= 60$

$x= -60 \textrm{ or } x = 20$

x = 60

x = -60

Correct answer:

x = 20

Explanation:

Case 1: $x \geq 0$

Then $\left | x\right | = x$ , and the equation becomes

2x + x= 60

3x= 60

$3x \div 3 = 60 \div 3$

x = 20

Case 2: x < 0

Then $\left | x\right | = -x$ , and the equation becomes

$2x +\left ( - x \right ) = 60$

x = 60

However, this conflicts with the fact that x < 0 , so this is a false solution.

The only solution is therefore x = 20 .

Report an Error

Example Question #21 : Solving Equations

Give the solution set of the equation:

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

Possible Answers:

$x \in\left \{ 2,3\right \}$

$x \in \left \{ -3,3\right \}$

$x \in\left \{ -2,2\right \}$

$x \in\left \{ -3,-2,2,3\right \}$

$x \in\left \{ -3,-2\right \}$

Correct answer:

$x \in \left \{ -3,3\right \}$

Explanation:

Case 1: is nonnegative - that is, |x| = x .

The equation becomes

$x^{2} =x+ 6$

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

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

(x-3) (x+2 )=0

Either x-3 = 0 , in which case x = 3 ,

or x + 2 = 0 , in which case x = -2 , which is impossible, as we are assuming that is nonnegative.

case 2: is negative - that is, |x| = -x

The equation becomes

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

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

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

(x-2) (x+3 )=0

Either x-2= 0 , in which case x = 2 , which is impossible since we are assuming that is negative,

or x + 3 = 0 , in which case x = -3 .

x = -3 and x = 3 can both be confirmed as solutions.

Report an Error

Example Question #21 : Solving Equations

What is the equation of the line that goes through (1,2) and is parallel to y=3x+4 ?

Possible Answers:

y=3x+1

y=3x-1

y=3x+3

y=3x-4

Correct answer:

y=3x-1

Explanation:

First, we have to find the slope from y=3x+4 using the general form y=mx+b. Therefore m=3

Parallel lines have the same slope, so the new line has a slope of and point (1,2) .

Use the point-slope equation: $y-y_{1}=m(x-x_{1})$

y-2=3(x-1)

y-2=3x-3

y=3x-1

Report an Error

Example Question #22 : Solving Equations

What is the -intercept of 5y+2x=4 ?

Possible Answers:

(2,0)

(4,0)

(0,2)

(0,4)

Correct answer:

(2,0)

Explanation:

To solve for the -intercept, you set the to zero and solve for :

5y+2x=4

5(0)+2x=4

2x=4

x=2

-intercept: (2,0)

Report an Error

Example Question #21 : Solving Equations

What is the y-intercept of 5y+2x=4 ?

Possible Answers:

(0,5)

(5,0)

$\left(\frac{4}{5},0\right)$

$\left(0,\frac{4}{5}\right)$

Correct answer:

$\left(0,\frac{4}{5}\right)$

Explanation:

To solve for the y-intercept, you set to zero and solve for :

5y+2x=4

5y+2(0)=4

5y=4

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

Therefore, the y-intercept is: $\left(0,\frac{4}{5}\right)$

Report an Error

Example Question #22 : Solving Equations

What is the -intercept of y=3x-1 ?

Possible Answers:

$\left(\frac{1}{3},0\right)$

(3,0)

(0,3)

$\left(0,\frac{1}{3}\right)$

Correct answer:

$\left(\frac{1}{3},0\right)$

Explanation:

To solve for the -inter, you set to zero and solve for :

y=3x-1

0=3x-1

1=3x

$x=\frac{1}{3}$

x-intercept:

$\left(\frac{1}{3},0\right)$

Report an Error

Example Question #22 : Equations

What is the y-intercept of y=3x-1 ?

Possible Answers:

(0,-1)

(0,1)

(1,0)

(-1,0)

Correct answer:

(0,-1)

Explanation:

To solve for the y-intercept of y=3x-1 , you set to zero and solve for :

y=3x-1

y=3(0)-1

y=-1

y-intercept: (0,-1)

Report an Error

All GMAT Math Resources

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

Popular Subjects

Spanish Tutors in Los Angeles, Computer Science Tutors in Dallas Fort Worth, Computer Science Tutors in Denver, Chemistry Tutors in Houston, MCAT Tutors in Atlanta, Biology Tutors in Houston, Spanish Tutors in Philadelphia, Calculus Tutors in Miami, Math Tutors in Denver, Spanish Tutors in Miami

Popular Courses & Classes

GRE Courses & Classes in Los Angeles, SAT Courses & Classes in Seattle, Spanish Courses & Classes in Houston, GRE Courses & Classes in Washington DC, GRE Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Philadelphia, SAT Courses & Classes in New York City, MCAT Courses & Classes in Los Angeles, SSAT Courses & Classes in San Diego, ISEE Courses & Classes in San Diego

Popular Test Prep

ISEE Test Prep in San Diego, LSAT Test Prep in New York City, SAT Test Prep in New York City, SAT Test Prep in Philadelphia, SSAT Test Prep in Los Angeles, SSAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Denver, LSAT Test Prep in Dallas Fort Worth, GRE Test Prep in Boston, GRE 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 #331 : Algebra

Example Question #1415 : Gmat Quantitative Reasoning

Example Question #12 : Equations

Example Question #1414 : Gmat Quantitative Reasoning

Example Question #21 : Solving Equations

Example Question #21 : Solving Equations

Example Question #22 : Solving Equations

Example Question #21 : Solving Equations

Example Question #22 : Solving Equations

Example Question #22 : Equations

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details