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 #431 : Algebra

Solve for .

(x-3)^2=2x^2+14

Possible Answers:

x=-1, -5

x=1, 5

x=2,3

x=-2,-3

Correct answer:

x=-1, -5

Explanation:

In order to solve this problem, we need to combine like terms and then factor:

(x-3)^2=2x^2+14

x^2-6x+9=2x^2+14

0=x^2+6x+5

0=(x+5)(x+1)

x=-1, -5

Report an Error

Example Question #21 : Solving By Factoring

Solve for :

$4x^{3} - 28x^{2} + 48x = 0$

Possible Answers:

x=28,48

x=0,3,4

x=3,4

x=-3,-4

x=0,-3,-4

Correct answer:

x=0,3,4

Explanation:

To solve this we must factor:

The first step is to recognize that all of the terms on the equation's left side contain 4x. Therefore we can pull 4x out:

$4x(x^{2}-7x +12) = 0$

Then we factor the inside of the parentheses, realizing that only -3, and -4 add to form -7, and multiply to form 12:

4x(x - 3)(x - 4) = 0

Now we can see that, for the left side of the equation to equal zero, x can only equal 0, 3, or 4.

Report an Error

Example Question #1511 : Gmat Quantitative Reasoning

Solve the following by factoring:

2x^2-6x-8=0

Possible Answers:

x=4,-1

x=2,-6

x=-4,1

x=6,-2

Correct answer:

x=4,-1

Explanation:

To solve, divide out a and then factor.

2(x^2-3x-4)=0

x^2-3x-4=0

(x-4)(x+1)=0

x=4,-1

Report an Error

Example Question #21 : Solving By Factoring

Simplify $\frac{3x^{2}-27}{x-3}$ .

Possible Answers:

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

3x+9

x+3

3x+3

$\frac{3}{x-3}$

Correct answer:

3x+9

Explanation:

$\frac{3x^{2}-27}{x-3}=\frac{3(x^{2}-9)}{x-3}=\frac{3(x-3)(x+3)}{x-3}$

=3(x+3)=3x+9.

Report an Error

Example Question #1 : Absolute Value

Solve $\left | 3x - 7 \right |=8$ .

Possible Answers:

x=5

x=5 or $\dpi{100} -\frac{1}{3}$

x=-5 or $\frac{1}{3}$

x=5 or $\frac{1}{3}$

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

Correct answer:

x=5 or $\dpi{100} -\frac{1}{3}$

Explanation:

$\left | 3x - 7 \right |=8$ really consists of two equations: $3x - 7 = \pm 8$

We must solve them both to find two possible solutions.

$3x - 7 = 8 \Rightarrow 3x = 15\Rightarrow x = 5$

$3x - 7 = - 8 \Rightarrow 3x = -1\Rightarrow x = -1/3$

So x=5 or $\dpi{100} -\frac{1}{3}$ .

Report an Error

Example Question #2 : Absolute Value

Solve $\left | 2x - 5 \right |\geq 3$ .

Possible Answers:

$x < 1, x > 4$

$x \leq 1, x\geq 4$

$-2 \leq x\leq 5$

$x \leq -1, x\geq -4$

$1 < x < 4$

Correct answer:

$x \leq 1, x\geq 4$

Explanation:

It's actually easier to solve for the complement first. Let's solve $\left | 2x-5 \right |<3$ . That gives -3 < 2x - 5 < 3. Add 5 to get 2 < 2x < 8, and divide by 2 to get 1 < x < 4. To find the real solution then, we take the opposites of the two inequality signs. Then our answer becomes $x\leq 1 \textsc{ or } x\geq 4$ .

Report an Error

Example Question #3 : Absolute Value

Give the -intercept(s), if any, of the graph of the function $f (x) = \left | 4x + B \right | - 8$ in terms of .

Possible Answers:

$\left ( \frac{-B -8 }{4}, 0 \right ), \left ( \frac{-B +8 }{4}, 0 \right )$

$\left ( \frac{B -8 }{4}, 0 \right ), \left ( \frac{B +8 }{4}, 0 \right )$

$\left ( B-2, 0 \right ), \left ( B+2, 0 \right )$

(B- 8, 0)

$\left ( -B-2, 0 \right ), \left ( -B+2, 0 \right )$

Correct answer:

$\left ( \frac{-B -8 }{4}, 0 \right ), \left ( \frac{-B +8 }{4}, 0 \right )$

Explanation:

Set f (x) = 0 and solve for :

f (x) = 0

$\left | 4x + B \right | - 8 = 0$

$\left | 4x + B \right | = 8$

Rewrite as a compound equation and solve each part separately:

$4x + B = -8 \textrm{ or } 4x + B = 8$

4x + B = -8

4x + B -B = -B -8

4x = -B -8

$4x \div 4 =\left ( -B -8 \right ) \div 4$

$x = \frac{-B -8 }{4}$

4x + B = 8

4x + B -B = -B + 8

4x = -B +8

$4x \div 4 =\left ( -B +8 \right ) \div 4$

$x = \frac{-B +8 }{4}$

Report an Error

Example Question #4 : Absolute Value

A number is ten less than its own absolute value. What is this number?

Possible Answers:

No such number exists.

Correct answer:

Explanation:

We can rewrite this as an equation, where is the number in question:

N = |N| - 10

A nonnegative number is equal to its own absolute value, so if this number exists, it must be negative.

In thsi case, |N| = - N , and we can rewrite that equation as

N = -N- 10

N +N= -N- 10 +N

2N = -10

$2N \div 2 = -10\div 2$

N = -5

This is the only number that fits the criterion.

Report an Error

Example Question #2 : Understanding Absolute Value

If -1<n<0 , which of the following has the greatest absolute value?

Possible Answers:

$\frac{1}{n^{2}}$

n^2

$\frac{1}{n}$

n+1

$\frac{n}{2}$

Correct answer:

$\frac{1}{n^{2}}$

Explanation:

Since -1<n<0 , we know the following:

0< n^2<1 ;

$-1<\frac{n}{2}<0$ ;

$\frac{1}{n^2}>1$ ;

$\frac{1}{n}<-1$ ;

0<n+1<1 .

Also, we need to compare absolute values, so the greatest one must be either $\left | \frac{1}{n^2}\right |$ or $\left | \frac{1}{n}\right |$ .

We also know that $\left | n^2\right |<\left | n\right |$ when -1<n<0 .

Thus, we know for sure that $\left | \frac{1}{n^2}\right |>\left | \frac{1}{n}\right |$ .

Report an Error

Example Question #3 : Understanding Absolute Value

Give all numbers that are twenty less than twice their own absolute value.

Possible Answers:

$- 10 \textrm{ and } 20$

$- 10 \textrm{ and } 10$

$- 6\frac{2}{3} \textrm{ and } 20$

$- 6\frac{2}{3} \textrm{ and } 10$

No such number exists.

Correct answer:

$- 6\frac{2}{3} \textrm{ and } 20$

Explanation:

We can rewrite this as an equation, where is the number in question:

$N = 2\cdot |N| - 20$

If is nonnegative, then | N | = N , and we can rewrite this as

N = 2N - 20

Solve:

N -2N= 2N - 20-2N

-N= - 20

N = 20

If is negative, then | N | =- N , and we can rewrite this as

$N = 2\left (-N \right ) - 20$

N = -2N - 20

N + 2N= -2N - 20 + 2N

3N=- 20

$3N \div 3=- 20\div 3$

$N=- 6\frac{2}{3}$

The numbers $- 6\frac{2}{3}, 20$ have the given characteristics.

Report an Error

All GMAT Math Resources

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

Popular Subjects

Statistics Tutors in San Diego, Reading Tutors in San Diego, Math Tutors in Seattle, Reading Tutors in Chicago, SSAT Tutors in Denver, Algebra Tutors in Miami, Algebra Tutors in New York City, Statistics Tutors in Phoenix, Chemistry Tutors in Houston, Reading Tutors in Denver

Popular Courses & Classes

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

Popular Test Prep

GMAT Test Prep in Washington DC, MCAT Test Prep in Washington DC, GRE Test Prep in New York City, GMAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Philadelphia, MCAT Test Prep in Dallas Fort Worth, MCAT Test Prep in San Diego, ISEE Test Prep in San Francisco-Bay Area, ACT Test Prep in Atlanta, SSAT 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 : Algebra

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #431 : Algebra

Example Question #21 : Solving By Factoring

Example Question #1511 : Gmat Quantitative Reasoning

Example Question #21 : Solving By Factoring

Example Question #1 : Absolute Value

Example Question #2 : Absolute Value

Example Question #3 : Absolute Value

Example Question #4 : Absolute Value

Example Question #2 : Understanding Absolute Value

Example Question #3 : Understanding Absolute Value

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details