GMAT Math : Understanding absolute value

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 #1 : Absolute Value

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

Possible Answers:

x=5

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

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

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

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

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 #1 : Understanding Absolute Value

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

Possible Answers:

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

$-2 \leq x\leq 5$

$1 < x < 4$

$x < 1, x > 4$

$x \leq 1, x\geq 4$

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 #2 : 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:

(B- 8, 0)

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

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

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

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

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 #3 : 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 #4 : Absolute Value

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

Possible Answers:

$\frac{n}{2}$

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

$\frac{1}{n}$

n^2

n+1

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 #5 : Absolute Value

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

Possible Answers:

No such number exists.

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

$- 10 \textrm{ and } 20$

$- 10 \textrm{ and } 10$

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

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

Example Question #7 : Absolute Value

Solve for in the absolute value equation

$1-\frac{5}{2}\left |x-5 \right | = 15$

Possible Answers:

$\frac{53}{3}$

$-\frac{3}{5}$

$\frac{3}{5}$

None of the other answers

$-\frac{53}{3}$

Correct answer:

None of the other answers

Explanation:

The correct answer is that there is no .

We start by adding to both sides giving

$-\frac{5}{2} \left|x-5\right|=14$

Then multiply both sides by .

$-5\left|x-5|=28$

Then divide both sides by

$|x-5|=-\frac{28}{5}$

Now it is impossible to go any further. The absolute value of any quantity is always positive (or sometimes ). Here we have the absolute value of something equaling a negative number. That's never possible, hence there is no that makes this a true equation.

Report an Error

Example Question #7 : Absolute Value

Solve the following equation:

$32-\left | x-23\right |=13$

Possible Answers:

x={42,4}

x={-22,10}

x={10,19}

x={-19,19}

x={-23,0}

Correct answer:

x={42,4}

Explanation:

We start by isolating the expression with the absolute value:

$32-\left | x-23\right |=13$ becomes $-\left | x-23\right |=13-32=-19$

So: x-23=19 or x-23=-19

We then solve the two equations above, which gives us 42 and 4 respectively.

So the solution is x={42,4}

Report an Error

Example Question #6 : Absolute Value

Solve the absolute value equation for .

|2x-5|+3=5

Possible Answers:

The equation has no solution

$x = \frac{7}{2}, \frac{3}{2}$

$x = -\frac{7}{2}, \frac{7}{2}$

$x = 2,\frac{3}{2}$

None of the other answers.

Correct answer:

$x = \frac{7}{2}, \frac{3}{2}$

Explanation:

We proceed as follows

|2x-5| +3 =5 (Start)

|2x -5| =2 (Subtract 3 from both sides)

2x-5 =2 or 2x-5 = -2 (Quantity inside the absolute value can be positive or negative)

2x = 7 or 2x = 3 (add five to both sides)

$x = \frac{7}{2}$ or $x = \frac{3}{2}$

Another way to say this is $x = \frac{7}{2},\frac{3}{2}$

Report an Error

Example Question #6 : Absolute Value

$\left | 2m-\frac{1}{2}\right |<4$

Which of the following could be a value of ?

Possible Answers:

$-\frac{7}{2}$

$\frac{7}{4}$

$-\frac{7}{4}$

$\frac{9}{4}$

$\frac{9}{2}$

Correct answer:

$\frac{7}{4}$

Explanation:

To solve an inequality we need to remember what the absolute value sign says about our expression. In this case it says that

$\left | 2m-\frac{1}{2}\right |<4$

can be written as

$2m-\frac{1}{2}<4$ Of $2m-\frac{1}{2}>-4$ .

Rewriting this in one inequality we get:

$-4<2m-\frac{1}{2}<4$

From here we add one half to both sides .

$-\frac{7}{2}<2m<\frac{9}{2}$

Finally, we divide by two to isolate and solve for m.

$-\frac{7}{4}<m<\frac{9}{4}$

-1.75<m<2.25

Only $\frac{7}{4}$ is between -1.75 and 2.25

Report an Error

All GMAT Math Resources

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

Popular Subjects

MCAT Tutors in Denver, Algebra Tutors in Boston, English Tutors in San Diego, Reading Tutors in Seattle, Statistics Tutors in Boston, Chemistry Tutors in New York City, Reading Tutors in Houston, Spanish Tutors in Philadelphia, Computer Science Tutors in Washington DC, GRE Tutors in Denver

Popular Courses & Classes

SSAT Courses & Classes in Houston, Spanish Courses & Classes in San Diego, LSAT Courses & Classes in Houston, GMAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Boston, ACT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Houston, GRE Courses & Classes in Denver, LSAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

SAT Test Prep in Miami, GMAT Test Prep in Dallas Fort Worth, LSAT Test Prep in Denver, ISEE Test Prep in Dallas Fort Worth, SAT Test Prep in Philadelphia, ISEE Test Prep in New York City, LSAT Test Prep in Seattle, LSAT Test Prep in Phoenix, GRE Test Prep in Dallas Fort Worth, SAT 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 : Understanding absolute value

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Absolute Value

Example Question #1 : Understanding Absolute Value

Example Question #2 : Absolute Value

Example Question #3 : Absolute Value

Example Question #4 : Absolute Value

Example Question #5 : Absolute Value

Example Question #7 : Absolute Value

Example Question #7 : Absolute Value

Example Question #6 : Absolute Value

Example Question #6 : Absolute Value

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details