GMAT Math : 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

← Previous 1 2 Next →

Example Question #1 : Dsq: Understanding Absolute Value

Given that x + y = 10 , evaluate x - y .

1) $x^{2} - y^{2} = 40$

2) xy = 21

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is not sufficient.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

EITHER Statement 1 or Statement 2 ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is not sufficient.

BOTH statements TOGETHER are NOT sufficient to answer the question.

Correct answer:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is not sufficient.

Explanation:

$x^{2} - y^{2} = (x + y) (x - y)$ ,

so, if we know x + y = 10 and $x^{2} - y^{2} = 40$ , then the above becomes

40 = 10 (x - y)

and $x - y = 40 \div 10 = 4$

If we know x + y = 10 and xy = 21 , then we need two numbers whose sum is 10 and whose product is 21; by inspection, these are 3 and 7. However, we do not know whether x = 3 and y = 7 or vice versa just by knowing their sum and product. Therefore, either x - y = 7 - 3 = 4 , or x - y = 3 - 7 = -4 .

The answer is that Statement 1 alone is sufficient, but not Statement 2.

Report an Error

Example Question #2 : Dsq: Understanding Absolute Value

Using the following statements, Solve for .

x=|A-B| (read as equals the absolute value of minus )

1. B-A= 4

2. A+B=10

Possible Answers:

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Correct answer:

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient

Explanation:

This question tests your understanding of absolute value. You should know that

|B-A|=|A-B| since we are finding the absolute value of the difference. We can prove this easily. Since B-A= -(A-B) , we know their absolute values have to be the same.

Therefore, statement 1 alone is enough to solve for . and we get x=4 .

Report an Error

Example Question #3 : Dsq: Understanding Absolute Value

Is $\left | a-b \right |<\left | a-c \right |?$

(1) a>0

(2) $\left | b \right |<\left | c \right |$

Possible Answers:

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Correct answer:

Statements (1) and (2) TOGETHER are NOT sufficient.

Explanation:

For statement (1), since we don’t know the value of and , we have no idea about the value of $\left | a-b \right |$ and $\left | a-c \right |$ .

For statement (2), since we don’t know the sign of and , we cannot compare $\left | a-b \right |$ and $\left | a-c \right |$ .

Putting the two statements together, if a-b>0 and a-c>0 , then $\left | a-b \right |<\left | a-c \right |$ .

But if a-b<0 and a-c<0 , then $\left | a-b \right |>\left | a-c \right |$ .

Therefore, we cannot get the only correct answer for the questions, suggesting that the two statements together are not sufficient. For this problem, we can also plug in actual numbers to check the answer.

Report an Error

Example Question #1 : Dsq: Understanding Absolute Value

Is nonzero number positive or negative?

Statement 1: N + |N| = 0

Statement 2: $N^{2} + 5N < 0$

Possible Answers:

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

If we assume that N + |N| = 0 , then it follows that:

N + |N| - |N| = 0- |N|

N = - |N|

Since we know $N \neq 0$ , we know |N| is positive, and - |N| and are negative.

If we assume that $N^{2} + 5N < 0$ , then it follows that:

$N^{2} + 5N -N^{2} < 0-N^{2}$

$5N < -N^{2}$

$N < -\frac{N^{2}}{5}$

Since we know $N \neq 0$ , we know $N^{2}$ is positive. $\frac{N^{2}}{5}$ is also positive and $-\frac{N^{2}}{5}$ is negative; since is less than a negative number, is also negative.

Report an Error

Example Question #5 : Dsq: Understanding Absolute Value

True or false: N < 7

Statement 1: $\left | N\right | <7$

Statement 2: $N^{2} < 49$

Possible Answers:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

Statement 1 and Statement 2 are actually equivalent.

If $\left | N\right | <7$ , then either -7 < N < 7 by definition.

If $N^{2} < 49$ , then either -7 < N < 7 .

From either statement alone, it can be deduced that N < 7 .

Report an Error

Example Question #6 : Dsq: Understanding Absolute Value

is a real number. True or false: N > 10

Statement 1: $\left | N\right | > 10$

Statement 2: $N^{2} > 100$

Possible Answers:

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

Statement 1 and Statement 2 are actually equivalent.

If $\left | N\right | > 10$ , then either N > 10 or N < -10 by definition.

If $N^{2} > 100$ , then either N > 10 or N < -10 .

The correct answer is that the two statements together are not enough to answer the question.

Report an Error

Example Question #2 : Absolute Value

is a real number. True or false: $\left | N\right | < 5$

Statement 1: $\left | N - 1\right | < 4$

Statement 2: $\left | N +1 \right | <6$

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Correct answer:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Explanation:

If $\left | N\right | < 5$ , then, by definition, -5 < N < 5 .

If Statement 1 is true, then

$\left | N - 1\right | < 4$

-4 < N - 1 < 4

-3 < N < 5 ,

so must be in the desired range.

If Statement 2 is true, then

$\left | N +1 \right | <6$

-6 < N +1 <6

-7< N <5

and is not necessarily in the desired range.

Report an Error

Example Question #8 : Dsq: Understanding Absolute Value

is a real number. True or false: N > 5

Statement 1: $\left | N\right | > 5$

Statement 2: $N^{3} > 125$

Possible Answers:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Correct answer:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Explanation:

If $\left | N\right | > 5$ , then we can deduce only that either N > 5 or N < -5 . Statement 1 alone does not answer the question.

If $N^{3} > 125$ , then must be positive, as no negative number can have a positive cube. The positive numbers whose cubes are greater than 125 are those greater than 5. Therefore, Statement 2 alone proves that N > 5 .

Report an Error

Example Question #9 : Dsq: Understanding Absolute Value

is a real number. True or false: $\left | N\right | < 6$

Statement 1: $N^{2} > 36$

Statement 2: $N^{3} > 216$

Possible Answers:

BOTH statements TOGETHER are insufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

If $\left | N\right | < 6$ , then, by definition, -6 < N < 6 .

If Statement 1 holds, that is, if $N^{2} > 36$ , one of two things happens:

If is positive, then $N > \sqrt{36} = 6$ .

If is negative, then $N < - \sqrt{36} = -6$ .

$\left | N\right | < 6$ is a false statement.

If Statement 2 holds, that is, if $N^{3} > 216$ , we know that is positive, and

$N >\sqrt[3]{ 216} = 6$

$\left | N\right | < 6$ is a false statement.

Report an Error

Example Question #10 : Dsq: Understanding Absolute Value

is a real number. True or false: $\left | N \right | < 5$

Statement 1: 2 N + 7 < 17

Statement 2: 4N - 17 > -37

Possible Answers:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Explanation:

If $\left | N\right | < 5$ , then, by definition, -5 < N < 5 - that is, both N < 5 and N > -5 .

If Statement 1 is true, then

2 N + 7 < 17

2 N < 10

N < 5

Statement 1 alone does not answer the question, as N < 5 follows, but not necessarily N > -5 .

If Statement 2 is true, then

4N - 17 > -37

4N >-20

N > -5

Statement 2 alone does not answer the question, as N > -5 follows, but not necessarily N < 5 .

If both statements are true, then N > -5 and N < 5 both follow, and -5 < N < 5 , meaning that $\left | N \right | < 5$ .

Report an Error

← Previous 1 2 Next →

All GMAT Math Resources

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

Popular Subjects

Algebra Tutors in Seattle, MCAT Tutors in Boston, ISEE Tutors in Houston, GRE Tutors in Philadelphia, Reading Tutors in Denver, Physics Tutors in Chicago, GRE Tutors in Miami, Algebra Tutors in Boston, Spanish Tutors in Seattle, LSAT Tutors in Houston

Popular Courses & Classes

ISEE Courses & Classes in Washington DC, SAT Courses & Classes in Miami, Spanish Courses & Classes in Phoenix, SSAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Miami, ISEE Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Washington DC, ISEE Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Houston, Spanish Courses & Classes in Boston

Popular Test Prep

SSAT Test Prep in Houston, SAT Test Prep in Phoenix, ISEE Test Prep in Phoenix, SSAT Test Prep in Boston, GMAT Test Prep in Washington DC, MCAT Test Prep in Denver, GMAT Test Prep in Boston, GRE Test Prep in Dallas Fort Worth, ACT Test Prep in Philadelphia, GRE Test Prep in Philadelphia

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 : Absolute Value

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Dsq: Understanding Absolute Value

Example Question #2 : Dsq: Understanding Absolute Value

Example Question #3 : Dsq: Understanding Absolute Value

Example Question #1 : Dsq: Understanding Absolute Value

Example Question #5 : Dsq: Understanding Absolute Value

Example Question #6 : Dsq: Understanding Absolute Value

Example Question #2 : Absolute Value

Example Question #8 : Dsq: Understanding Absolute Value

Example Question #9 : Dsq: Understanding Absolute Value

Example Question #10 : Dsq: Understanding Absolute Value

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details