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 #1181 : Gmat Quantitative Reasoning

is the multiplicative inverse of ; is the additive inverse of . Which of the following is equal to the expression

$(A+B)^{C+D}$

regardless of the values of the variables?

Possible Answers:

$A + \frac{1}{A}$

$(A+B)^{C+D}$ must be an undefined quantity

A+B

Correct answer:

Explanation:

The multiplicative inverse of a number is the number which, when multiplied by that number, yields product 1. Since is the multiplicative inverse of , then

AB = 1 , or $B = \frac{1}{A}$ .

The additive inverse of a number is the number which, when added to that number, yields sum 0. Since is the additive inverse of ,

C+D= 0

It follows that

$(A+B)^{C+D} = (A+\frac{1}{A})^{0}$

Any nonzero number raised to the power of 0 is equal to 1. Therefore,

$(A+\frac{1}{A})^{0} = 1$ , the correct choice.

Report an Error

Example Question #1181 : Problem Solving Questions

is the additive inverse of ; is the multiplicative inverse of . Which of the following is equal to the expression

$(AB)^{CD}$

regardless of the values of the variables?

Possible Answers:

$(AB)^{CD}$ is an undefined quantity.

$-A ^{2}$

$A ^{2}$

Correct answer:

$-A ^{2}$

Explanation:

The additive inverse of a number is the number which, when added to that number, yields sum 0. Since is the additive inverse of ,

A + B = 0 , or B = -A

The multiplicative inverse of a number is the number which, when multiplied by that number, yields product 1. Since is the multiplicative inverse of , then

CD = 1 .

It follows that

$[A \cdot (-A)] ^{1} =( -A ^{2} )^{1} = -A ^{2}$ , the correct response.

Report an Error

Example Question #1183 : Gmat Quantitative Reasoning

is the multiplicative inverse of ; is the additive inverse of . Which of the following is equal to the expression

$(AB)^{CD}$

regardless of the values of the variables?

Possible Answers:

$A ^{2}$

$(AB)^{CD}$ is an undefined quantity.

$-A ^{2}$

Correct answer:

Explanation:

The multiplicative inverse of a number is the number which, when multiplied by that number, yields product 1. Since is the multiplicative inverse of , then

AB = 1 .

The additive inverse of a number is the number which, when added to that number, yields sum 0. Since is the additive inverse of ,

C+D= 0 , or D = -C .

It follows that

$(AB)^{CD} = 1^{C(-C)}= 1^{-C^{2}} = 1$ , the correct response.

Report an Error

Example Question #81 : Understanding Exponents

is the additive inverse of the multiplicative inverse of ; is the additive inverse of the multiplicative inverse of . Which of the following is equal to the expression

$(AB)^{CD}$

regardless of the values of the variables?

Possible Answers:

$(AB)^{CD}$ is an undefined quantity

Correct answer:

Explanation:

The additive inverse of a number is the number which, when added to that number, yields sum 0; the multiplicative inverse of a number is the number which, when multiplied by that number, yields product 1.

Let be the multiplicative inverse of . Then

BX= 1 , or, equivalently, $X = \frac{1}{B}$ .

is the additive inverse of this number, so

A + X = 0

$A + \frac{1}{B}= 0$

$A = - \frac{1}{B}$

$A \cdot B = - \frac{1}{B} \cdot B$

AB = -1

By similar reasoning, CD = -1 , and

$(AB)^{CD} = \left ( -1\right ) ^{-1} = \frac{1}{-1} = -1$

Report an Error

Example Question #81 : Exponents

$FG= 2^{100}$

$HJ = 2^{10}$

$\frac{F}{J} = 4^{40}$

Which of the following is equal to $\frac{H}{G}$ ?

Possible Answers:

$\frac{1}{2^{170}}$

$\frac{1}{2^{50}}$

$\frac{1}{2^{10}}$

$\frac{1}{2^{130}}$

$\frac{1}{2^{70}}$

Correct answer:

$\frac{1}{2^{10}}$

Explanation:

Divide:

$\frac{HJ}{FG}=\frac{ 2^{10}}{2^{100}} = 2^{10-100} = 2^{-90}$

$\frac{HJ}{FG}= \frac{H}{G} \cdot \frac{J}{F} = \frac{H}{G} \div \frac{F} {J}$

$\frac{F}{J} = 4^{40} = (2 ^{2})^{40} = 2 ^{2 \cdot 40 } = 2 ^{80}$

Substitute:

$\frac{H}{G} \div \frac{F} {J} = \frac{HJ}{FG}$

$\frac{H}{G} \div 2 ^{80}= 2^{-90}$

$\frac{H}{G} \div 2 ^{80}\cdot 2 ^{80} = 2^{-90} \cdot 2 ^{80}$

$\frac{H}{G} = 2^{-90+ 80} = 2^{-10} = \frac{1}{2^{10}}$

Report an Error

Example Question #82 : Exponents

is the additive inverse of ; is the multiplicative inverse of . Which of the following is equal to the expression

$(A+B)^{C+D}$

regardless of the values of the variables?

Possible Answers:

$A - \frac{1}{A}$

$A + \frac{1}{A}$

$(A+B)^{C+D}$ must be an undefined quantity.

Correct answer:

Explanation:

The additive inverse of a number is the number which, when added to that number, yields sum 0. Since is the additive inverse of ,

A + B = 0

The multiplicative inverse of a number is the number which, when multiplied by that number, yields product 1. Since is the multiplicative inverse of , then

CD = 1 , or $D = \frac{1}{C}$ .

It follows that

$(A+B)^{C+D} = 0^{C+ \frac{1}{C}}$ .

0 raised to any nonzero power is equal to 0, and $C + \frac{1}{C}$ must be nonzero, so

$0^{C+ \frac{1}{C}} = 0$ , the correct response.

Report an Error

Example Question #84 : Understanding Exponents

is the additive inverse of ; is the additive inverse of . Which of the following is equal to the expression

$(A+B)^{C+D}$

regardless of the values of the variables?

Possible Answers:

$(A+B)^{C+D}$ must be an undefined quantity

$A - \frac{1}{A}$

$A + \frac{1}{A}$

Correct answer:

$(A+B)^{C+D}$ must be an undefined quantity

Explanation:

The additive inverse of a number is the number which, when added to that number, yields sum 0. Since is the additive inverse of and is the additive inverse of ,

A + B = C+D = 0

and

$(A+B)^{C+D} = 0^{0}$ ,

which is an undefined expression.

Report an Error

Example Question #1 : Solving Inequalities

How many integers $\dpi{100} \small (x)$ can complete this inequality?

$7< 2x-3 <15$

Possible Answers:

$\dpi{100} \small 4$

$\dpi{100} \small 5$

$\dpi{100} \small 6$

$\dpi{100} \small 9$

$\dpi{100} \small 3$

Correct answer:

$\dpi{100} \small 3$

Explanation:

$7< 2x-3 <15$

3 is added to each side to isolate the $\dpi{100} \small x$ term:

$10< 2x <18$

Then each side is divided by 2 to find the range of $\dpi{100} \small x$ :

$5< x <9$

The only integers that are between 5 and 9 are 6, 7, and 8.

The answer is 3 integers.

Report an Error

Example Question #2 : Solving Inequalities

Solve $5 < 3x + 10 \leq 16$ .

Possible Answers:

$\left ( \frac{5}{3}, 2 \right ]$

$\left [ \frac{5}{3}, 2\right )$

$\left ( -\frac{5}{3}, 2 \right )$

$\left ( -\frac{5}{3}, 2 \right ]$

$\left [ -\frac{5}{3}, 2 \right ]$

Correct answer:

$\left ( -\frac{5}{3}, 2 \right ]$

Explanation:

$5 < 3x + 10 \leq 16$

Subtract 10: $-5 < 3x \leq 6$

Divide by 3: $-5/3 < x \leq 2$

We must carefully check the endpoints. is greater than $-\frac{5}{3}$ and cannot equal $-\frac{5}{3}$ , yet CAN equal 2. Therefore $-\frac{5}{3}$ should have a parentheses around it, and 2 should have a bracket: is in

$\left ( -\frac{5}{3}, 2 \right ]$

Report an Error

Example Question #1 : Inequalities

Solve -2x+3<7 .

Possible Answers:

$(- \infty , -2)$

$(2, \infty )$

$(-2, \infty )$

$[-2, \infty ]$

$[-2, \infty )$

Correct answer:

$(-2, \infty )$

Explanation:

-2x+3<7

Subtract 3 from both sides: -2x<4

Divide both sides by : x>-2

Remember: when dividing by a negative number, reverse the inequality sign!

Now we need to decide if our numbers should have parentheses or brackets. is strictly greater than , so should have a parentheses around it. Since there is no upper limit here, is in $(-2, \infty )$ .

Note: Infinity should ALWAYS have a parentheses around it, NEVER a bracket.

Report an Error

All GMAT Math Resources

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

Popular Subjects

GRE Tutors in Philadelphia, ACT Tutors in San Francisco-Bay Area, GMAT Tutors in Dallas Fort Worth, Math Tutors in Dallas Fort Worth, Computer Science Tutors in Boston, Calculus Tutors in San Francisco-Bay Area, GMAT Tutors in Boston, Computer Science Tutors in Seattle, Physics Tutors in Atlanta, Reading Tutors in Phoenix

Popular Courses & Classes

MCAT Courses & Classes in Miami, Spanish Courses & Classes in New York City, ACT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Atlanta, ACT Courses & Classes in Los Angeles, GRE Courses & Classes in San Diego, SSAT Courses & Classes in Chicago, GRE Courses & Classes in New York City, GRE Courses & Classes in Los Angeles, Spanish Courses & Classes in Atlanta

Popular Test Prep

ACT Test Prep in Dallas Fort Worth, GMAT Test Prep in Miami, MCAT Test Prep in Seattle, LSAT Test Prep in Phoenix, SAT Test Prep in Phoenix, GRE Test Prep in Los Angeles, SAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Atlanta, SSAT Test Prep in Seattle, GRE Test Prep in San Diego

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 #1181 : Gmat Quantitative Reasoning

Example Question #1181 : Problem Solving Questions

Example Question #1183 : Gmat Quantitative Reasoning

Example Question #81 : Understanding Exponents

Example Question #81 : Exponents

Example Question #82 : Exponents

Example Question #84 : Understanding Exponents

Example Question #1 : Solving Inequalities

Example Question #2 : Solving Inequalities

Example Question #1 : Inequalities

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details