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 #13 : Exponents

Express the quotient in scientific notation:

$\left ( 2.4 \times 10 ^{12}\right ) \div \left (6.4 \times 10^{4} \right )$

Possible Answers:

$\frac{15}{4}\times 10 ^ {7 }$

$3.75\times 10 ^ {7 }$

$\frac{3}{8} \times 10 ^{8}$

$0.375 \times 10 ^{8}$

$3.75\times 10 ^ {9 }$

Correct answer:

$3.75\times 10 ^ {7 }$

Explanation:

$\left ( 2.4 \times 10 ^{12}\right ) \div \left (6.4 \times 10^{4} \right )$

$= \frac{ 2.4 \times 10 ^{12} }{6.4 \times 10^{4}}$

$= \frac{ 2.4 }{6.4 } \times \frac{ 10 ^{12} }{ 10^{4}}$

$=0.375 \times 10 ^{12-4}$

$=0.375 \times 10 ^{8}$

Since 0.375 is not in the range $\left [1,10 \right )$ , we adjust the answer as follows:

$0.375 \times 10 ^{8}$

$= 3.75\times 10 ^ {-1} \times 10 ^{8}$

$= 3.75\times 10 ^ {-1+8 }$

$= 3.75\times 10 ^ {7 }$

Report an Error

Example Question #13 : Exponents

Give the result in scientific notation:

$\left ( 4 \times 10 ^{-7}\right ) ^{3}$

Possible Answers:

$64 \times 10 ^{-4}$

$64 \times 10 ^{-21}$

$6.4 \times 10 ^{-20 }$

$6.4 \times 10 ^{-10}$

$6.4 \times 10 ^{-22}$

Correct answer:

$6.4 \times 10 ^{-20 }$

Explanation:

$\left ( 4 \times 10 ^{-7}\right ) ^{3}$

$= 4^{3} \times \left ( 10 ^{-7}\right ) ^{3}$

$= 64 \times 10 ^{-7\cdot 3}$

$= 64 \times 10 ^{-21}$

Since 64 does not fall in the range [1, 10) , we adjust as follows:

$64 \times 10 ^{-21}$

$= 6.4\times 10 ^{1} \times 10 ^{-21}$

$= 6.4 \times 10 ^{1+ \left (-21 \right )}$

$= 6.4 \times 10 ^{-20 }$

Report an Error

Example Question #12 : Exponents

Give the sum in scientific notation:

$(8.4 \times 10^{8} ) + (5.7 \times 10 ^{7})$

Possible Answers:

$14.1 \times 10^{15}$

$8.97 \times 10^{8}$

$8.97 \times 10^{16}$

$1.41 \times 10^{16}$

$89.7 \times 10 ^{7}$

Correct answer:

$8.97 \times 10^{8}$

Explanation:

Rewrite the second addend as follows:

$(8.4 \times 10^{8} ) + (5.7 \times 10 ^{7})$

$=(8.4 \times 10^{8} ) + (0.57 \times 10 ^{1} \times 10 ^{7})$

$= (8.4 \times 10^{8} ) + (0.57 \times 10 ^{1+7} )$

$= (8.4 \times 10^{8} ) + (0.57 \times 10 ^{8} )$

$= (8.4 + 0.57 ) \times 10 ^{8}$

$= 8.97 \times 10 ^{8}$

Report an Error

Example Question #43 : Algebra

Give the sum in scientific notation:

$(9.63 \times 10^{8} ) + \left ( 8.5 \times 10^{7}\right )$

Possible Answers:

$1.048 \times 10^ {16}$

$1.713 \times 10 ^{16}$

$10.48 \times 10^ {8}$

$17.13 \times 10 ^{15}$

$1.048 \times 10^ {9}$

Correct answer:

$1.048 \times 10^ {9}$

Explanation:

Rewrite the second addend as follows:

$(9.63 \times 10^{8} ) + \left ( 8.5 \times 10^{7}\right )$

$= (9.63 \times 10^{8} ) + \left ( 0.85 \times 10^ {1} \times 10^{7}\right )$

$= (9.63 \times 10^{8} ) + \left ( 0.85 \times 10^ {1+7} \right )$

$= (9.63 \times 10^{8} ) + \left ( 0.85 \times 10^ {8} \right )$

$= (9.63 + 0.85 ) \times 10^ {8}$

$= 10.48 \times 10^ {8}$

This is not in scientific notation; we adjust as follows:

$10.48 \times 10^ {8}$

$= 1.048 \times 10^{1} \times 10^ {8}$

$= 1.048 \times 10^ {1+ 8}$

$= 1.048 \times 10^ {9}$

Report an Error

Example Question #44 : Algebra

Give the quotient in scientific notation:

$(1.5 \times 10^{-20}) \div (1.6 \times 10^{-5})$

Possible Answers:

$0.9375 \times 10^{-4}$

$9.375\times 10^{ -5}$

$9.375\times 10^{ -16}$

$0.9375 \times 10^{-15}$

$9.375\times 10^{ -14}$

Correct answer:

$9.375\times 10^{ -16}$

Explanation:

$(1.5 \times 10^{-20}) \div (1.6 \times 10^{-5})$

$=\frac{ 1.5 \times 10^{-20} }{1.6 \times 10^{- 5}}$

$=\frac{ 1.5 }{1.6 } \times \frac{ 10^{-20} }{ 10^{- 5}}$

$=0.9375 \times 10^{-20- (-5)}$

$=0.9375 \times 10^{-20+5}$

$=0.9375 \times 10^{-15}$

Since 0.9375 does not fall in the range $\left [1,10 \right )$ , we adjust the answer as follows:

$0.9375 \times 10^{-15}$

$= 9.375\times 10^{-1} \times 10^{-15}$

$= 9.375\times 10^{-1 + (-15)}$

$= 9.375\times 10^{ -16}$

Report an Error

Example Question #21 : Understanding Exponents

Give the difference in scientific notation:

$\left (7 \times 10 ^{9} \right ) - \left (7 \times 10 ^{6} \right )$

Possible Answers:

$7\times 10^{15}$

$1 \times 10^{3}$

$7\times 10^{3}$

$6.93 \times 10 ^{9} \right )$

$6.993 \times 10 ^{9} \right )$

Correct answer:

$6.993 \times 10 ^{9} \right )$

Explanation:

Rewrite the second addend as follows:

$\left (7 \times 10 ^{9} \right ) - \left (7 \times 10 ^{6} \right )$

$= \left (7 \times 10 ^{9} \right ) - \left (0.007 \times 10 ^{9} \right )$

$= \left (7 - 0.007 \right ) \times 10 ^{9} \right )$

$=6.993 \times 10 ^{9} \right )$

Report an Error

Example Question #21 : Exponents

Express the product in scientific notation:

$\left ( 8 \times 10 ^{8}\right ) ( 5 \times 10 ^{7})$

Possible Answers:

$4 \times 10 ^{57}$

$4 \times 10 ^{16}$

$40 \times 10 ^{15}$

$40 \times 10 ^{56}$

$0.4 \times 10 ^{58}$

Correct answer:

$4 \times 10 ^{16}$

Explanation:

$\left ( 8 \times 10 ^{8}\right ) ( 5 \times 10 ^{7})$

$= 8 \times 5 \times 10 ^{8} \times 10 ^{7}$

$= 40 \times 10 ^{8+7}$

$= 40 \times 10 ^{15 }$

Since 40 does not fall inside the rangle [1,10) , we adjust the answer as follows:

$40 \times 10 ^{15 }$

$= 4 \times 10^{1} \times 10 ^{15 }$

$= 4 \times 10 ^{1+ 15 }$

$= 4 \times 10 ^{16 }$

Report an Error

Example Question #21 : Exponents

If x^2=5 , what does x^6 equal?

Possible Answers:

100

125

Correct answer:

125

Explanation:

We can use the fact that $(x^a)^b=x^{a*b}$ to see that (x^2)^3=x^6.

Since x^2=5 , we have

(x^2)^3=(x^2)(x^2)(x^2)=(5)(5)(5)=125 .

Report an Error

Example Question #22 : Exponents

Simplify:

$\left ( 2x^{2} \right )^{3} \cdot \left ( 2x^{3} \right )^{2}$

Possible Answers:

$4,096 x ^{12}$

$32x ^{10}$

$32x ^{12}$

$24x ^{12}$

$4,096 x ^{10}$

Correct answer:

$32x ^{12}$

Explanation:

Use the properties of exponents as follows:

$\left ( 2x^{2} \right )^{3} \cdot \left ( 2x^{3} \right )^{2}$

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

$=8 \cdot x^{2 \; \cdot \; 3} \cdot 4 \cdot x^{3 \; \cdot \; 2}$

$=32 \cdot x^{6} \cdot x^{6}$

$=32 \cdot x^{6+6}$

$=32x^{12}$

Report an Error

Example Question #23 : Exponents

Solve for :

$\left (3 ^{4} \right )^{N}\cdot 3^{5} =\frac{1}{27}$

Possible Answers:

The equation has no solution.

$N = - \frac{3}{20}$

$N = \frac{7}{6}$

N= -2

N = 6

Correct answer:

N= -2

Explanation:

$\left (3 ^{4} \right )^{N}\cdot 3^{5} =\frac{1}{27}$

$3 ^{4\cdot N} \cdot 3^{5} =3 ^{-3 }$

$3 ^{4\cdot N+5} =3 ^{-3 }$

The left and right sides of the equation have the same base, so we can equate the exponents and solve:

4N + 5 = -3

4N + 5 -5 = -3 -5

4N = -8

$4N\div 4 = -8 \div 4$

N= -2

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 Philadelphia, GRE Tutors in Chicago, English Tutors in Washington DC, SAT Tutors in Miami, GMAT Tutors in San Diego, GRE Tutors in Phoenix, MCAT Tutors in San Francisco-Bay Area, English Tutors in Chicago, SAT Tutors in New York City, SSAT Tutors in Seattle

Popular Courses & Classes

Spanish Courses & Classes in Miami, GMAT Courses & Classes in Phoenix, MCAT Courses & Classes in Phoenix, GMAT Courses & Classes in San Diego, SSAT Courses & Classes in Boston, ACT Courses & Classes in Atlanta, ACT Courses & Classes in San Diego, LSAT Courses & Classes in Seattle, SAT Courses & Classes in Atlanta, Spanish Courses & Classes in San Diego

Popular Test Prep

ACT Test Prep in San Diego, ISEE Test Prep in Phoenix, MCAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Phoenix, ACT Test Prep in Dallas Fort Worth, SSAT Test Prep in Washington DC, GRE Test Prep in Atlanta, SAT Test Prep in Atlanta, SAT Test Prep in Chicago, GRE Test Prep in Washington DC

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 #13 : Exponents

Example Question #13 : Exponents

Example Question #12 : Exponents

Example Question #43 : Algebra

Example Question #44 : Algebra

Example Question #21 : Understanding Exponents

Example Question #21 : Exponents

Example Question #21 : Exponents

Example Question #22 : Exponents

Example Question #23 : Exponents

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details