GMAT Math : GMAT Quantitative Reasoning

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 #65 : Solving Equations

3D + 5E = 17

D - 3F = 19

$\frac{1}{2}E - \frac{1}{3}G = 8$

Express in terms of .

Possible Answers:

$F =- \frac{10}{27}G- \frac{40}{3}$

$F =- \frac{5}{6}G- \frac{160}{9}$

F= 9G + 99

$F =- \frac{10}{3}G- 82$

$F= \frac{1}{9}G + \frac{11}{9}$

Correct answer:

$F =- \frac{10}{27}G- \frac{40}{3}$

Explanation:

3D + 5E = 17

D - 3F = 19 , so

D - 3F + 3F = 19 + 3F

D = 3F + 19

$\frac{1}{2}E - \frac{1}{3}G = 8$ , so

$2 \cdot \left (\frac{1}{2}E - \frac{1}{3}G \right )= 2\cdot 8$

$E - \frac{2}{3}G =16$

$E - \frac{2}{3}G + \frac{2}{3}G =16 + \frac{2}{3}G$

$E = \frac{2}{3}G + 16$

Now substitute twice, and solve for :

3D + 5E = 17

$3 (3F + 19) + 5 \left ( \frac{2}{3}G + 16 \right ) = 17$

$9F +57 + \frac{10}{3}G + 80 = 17$

$9F + \frac{10}{3}G + 137= 17$

$9F + \frac{10}{3}G + 137- \frac{10}{3}G - 137 = 17 - \frac{10}{3}G - 137$

$9F = - \frac{10}{3}G - 120$

$\frac{1}{9} \cdot 9F = \frac{1}{9} \cdot \left ( - \frac{10}{3}G - 120 \right )$

$F =- \frac{10}{27}G- \frac{40}{3}$

Report an Error

Example Question #373 : Algebra

P = 3Q

Q = R + 7

$R = S \div 5$

Express in terms of .

Possible Answers:

S =15P+21

$S = \frac{3}{5}P+21$

$S = \frac{5}{3}P - \frac{5}{3}$

$S = \frac{5}{3}P - 35$

$S = \frac{3}{5}P - \frac{7}{5}$

Correct answer:

$S = \frac{5}{3}P - 35$

Explanation:

$R = S \div 5$

$R \cdot 5 = S \div 5 \cdot 5$

S = 5R

Q = R + 7

Q - 7 = R + 7 - 7

R = Q - 7

P = 3Q

$\frac{P }{3} = \frac{3Q}{3}$

$Q = \frac{P }{3} = \frac{1 }{3} P$

Substituting twice:

$S = 5R = 5(Q-7) = 5Q - 35 = 5 \cdot \frac{1}{3}P - 35 = \frac{5}{3}P - 35$

Report an Error

Example Question #67 : Solving Equations

A = 3B

$B = C^{3}$

C = - 4D

Express in terms of .

Possible Answers:

$D = -4 \sqrt[3 ]{\frac{1}{3}A}$

$D = -\frac{1}{4} \sqrt[3 ]{\frac{1}{3}A}$

$D =-12 \sqrt[3 ]{A}$

$D = -\frac{4}{3} \sqrt[3 ]{A}$

$D = -\frac{1}{12} \sqrt[3 ]{A}$

Correct answer:

$D = -\frac{1}{4} \sqrt[3 ]{\frac{1}{3}A}$

Explanation:

A = 3B

$A \div 3 = 3B \div 3$

$B = \frac{1}{3}A$

$B = C^{3}$

$\sqrt[3 ]{B} =\sqrt[3 ]{ C^{3}}$

$C = \sqrt[3 ]{B}$

C = - 4D

$C \div (-4) = - 4D \div (-4)$

$D = -\frac{1}{4} C$

Substitute twice:

$D = -\frac{1}{4} C = -\frac{1}{4} \sqrt[3 ]{B}= -\frac{1}{4} \sqrt[3 ]{\frac{1}{3}A}$

Report an Error

Example Question #68 : Solving Equations

AB = 100,000

AC = 25

BD = 40

Which of the following is equal to ?

Possible Answers:

160,000

0.01

0.00000625

100

62,500

Correct answer:

0.01

Explanation:

AC = 25 and BD = 40 , so

$AC \cdot BD = 25 \cdot 40 = 1,000$

$AB \cdot CD = 1,000$

Since AB= 100,000 , it follows that

$100,000 \cdot CD = 1,000$

$CD = 1,000 \div 100,000 = 0.01$

Report an Error

Example Question #1461 : Problem Solving Questions

True or false: N = 5 .

Statement 1: $(N+2)^{2} = 2N + 19$

Statement 2: $1 + \frac{10}{N-5} = 0$

Possible Answers:

BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.

BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.

BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.x

STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.

EITHER STATEMENT ALONE provides sufficient information to answer the question.

STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.

Correct answer:

EITHER STATEMENT ALONE provides sufficient information to answer the question.

Explanation:

Substitute 5 for in both statements, and it becomes immediately apparent that it is a solution of neither statement:

$(N+2)^{2} = 2N + 19$

$(5+2)^{2} = 2 \cdot 5 + 19$

$7^{2} = 10+19$

49= 29 , a false statement.

$1 + \frac{10}{N-5} = 0$

$1 + \frac{10}{5-5} = 0$

$1 + \frac{10}{0} = 0$ , a false statement since the left quantity, having a zero denominator, is undefined.

Therefore, it follows from either statement alone that N = 5 is false.

Report an Error

Example Question #70 : Solving Equations

is a rational number. True or false: x = 5

Statement 1: $x^{2} - 3x - 10 = 0$

Statement 2: $1 - \frac{7}{x+2} = 0$

Possible Answers:

STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.

EITHER STATEMENT ALONE provides sufficient information to answer the question.

BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.

BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.

STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.

Correct answer:

STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.

Explanation:

Assume Statement 1 alone and solve for :

$x^{2} - 3x - 10 = 0$

(x-5)(x+2) = 0

Either:

x - 5 = 0 , in which case x = 5 ,

x+2 = 0 , in which case x = -2 .

Therefore, Statement 1 alone is inconclusive.

Assume Statement 2 alone and solve for :

$1 - \frac{7}{x+2} = 0$

$1 =\frac{7}{x+2}$

$1 \cdot (x+ 2) =\frac{7}{x+2} \cdot (x+ 2)$

x+ 2 = 7

x = 5

The only solution to this equation is x = 5 , so Statement 2 alone answers the question.

Report an Error

Example Question #381 : Algebra

D = E - 12

$E = \sqrt{F}$

F = 2 G

Express in terms of .

Possible Answers:

$G = \sqrt{2D}- 12$

$G = 4D^{2} - 96D + 576$

$G = \sqrt{2D-24}$

$G = \frac{1}{2} D^{2} -12D +72$

$G = \frac{1}{2} D^{2} +12D +72$

Correct answer:

$G = \frac{1}{2} D^{2} +12D +72$

Explanation:

F = 2 G

$F\div 2 = 2 G \div 2$

$\frac{1}{2} F = G$

$E = \sqrt{F}$

$E^{2} = (\sqrt{F})^{2}$

$E^{2} =F$

D = E - 12

D + 12 = E - 12 + 12

D + 12 = E

By two substitutions:

$G = \frac{1}{2} F = \frac{1}{2} E^{2} = \frac{1}{2} (D+12)^{2}$

$G = \frac{1}{2} (D^{2} +2 \cdot 12 \cdot D +12^{2})$

$G = \frac{1}{2} (D^{2} +24 D +144)$

$G = \frac{1}{2} D^{2} +12D +72$

Report an Error

Example Question #382 : Algebra

Which of the following is the solution set of the equation:

$x-3 = \sqrt{2x+9}$

Possible Answers:

$\left \{ 0,8\right \}$

$\left \{ 8\right \}$

$\left \{ -8\right \}$

$\left \{ 0\right \}$

$\left \{ -8, 0\right \}$

Correct answer:

$\left \{ 8\right \}$

Explanation:

Square both sides of the equation, then solve the resulting quadratic equation by factoring:

$x-3 = \sqrt{2x+9}$

$\left (x-3 \right ) ^{2}=\left ( \sqrt{2x+9 \right )}^{2}$

$x^{2}-6x+9=2x+9$

$x^{2}-8x=0$

x(x-8)=0

Either x=0

x-8=0

x=8

Checking both solutions, however:

$0-3 = \sqrt{2\cdot 0+9}$

-3 = 3

This eliminates 0 as a solution.

$8-3 = \sqrt{2\cdot 8+9}$

5=5

8 turns out to be the only solution.

Report an Error

Example Question #1 : Solving Quadratic Equations

Solve for .

x^2+4x+9=15

Possible Answers:

$x=-4\pm2\sqrt{10}$

$x=4\pm4\sqrt{10}$

$x=\pm 3$

$x=-2\pm \sqrt{10}$

Correct answer:

$x=-2\pm \sqrt{10}$

Explanation:

Solve using the quadratic formula:

$ax^2+bx+c=0;\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

x^2+4x+9=15

$x=\frac{-4\pm\sqrt{4^2-(4)(1)(-6)}}{(2)(1)}$

$x=\frac{-4\pm\sqrt{16+24}}{2}$

$x=\frac{-4\pm\sqrt{40}}{2}$

$x=\frac{-4\pm2\sqrt10}{2}$

$x=-2\pm\sqrt{10}$

Report an Error

Example Question #2 : Solving Quadratic Equations

Multiply: $(x^{2} - 5x + 3) (x - 2)$

Possible Answers:

$x^{3} +3 x^{2}+13x - 6$

$x^{3} - 7 x^{2}+13x - 6$

$x^{3} +3 x^{2}+7x - 6$

$x^{3} - 7 x^{2}+7x - 6$

$x^{3} +7 x^{2}+10x - 6$

Correct answer:

$x^{3} - 7 x^{2}+13x - 6$

Explanation:

Distribute:

$(x^{2} - 5x + 3) (x - 2)$

$=x^{2}(x - 2) - 5x(x - 2) + 3(x - 2)$

$=x^{2}\cdot x - x^{2}\cdot 2- 5x \cdot x +5x \cdot 2 + 3 \cdot x - 3 \cdot 2$

$=x^{3} - 2 x^{2}- 5 x^{2} +10x + 3 x - 6$

$=x^{3} - 7 x^{2}+13x - 6$

Report an Error

All GMAT Math Resources

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

Popular Subjects

Algebra Tutors in Atlanta, LSAT Tutors in Atlanta, Biology Tutors in Philadelphia, Statistics Tutors in Philadelphia, Math Tutors in Chicago, Math Tutors in Denver, Reading Tutors in Miami, ACT Tutors in Atlanta, ACT Tutors in New York City, Physics Tutors in Atlanta

Popular Courses & Classes

SSAT Courses & Classes in Atlanta, GRE Courses & Classes in Boston, GRE Courses & Classes in Miami, MCAT Courses & Classes in Chicago, ISEE Courses & Classes in Atlanta, GRE Courses & Classes in Houston, ISEE Courses & Classes in Houston, LSAT Courses & Classes in Miami, GMAT Courses & Classes in Seattle, SAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

GRE Test Prep in Los Angeles, SAT Test Prep in Denver, LSAT Test Prep in Philadelphia, ACT Test Prep in Washington DC, SSAT Test Prep in Philadelphia, SSAT Test Prep in Atlanta, MCAT Test Prep in Miami, MCAT Test Prep in Dallas Fort Worth, GRE Test Prep in Houston, SSAT Test Prep in Seattle

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 : GMAT Quantitative Reasoning

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #65 : Solving Equations

Example Question #373 : Algebra

Example Question #67 : Solving Equations

Example Question #68 : Solving Equations

Example Question #1461 : Problem Solving Questions

Example Question #70 : Solving Equations

Example Question #381 : Algebra

Example Question #382 : Algebra

Example Question #1 : Solving Quadratic Equations

Example Question #2 : Solving Quadratic Equations

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details