GMAT Math : Geometry

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 : How To Graph Complex Numbers

In which quadrant does the complex number 9-4i lie?

Possible Answers:

III

Correct answer:

Explanation:

If we graphed the given complex number on a set of real-imaginary axes, we would plot the real value of the complex number as the x coordinate, and the imaginary value of the complex number as the y coordinate. Because the given complex number is as follows:

9-4i

We are essentially doing the same as plotting the point (9,-4) on a set of Cartesian axes. We move units right in the x direction, and units down in the y direction, which puts us in the fourth quadrant, or in terms of Roman numerals:

Answer:IV

Report an Error

Example Question #1 : How To Graph Complex Numbers

In which quadrant does the complex number -13-5i lie?

Possible Answers:

III

Correct answer:

III

Explanation:

-13-5i

We are essentially doing the same as plotting the point (-13,-5) on a set of Cartesian axes. We move units left of the origin in the x direction, and units down from the origin in the y direction, which puts us in the third quadrant, or in terms of Roman numerals:

Answer:III

Report an Error

Example Question #2 : How To Graph Complex Numbers

In which quadrant does the complex number 23+14i lie?

Possible Answers:

III

Correct answer:

Explanation:

23+14i

We are essentially doing the same as plotting the point (23,14) on a set of Cartesian axes. We move units right of the origin in the x direction, and units up from the origin in the y direction, which puts us in the first quadrant, or in terms of Roman numerals:

Answer:I

Report an Error

Example Question #1 : Graphing Complex Numbers

Raise 3+i to the power of four.

Possible Answers:

28+96i

28-96i

100+96i

100-96i

None of the other responses gives the correct answer.

Correct answer:

28+96i

Explanation:

Squaring an expression, then squaring the result, amounts to taking the original expression to the fourth power. Therefore, we can first square 3+i :

$(3+i)^{2} = 3^{2}+ 2 \cdot 3 \cdot i + i^{2}$

= 9+ 6i +(-1)

= 8+ 6i

Now square this result:

$( 8+ 6i)^{2}= 8^{2}+ 2 \cdot 8 \cdot 6i + (6i) ^{2}$

$= 8^{2}+ 2 \cdot 8 \cdot 6i + 6^{2}i^{2}$

= 64 + 9 6i + 3 6 (-1)

= 64 -36 + 9 6i

= 28 + 9 6i

Report an Error

Example Question #2 : Graphing Complex Numbers

Raise 1-i to the power of eight.

Possible Answers:

$\small 16i$

$\small -16i$

$\small -16$

$\small 16 -16i$

$\small 16$

Correct answer:

$\small 16$

Explanation:

For any expression , $((N^{2})^{2})^{2} = N ^{2 \cdot 2 \cdot 2} = N^{8}$ . That is, we can raise an expression to the power of eight by squaring it, then squaring the result, then squaring that result.

First, we square:

$\small (1-i)^{2}= 1^{2}- 2 \cdot 1 \cdot i + i^{2}$

$\small = 1 -2 i +(-1)$

$\small = -2i$

Square this result to obtain the fourth power:

$\small (-2i)^{2} = (-2 )^{2} \cdot i ^{2}= 4 (-1) = -4$

Square this result to obtain the eighth power:

$\small (-4)^{2}= 16$

Report an Error

Example Question #831 : Geometry

Give the vertical asymptote of the graph of the equation

$y = \frac{2x-1}{3x+ 5}$

Possible Answers:

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

x = 2

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

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

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

Correct answer:

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

Explanation:

The vertical asymptote is x = a , where is found by setting the denominator equal to 0 and solving for :

3x+ 5 = 0

3x+ 5 - 5 = 0 - 5

3x = - 5

$3x \div 3 = - 5 \div 3$

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

This is the equation of the vertical asymptote.

Report an Error

Example Question #1 : Graphing Inverse Variation

Give the -intercept(s), if any, of the graph of the equation

$y = \frac{4}{2x+ 5}$

Possible Answers:

$\left ( \frac{5}{2},0 \right )$

(4,0)

$\left ( - \frac{5}{2},0 \right )$

$\left ( \frac{4}{5},0 \right )$

The graph has no -intercept.

Correct answer:

The graph has no -intercept.

Explanation:

Set y = 0 in the equation and solve for .

$y = \frac{4}{2x+ 5}$

$\frac{4}{2x+ 5} = 0$

$\frac{4}{2x+ 5} \cdot (2x+5) = 0 \cdot (2x+5)$

4 = 0

This is impossible, so the equation has no solution. Therefore, the graph has no -intercept.

Report an Error

Example Question #192 : Graphing

Give the -intercept(s), if any, of the graph of the equation

$y = \frac{2x-7}{3x+5}$

Possible Answers:

$\left ( \frac {2}{3}, 0 \right )$

The graph has no -intercept.

$\left ( - \frac {5}{3}, 0 \right )$

$\left ( - \frac{7}{5}, 0 \right )$

$\left ( \frac{7}{2}, 0 \right )$

Correct answer:

$\left ( \frac{7}{2}, 0 \right )$

Explanation:

Set y = 0 in the equation and solve for .

$y = \frac{2x-7}{3x+5}$

$0 = \frac{2x-7}{3x+5}$

$0 = \frac{2x-7}{3x+5} \cdot (3x+5)$

2x-7 = 0

2x-7+ 7 = 0 + 7

2x = 7

$2x \div 2 = 7 \div 2$

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

The -intercept is $\left ( \frac{7}{2}, 0 \right )$

Report an Error

Example Question #1 : Graphing Inverse Variation

Give the horizontal asymptote, if there is one, of the graph of the equation

$y = \frac{2x-7}{3x+5}$

Possible Answers:

$y = \frac{7 }{2 }$

The graph of the equation has no horizontal asymptote.

$y = - \frac{5 }{3 }$

$y = \frac{2 }{3 }$

$y = - \frac{7 }{5 }$

Correct answer:

$y = \frac{2 }{3 }$

Explanation:

To find the horizontal asymptote, we can divide both numerator and denominator in the right expression by :

$y = \frac{2x-7}{3x+5}$

$y = \frac{\frac{2x-7}{x}}{\frac{3x+5}{x}}$

$y = \frac{2- \frac{7}{x}}{3+ \frac{5}{x}}$

As approaches positive or negative infinity, $\frac{7}{x}$ and $\frac{5}{x}$ both approach 0. Therefore, approaches $\frac{2 }{3 }$ , making the horizontal asymptote the line of the equation $y = \frac{2 }{3 }$ .

Report an Error

Example Question #2 : Graphing Inverse Variation

Give the -intercept of the graph of the equation $y = \frac{4}{2x+ 5}$ .

Possible Answers:

$\left ( 0, - \frac{5}{2} \right )$

$\left (0, \frac{4}{5} \right )$

$\left ( 0, \frac{5}{2} \right )$

The graph has no -intercept.

(0,4)

Correct answer:

$\left (0, \frac{4}{5} \right )$

Explanation:

Set x= 0 in the equation:

$y = \frac{4}{2x+ 5}$

$y = \frac{4}{2 \cdot 0+ 5} = \frac{4}{ 5}$

The -intercept is $\left (0, \frac{4}{5} \right )$ .

Report an Error

All GMAT Math Resources

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

Popular Subjects

SSAT Tutors in San Francisco-Bay Area, GRE Tutors in Houston, SSAT Tutors in Dallas Fort Worth, French Tutors in Los Angeles, English Tutors in Philadelphia, Physics Tutors in New York City, Physics Tutors in Houston, SSAT Tutors in San Diego, French Tutors in Denver, French Tutors in Seattle

Popular Courses & Classes

GRE Courses & Classes in Washington DC, MCAT Courses & Classes in Chicago, ACT Courses & Classes in Boston, LSAT Courses & Classes in Phoenix, GMAT Courses & Classes in New York City, GMAT Courses & Classes in Philadelphia, LSAT Courses & Classes in Boston, GRE Courses & Classes in Boston, SAT Courses & Classes in Boston, ISEE Courses & Classes in New York City

Popular Test Prep

ACT Test Prep in Dallas Fort Worth, GMAT Test Prep in New York City, ISEE Test Prep in Chicago, GMAT Test Prep in Atlanta, ACT Test Prep in Washington DC, LSAT Test Prep in Chicago, SAT Test Prep in Phoenix, GMAT Test Prep in Philadelphia, LSAT Test Prep in Seattle, MCAT 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 : Geometry

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : How To Graph Complex Numbers

Example Question #1 : How To Graph Complex Numbers

Example Question #2 : How To Graph Complex Numbers

Example Question #1 : Graphing Complex Numbers

Example Question #2 : Graphing Complex Numbers

Example Question #831 : Geometry

Example Question #1 : Graphing Inverse Variation

Example Question #192 : Graphing

Example Question #1 : Graphing Inverse Variation

Example Question #2 : Graphing Inverse Variation

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details