GMAT Math : GMAT Quantitative Reasoning

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

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

Example Questions

Example Question #941 : Gmat Quantitative Reasoning

Give the area of the region on the coordinate plane bounded by the -axis, the -axis, and the graph of the equation 3x + 4y = 15 .

Possible Answers:

$7\frac{1}{2}$

$18\frac{3}{4}$

$9 \frac{3}{8}$

Correct answer:

$9 \frac{3}{8}$

Explanation:

This can best be solved using a diagram and noting the intercepts of the line of the equation 3x + 4y = 15 , which are calculated by substituting 0 for and separately and solving for the other variable.

-intercept:

3x + 4y = 15

$3x + 4 \cdot 0 = 15$

3x = 15

x = 5

-intercept:

3x + 4y = 15

$3 \cdot 0 + 4y = 15$

4y = 15

$y = 3 \frac{3}{4}$

Now, we can make and examine the diagram below - the red line is the graph of the equation 3x + 4y = 15 :

Triangle_2

The pink triangle is the one whose area we want; it is a right triangle whose legs, which can serve as base and height, are of length $5, 3\frac{3}{4}$ . We can compute its area:

$\frac{1}{2} \cdot 5 \cdot 3\frac{3}{4}= \frac{1}{2} \cdot \frac{5}{1} \cdot \frac{15}{4} = \frac{75}{8} = 9 \frac{3}{8}$

Report an Error

Example Question #942 : Problem Solving Questions

What is the -intercept of 3x+2y=2

Possible Answers:

(3,0)

(2,0)

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

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

Correct answer:

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

Explanation:

To solve for the -intercept, you have to set to zero and solve for :

3x+2y=2

3x+2(0)=2

3x=2

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

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

Report an Error

Example Question #702 : Geometry

What is -intercept for 3x+2y=2

Possible Answers:

(1,0)

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

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

(0,1)

Correct answer:

(0,1)

Explanation:

To solve for the -intercept, you have to set to zero and solve for :

3x+2y=2

3(0)+2y=2

2y=2

y=1

(0,1)

Report an Error

Example Question #6 : X And Y Intercept

A line with slope $-\frac{4}{5}$ includes point (6,N) . What is the -intercept of this line in terms of ?

Possible Answers:

$\left (0, N+ \frac{24}{5} \right )$

$\left (0, N- \frac{24}{5} \right )$

$\left (0, \frac{4}{5}N+6 \right )$

$\left (0, \frac{4}{5}N-6 \right )$

$\left (0, \frac{4}{5}N-\frac{6}{5} \right )$

Correct answer:

$\left (0, N+ \frac{24}{5} \right )$

Explanation:

For some real number , the -intercept of the line will be some point (0,b) . We can set up the slope equation and solve for as follows:

$\frac{y_2-y_1}{x_2-x_1} = m$

$\frac{b-N}{0-6} =-\frac{4}{5}$

$\frac{b-N}{-6} =-\frac{4}{5}$

$\frac{b-N}{-6} \cdot (-6)=-\frac{4}{5}\cdot (-6)$

$b-N = \frac{24}{5}$

$b-N+N =N+ \frac{24}{5}$

$b =N+ \frac{24}{5}$

Report an Error

Example Question #3 : Calculating X Or Y Intercept

Give the $y \;$ -intercept(s) of the graph of the equation

$y = 3x^{2} -2x - 16$

Possible Answers:

The graph has no $y\;$ -intercept.

$\left ( 0, \frac{8}{3}\right )$

(0,-2 )

(0,-16 )

(0,3 )

Correct answer:

(0,-16 )

Explanation:

Substitute 0 for :

$y = 3x^{2} -2x - 16$

$y = 3 \cdot 0^{2} -2 \cdot 0 - 16 = 0 - 0 -16 = -16$

The $y \;$ -intercept is (0,-16)

Report an Error

Example Question #8 : X And Y Intercept

Give the -intercept(s) of the graph of the equation

$y = 3x^{2} -2x - 16$

Possible Answers:

$\left ( -8, 0 \right ), ( 2,0)$

$(-2,0), \left ( \frac{8}{3}, 0 \right )$

$(-2,0), \left ( 8, 0 \right )$

$\left (-16,0 \right )$

$\left ( -\frac{8}{3}, 0 \right ), ( 2,0)$

Correct answer:

$(-2,0), \left ( \frac{8}{3}, 0 \right )$

Explanation:

Set y = 0

$y = 3x^{2} -2x - 16$

$3x^{2} -2x - 16 = 0$

Using the -method, we look to split the middle term of the quadratic expression into two terms. We are looking for two integers whose sum is and whose product is $3 \left ( -16 \right ) = -48$ ; these numbers are -8,6 .

$3x^{2} -8x + 6x - 16 = 0$

$\left (3x^{2} -8x \right )+ \left ( 6x - 16 \right ) = 0$

$x \left (3x -8 \right )+ 2 \left (3 x - 8 \right ) = 0$

$\left ( x + 2 \right )\left (3x -8 \right ) = 0$

Set each linear binomial to 0 and solve:

x + 2 = 0

x + 2 - 2 = 0 - 2

x = -2

3x - 8 =0

3x - 8+ 8 =0 + 8

3x = 8

$3x\div 3 = 8 \div 3$

$x = \frac{8}{3}$

There are two -intercepts - $(-2,0), \left ( \frac{8}{3}, 0 \right )$

Report an Error

Example Question #942 : Problem Solving Questions

A line includes (5,3) and (5,9) . Give its -intercept.

Possible Answers:

(0,6)

The line has no -intercept.

(0,5)

(0,12)

(0,-3 )

Correct answer:

The line has no -intercept.

Explanation:

The two points have the same coordinate, which is 5; the line is therefore vertical. This makes the line parallel to the -axis, meaning that it does not intersect it. Therefore, the line has no -intercept.

Report an Error

Example Question #702 : Geometry

What are the and intercepts of the function $y= \ln(x+3)$ ?

Possible Answers:

y-intercept at (0,0)

x-intercept at (0,0)

y-intercept at (0,2)

x-intercept at (-3,2)

y-intercept at (-2, 0)

x-intercept at (0,3)

None of the other answers

Correct answer:

None of the other answers

Explanation:

The correct answer is

y-intercept at $(0,\ln(3))$

x-intercept at (-2,0)

To find the y-intercept, we plug in for and solve for

So we have $y = \ln(3+0) = \ln(3)$ . This is as simplified as we can get.

To find the x-intercept, we plug in for and solve for

So we have $0 = \ln(x+3)$

$e^0 = e^{\ln(x+3)}$ (Exponentiate both sides)

1 = x+3 ( e^0 is 1, and cancel the and ln on the right side)

x= -2

Report an Error

Example Question #943 : Problem Solving Questions

Fill in the circle with a number so that the graph of the resulting equation has -intercept (0,5) :

$4 x+ \bigcirc y = 18$

Possible Answers:

$\frac{5}{4}$

$\frac{4}{5}$

$\frac{5}{18}$

$\frac{18 }{5}$

Correct answer:

$\frac{18 }{5}$

Explanation:

Let be the number in the circle. The equation can be written as

4 x+N y = 18

Substitute 0 for and 5 for ; the equation becomes

$4 \cdot 0+N \cdot 5 = 18$

0+5N = 18

5N = 18

$N = \frac{18 }{5}$

Report an Error

Example Question #11 : Calculating X Or Y Intercept

Fill in the circle with a number so that the graph of the resulting equation has -intercept (6,0) :

$4x+5y = \bigcirc$

Possible Answers:

The graph cannot have (6,0) as its -intercept regardless of the value written in the circle.

$\frac{3}{2}$

$\frac{6}{5}$

Correct answer:

Explanation:

Let be the number in the circle. The equation can be written as

4x+5y = N

Substitute 0 for and 6 for ; the resulting equation is

$4 \cdot 6+5 \cdot 0 = N$

N = 24 + 0 = 24

24 is the correct choice.

Report an Error

All GMAT Math Resources

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

Popular Subjects

ISEE Tutors in New York City, GRE Tutors in Phoenix, Chemistry Tutors in Philadelphia, Physics Tutors in Miami, Biology Tutors in Miami, MCAT Tutors in Denver, Math Tutors in Boston, English Tutors in San Diego, Reading Tutors in Denver, Calculus Tutors in New York City

Popular Courses & Classes

Spanish Courses & Classes in Los Angeles, SSAT Courses & Classes in Houston, GRE Courses & Classes in Boston, SAT Courses & Classes in Seattle, GRE Courses & Classes in Houston, LSAT Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Phoenix, MCAT Courses & Classes in Washington DC, MCAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Los Angeles

Popular Test Prep

ISEE Test Prep in Philadelphia, LSAT Test Prep in Miami, GRE Test Prep in Boston, LSAT Test Prep in Washington DC, ISEE Test Prep in Seattle, GRE Test Prep in San Francisco-Bay Area, GMAT Test Prep in Los Angeles, SAT Test Prep in Atlanta, SSAT Test Prep in Denver, ACT Test Prep in New York City

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 #941 : Gmat Quantitative Reasoning

Example Question #942 : Problem Solving Questions

Example Question #702 : Geometry

Example Question #6 : X And Y Intercept

Example Question #3 : Calculating X Or Y Intercept

Example Question #8 : X And Y Intercept

Example Question #942 : Problem Solving Questions

Example Question #702 : Geometry

Example Question #943 : Problem Solving Questions

Example Question #11 : Calculating X Or Y Intercept

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details