GMAT Math : x and y intercept

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 #11 : Dsq: Calculating X Or Y Intercept

Mandy's teacher challenged her to write numbers in the circle, the square, and the triangle in the pattern below in order to make an equation whose graph has -intercept (5,0) and -intercept (0, 1) .

$\square x+ \bigcirc y = \triangle$

Did Mandy succeed?

Statement 1: Mandy wrote a 5 in the triangle.

Statement 2: The number Mandy wrote in the square was five times the number she wrote in the circle.

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Correct answer:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Explanation:

Let A,B,C stand for the values Mandy wrote in the square, the circle, and the triangle, respectively. The equation becomes

A x+ B y =C .

From Statement 1 alone, we know that Mandy wrote a 5 in the triangle, but we do not know any of the others. The question of Mandy's success is unresolved.

Now assume Statement 2 alone is known. Then

A = 5B .

The equation can be rewritten as

5B x+ B y =C

and it can be rewritten in slope-intercept form as

B y =-5B x+C

$\frac{B y}{B} =\frac{-5B x+C}{B}$

$y= -5x + \frac{C}{B}$

Mandy wrote an equation whose line has slope .

However, the slope of a line through (5,0) and (0, 1) is

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{1-0}{0-5} = \frac{1}{-5}= -\frac{1}{5}$ .

Statement 2 alone is sufficient to establish that Mandy did not succeed.

Report an Error

Example Question #12 : X And Y Intercept

A line on the coordinate plane is neither horizontal nor vertical. Give its -intercept.

Statement 1: The line has slope $\frac{1}{4}$ .

Statement 1: The line passes through the origin.

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Explanation:

Statement 1 provides insufficient information, since the slope of the line alone is not enough from which to deduce the -intercept. Statement 2 alone tells us that the line passes through the point (0,0) ; since this is on the -axis, this is the -intercept.

Report an Error

Example Question #13 : X And Y Intercept

Stanley's teacher challenged him to write numbers in the circle, the square, and the triangle in the pattern below in order to make an equation whose graph has -intercept (4,0) .

$\square x+ \bigcirc y = \triangle$

Did Stanley succeed?

Statement 1: Stanley wrote a 4 in the square.

Statement 2: Stanley wrote a 16 in the triangle.

Possible Answers:

BOTH statements TOGETHER are insufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Explanation:

Let A,B,C stand for the values Stanley wrote in the square, the circle, and the triangle, respectively. The equation becomes

A x+ B y =C .

To find the -coordinate of the -intercept, set y = 0 and solve for :

$Ax+ B \cdot 0 =C$

Ax=C

$x=\frac{C}{A}$

It is therefore necessary and sufficient to know the values of and - the values Ralph wrote in the square and the triangle - in order to determine the -intercept of Ralph's equation. Each statement alone give only one of those numbers; the two together give both.

Report an Error

Example Question #11 : Dsq: Calculating X Or Y Intercept

A function f(x) is graphed on the coordinate plane. It has exactly one -intercept. What is it?

Statement 1: f(5)= 0

Statement 2: f(0)= 7

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Explanation:

The -intercept of the graph of is the point at which it intersects the -axis. Since this point has -coordinate 0, the -coordinate is the value for which f(x)= 0 . Statement 1 gives us this value; Statement 2 does not.

Report an Error

Example Question #12 : Dsq: Calculating X Or Y Intercept

Continuous function g(x) has the set of all real numbers as its domain.

How many -intercepts does the graph g(x) have?

Statement 1: If M<N , then g(M)<g(N) .

Statement 2: g(0)= 0 .

Possible Answers:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Explanation:

Statement 1 alone establishes that is always increasing. Its graph cannot have more than one -intercept; if it does, then the graph of the function must have a vertex between two intercepts, violating this statement. But it does not answer the question as to how many intercepts has, as seen in these two cases:

Case 1:

g(x) = x+1

This is a linear function that is always increasing—it is in slope-intercept form, and its slope is 1, a positive number. The graph of has exactly one -intercept.

Case 2:

$g(x)=2^{x}$

An exponential function with a base greater than 1, such as this, is an increasing function; however, 2 raised to any power must be positive, so there is no value for which g(N)= 0 . The graph of has no -intercepts.

Statement 2 alone establishes that at least one -intercept exists - since g(0)= 0 , (0,0) is an -intercept. It does not, however, rule out the possibility of more -intercepts.

Now assume both statements are true. Since Statement 1 establishes that there is at most one -intercept, and Statement establishes that there is at least one -intercept, the two statements together establish that there is exactly one.

Report an Error

Example Question #13 : Dsq: Calculating X Or Y Intercept

Ray's teacher challenged him to write numbers in the circle and the square in the pattern below in order to make an equation whose graph has -intercept (0, 5) .

$y = \square x+ \bigcirc$

Did Ray succeed?

Statement 1: Ray wrote a 5 in the square.

Statement 2: Ray wrote a 7 in the circle.

Possible Answers:

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Correct answer:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Explanation:

If we let stand for the number Ray wrote in the square and stand for the number he wrote in the circle, the equation becomes

y = mx+b ,

the slope-intercept form of the equation of a line. In this form, the -intercept is solely determined by the value of —namely, the value that Ray wrote in the circle. Statement 1 is therefore irrelevant, and Statement 2 alone establishes that Ray did not succeed.

Report an Error

Example Question #17 : X And Y Intercept

Continuous function g(x) has the set of all real numbers as its domain.

How many -intercepts does the graph g(x) have?

Statement 1: If 0<M<N , then g(M)<g(N) .

Statement 2: If M<N < 0 , then g(M)>g(N) .

Possible Answers:

EITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

Assume both statements are true.

By Statement 1, is decreasing on the domain interval $\left ( -\infty, 0\right )$ ; by Statement 2, is increasing on the domain interval $(0, \infty)$ . Therefore, must have its minimum value when x= 0 .

This does not, however, tell us the number of -intercepts. For example, the graph of $g(x)=x^{2}$ has as its minimum point (0,0) , and, subsequently, exactly one -intercept. The graph of $g(x)=x^{2} + 1$ has as its minimum point (0,1) and, subsequently, no -intercepts.

Report an Error

Example Question #18 : X And Y Intercept

Ralph's teacher challenged him to write numbers in the circle, the square, and the triangle in the pattern below in order to make an equation whose graph has -intercept (0, 4) .

$\square x+ \bigcirc y = \triangle$

Did Ralph succeed?

Statement 1: Ralph wrote a in the square.

Statement 2: Ralph wrote a in the triangle.

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

Let A,B,C stand for the values Ralph wrote in the square, the circle, and the triangle, respectively. The equation becomes

A x+ B y =C .

To find the -coordinate of the -intercept, set x = 0 and solve for :

$A \cdot 0 + B y =C$

B y =C

$y =\frac{C}{B}$

It is therefore necessary and sufficient to know the values of and - the values Ralph wrote in the circle and the triangle - in order to determine the -intercept of Ralph's equation. Statement 1 is irrelevant, and Statement 2 only provides the value Ralph wrote in the triangle.

Report an Error

Example Question #19 : X And Y Intercept

Gloria's teacher challenged her to write numbers in the circle and the square in the pattern below in order to make an equation whose graph has -intercept (6,0) .

$y = \square x+ \bigcirc$

Did Gloria succeed?

Statement 1: Gloria wrote a in the square.

Statement 2: Gloria wrote a in the circle.

Possible Answers:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Explanation:

If we let stand for the number Gloria wrote in the square and stand for the number she wrote in the circle, the equation becomes

y = mx+b ,

the slope-intercept form of the equation of a line. We can find the -coordinate of the -intercept by setting y = 0 and solving for :

mx+b = 0

mx+b - b= 0 - b

mx = -b

$\frac{mx }{m}= \frac{-b}{m}$

$x = -\frac{b}{m}$

Therefore, it is necessary and sufficient to know both and - both of the numbers Gloria wrote - to determine the -intercept of the equation she made. Neither statement provides both values, but both statements together do.

Report an Error

Example Question #591 : Geometry

In the -plane, the equation of line is

ax+by+c=0 $\left ( abc\neq 0 \right )$ .

The slope of line is 2. What is the value of ?

(1) a+b=4

(2) c=-3

Possible Answers:

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Correct answer:

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Explanation:

The slope of line is $-\frac{a}{b}=2$

From statement (1) we get another function of and . Therefore, we can calculate the values of and .

From $-\frac{a}{b}=2$

we can get a=-2b .

Plug a=-2b into a+b=4 , then we can get

b=-4

and

$a=-2\cdot -4=8$

Statement (2) only tells us the value of , which is useless to get the value of , because we have three unknown numbers with only two equations given.

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, French Tutors in Houston, Computer Science Tutors in San Francisco-Bay Area, Spanish Tutors in Denver, MCAT Tutors in Los Angeles, Spanish Tutors in San Diego, LSAT Tutors in Los Angeles, Statistics Tutors in Phoenix, ISEE Tutors in San Francisco-Bay Area, Physics Tutors in Dallas Fort Worth

Popular Courses & Classes

ISEE Courses & Classes in Chicago, SSAT Courses & Classes in Philadelphia, GRE Courses & Classes in San Diego, LSAT Courses & Classes in Seattle, LSAT Courses & Classes in Philadelphia, Spanish Courses & Classes in Houston, ACT Courses & Classes in Phoenix, LSAT Courses & Classes in San Diego, GMAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Philadelphia

Popular Test Prep

ACT Test Prep in Phoenix, SAT Test Prep in San Diego, GRE Test Prep in Atlanta, GRE Test Prep in Dallas Fort Worth, GMAT Test Prep in Denver, SAT Test Prep in Denver, GRE Test Prep in New York City, GRE Test Prep in San Francisco-Bay Area, GMAT Test Prep in Dallas Fort Worth, LSAT 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 : x and y intercept

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #11 : Dsq: Calculating X Or Y Intercept

Example Question #12 : X And Y Intercept

Example Question #13 : X And Y Intercept

Example Question #11 : Dsq: Calculating X Or Y Intercept

Example Question #12 : Dsq: Calculating X Or Y Intercept

Example Question #13 : Dsq: Calculating X Or Y Intercept

Example Question #17 : X And Y Intercept

Example Question #18 : X And Y Intercept

Example Question #19 : X And Y Intercept

Example Question #591 : Geometry

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details