GMAT Math : Coordinate Geometry

Study concepts, example questions & explanations for GMAT Math

Create An Account Create Tests & Flashcards

All GMAT Math Resources

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

Example Questions

← Previous 1 2 3 4 5 6 7 8 9 … 16 17 Next →

Example Question #1 :Coordinate Geometry

Define a functionas follows:

$f(x) = A \ln (Bx + C) +D$

for nonzero real numbers A,B,C,D ．

Where is the vertical asymptote of the graph ofin relation to the-axis - is it to the left of it, to the right of it, or on it?

Statement 1:andare both positive.

Statement 2:andare of opposite sign.

Possible Answers:

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is 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.

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 insufficient to answer the question.

Explanation:

Since only positive numbers have logarithms, the expression Bx+C must be positive, so

Bx+C > 0

Bx > -C

$x > - \frac{C}{B}$

的refore, the vertical asymptote must be the vertical line of the equation

$x = - \frac{C}{B}$ ．

In order to determine which side of the-axis the vertical asymptote falls, it is necessary to find the sign of $- \frac{C}{B}$ ; if it is negative, it is on the left side, if it is positive, it is on the right side.

Assume both statements are true. By Statement 1,is positive. Ifis positive, then $- \frac{C}{B}$ is negative, and vice versa. However, Statement 2, which mentions, does not give its actual sign - just the fact that its sign is the opposite of that of, which we are not given either. The two statements therefore give insufficient information.

Report an Error

Example Question #2 :Coordinate Geometry

Define a functionas follows:

$f(x) = A \ln (Bx + C) +D$

for nonzero real numbers A,B,C,D ．

Give the equation of the vertical asymptote of the graph of．

Statement 1: B = 7

Statement 2: C = 10

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 insufficient to answer the question.

EITHER statement ALONE is 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.

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 sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Explanation:

Since a logarithm of a nonpositive number cannot be taken,

Bx+C > 0

Bx > -C

$x > - \frac{C}{B}$

的refore, the vertical asymptote must be the vertical line of the equation

$x = - \frac{C}{B}$ ．

Each of Statement 1 and Statement 2 gives us only one ofand．However, the two together tell us that

$- \frac{C}{B} =- \frac{10}{7}$

making the vertical asymptote

$x=- \frac{10}{7}$ ．

Report an Error

Example Question #3 :Coordinate Geometry

Define a functionas follows:

$f(x) = A \ln (Bx + C) +D$

for nonzero real numbers A,B,C,D ．

Where is the vertical asymptote of the graph ofin relation to the-axis - is it to the left of it, to the right of it, or on it?

Statement 1: B+C = 5

Statement 2: BC = -36

Possible Answers:

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.

EITHER statement ALONE is 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.

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:

Only positive numbers have logarithms, so:

Bx+C > 0

Bx > -C

$x > - \frac{C}{B}$

的refore, the vertical asymptote must be the vertical line of the equation

$x = - \frac{C}{B}$ ．

In order to determine which side of the-axis the vertical asymptote falls, it is necessary to find out whether the signs ofandare the same or different. Ifandare of the same sign, then their quotient $\frac{C}{B}$ is positive, and $- \frac{C}{B}$ is negative, putting $x = - \frac{C}{B}$ on the left side of the-axis. Ifandare of different sign, then their quotient $\frac{C}{B}$ is negative, and $- \frac{C}{B}$ is positive, putting $x = - \frac{C}{B}$ on the right side of the-axis.

Statement 1 alone does not give us enough information to determine whetherandhave different signs. 2 + 3 = 5 , for example, but 6 + (-1) = 5 , also.

From Statement 2, since the product ofandis negative, they must be of different sign. Therefore, $- \frac{C}{B}$ is positive, and $x = - \frac{C}{B}$ falls to the right of the-axis.

Report an Error

Example Question #4 :Coordinate Geometry

Define a functionas follows:

$f(x) = A \ln (Bx + C) +D$

for nonzero real numbers A,B,C,D ．

Give the equation of the vertical asymptote of the graph of．

Statement 1: $\frac{B}{C} = \frac{2}{3}$

Statement 2: $\frac{A}{D} = 2$

Possible Answers:

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.

BOTH statements TOGETHER are insufficient 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 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Explanation:

Only positive numbers have logarithms, so:

Bx+C > 0

Bx > -C

$x > - \frac{C}{B}$

的refore, the vertical asymptote must be the vertical line of the equation

$x = - \frac{C}{B}$ ．

Statement 1 alone gives that $\frac{B}{C} = \frac{2}{3}$ ． $\frac{C} {B}$ is the reciprocal of this, or $\frac{3}{2}$ , and $- \frac{C}{B} = -\frac{3}{2}$ , so the vertical asymptote is $x= -\frac{3}{2}$ ．

Statement 2 alone gives no clue about either,, or their relationship.

Report an Error

Example Question #5 :Coordinate Geometry

Define a functionas follows:

$f(x) = A \ln (Bx + C) +D$

for nonzero real numbers A,B,C,D ．

Give the equation of the vertical asymptote of the graph of．

Statement 1: B+C = 7

Statement 2: BC = 12

Possible Answers:

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.

EITHER statement ALONE is 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 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 insufficient to answer the question.

Explanation:

Since only positive numbers have logarithms,

Bx+C > 0

Bx > -C

$x > - \frac{C}{B}$

的refore, the vertical asymptote must be the vertical line of the equation

$x = - \frac{C}{B}$ ．

Assume both statements to be true. We need two numbersandwhose sum is 7 and whose product is 12; by trial and error, we can find these numbers to be 3 and 4. However, without further information, we have no way of determining which ofandis 3 and which is 4, so the asymptote can be either $x = - \frac{3}{4}$ or $x = - \frac{4}{3}$ ．

Report an Error

Example Question #6 :Coordinate Geometry

Define a functionas follows:

$f(x) = A \ln (Bx + C) +D$

for nonzero real numbers A,B,C,D ．

Does the graph ofhave a-intercept?

Statement 1: C = 8 ．

Statement 2: D = 9 ．

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.

EITHER statement ALONE is 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.

Correct answer:

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

Explanation:

的-intercept of the graph of the function $f(x) = A \ln (Bx + C) +D$ , if there is one, occurs at the point with-coordinate 0. Therefore, we find f(0) :

$f(0) = A \ln (B \cdot 0 + C) +D = A \ln C + D$

This expression is defined if and only ifis a positive value. Statement 1 givesas positive, so it follows that the graph indeed has a-intercept. Statement 2, which only gives, is irrelevant.

Report an Error

Example Question #7 :Coordinate Geometry

Define a functionas follows:

$f(x) = A \ln (Bx + C) +D$

for nonzero real numbers A,B,C,D ．

Where is the vertical asymptote of the graph ofin relation to the-axis - is it to the left of it, to the right of it, or on it?

Statement 1:andare both positive.

Statement 2:andare of opposite sign.

Possible Answers:

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.

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.

Correct answer:

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

Explanation:

Since only positive numbers have logarithms,

Bx+C > 0

Bx > -C

$x > - \frac{C}{B}$

的refore, the vertical asymptote must be the vertical line of the equation

$x = - \frac{C}{B}$ ．

Statement 1 gives irrelevant information. But Statement 2 alone gives sufficient information; sinceandare of opposite sign, their quotient $\frac{C}{B}$ is negative, and $- \frac{C}{B}$ is positive. This locates the vertical asymptote on the right side of the-axis.

Report an Error

Example Question #8 :Coordinate Geometry

Define a functionas follows:

$f(x) = A \ln (Bx + C) +D$

for nonzero real numbers A,B,C,D ．

What is the equation of the vertical asymptote of the graph of?

Statement 1:andare of opposite sign.

Statement 2: A+C = 0

Possible Answers:

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.

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.

Correct answer:

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

Explanation:

Since only positive numbers have logarithms,

Bx+C > 0

Bx > -C

$x > - \frac{C}{B}$

的refore, the vertical asymptote must be the vertical line of the equation

$x = - \frac{C}{B}$ ．

In order to determine which side of the $y\:$ -axis the vertical asymptote falls, it is necessary to find the sign of $- \frac{C}{B}$ ; if it is negative, it is on the left side, and if it is positive, it is on the right side.

Statement 1 alone only gives us thatis a different sign from; without any information about the sign of, we cannot answer the question.

Statement 2 alone gives us that A+C = 0 , and, consequently, A = -C ．这意味着andare of opposite sign. But again, with no information about the sign of, we cannot answer the question.

Assume both statements to be true. Since, from the two statements, bothandare of the opposite sign from,andare of the same sign. Their quotient $\frac{C}{B}$ is positive, and $- \frac{C}{B}$ is negative, so the vertical asymptote $x = - \frac{C}{B}$ is to the left of the-axis.

Report an Error

Example Question #9 :Coordinate Geometry

Define a functionas follows:

$f(x) = A \ln (Bx + C) +D$

for nonzero real numbers A,B,C,D ．

Does the graph ofhave a-intercept?

Statement 1: A> D ．

Statement 2:andhave different signs.

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.

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

的-intercept of the graph of the function $f(x) = A \ln (Bx + C) +D$ , if there is one, occurs at the point with-coordinate 0. Therefore, we find f(0) :

$f(0) = A \ln (B \cdot 0 + C) +D = A \ln C + D$

This expression is defined if and only ifis a positive value. However, the two statements together do not give this information; the values ofandfrom Statement 1 are irrelevant, and Statement 2 does not reveal which ofandis positive and which is negative.

Report an Error

Example Question #10 :Coordinate Geometry

Letandbe real numbers.

What is the product of a + bi and its complex conjugate?

Statement 1: $a^{2}+b^{2}= 71$

Statement 2: $a^{2}-b^{2}= 39$

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.

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.

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

的complex conjugate of an imaginary number a + bi is a - bi , and

$(a + bi)(a - bi) = a^{2}+b^{2}$ ．

的refore, Statement 1 alone, which gives that $a^{2}+b^{2} = 71$ , provides sufficient information to answer the question, whereas Statement 2 provides unhelpful information.

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 … 16 17 Next →

All GMAT Math Resources

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

Popular Subjects

ISEE Tutors in Seattle,Algebra Tutors in Chicago,Computer Science Tutors in New York City,MCAT Tutors in San Diego,Physics Tutors in Los Angeles,MCAT Tutors in Houston,Physics Tutors in Chicago,MCAT Tutors in Miami,SAT Tutors in Philadelphia,SAT Tutors in Washington DC

Popular Courses & Classes

Spanish Courses & Classes in Chicago,ACT Courses & Classes in Washington DC,SSAT Courses & Classes in Miami,SAT Courses & Classes in Dallas Fort Worth,SSAT Courses & Classes in Dallas Fort Worth,GRE Courses & Classes in Seattle,LSAT Courses & Classes in San Diego,Spanish Courses & Classes in Denver,ISEE Courses & Classes in Houston,ISEE Courses & Classes in Denver

Popular Test Prep

GMAT Test Prep in Philadelphia,ACT Test Prep in Washington DC,LSAT Test Prep in Seattle,ACT Test Prep in Los Angeles,SAT Test Prep in Phoenix,ISEE Test Prep in Houston,GMAT Test Prep in Chicago,LSAT Test Prep in Phoenix,SSAT Test Prep in Boston,ISEE Test Prep in Chicago

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)

GMAT Math : Coordinate Geometry

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 :Coordinate Geometry

Example Question #2 :Coordinate Geometry

Example Question #3 :Coordinate Geometry

Example Question #4 :Coordinate Geometry

Example Question #5 :Coordinate Geometry

Example Question #6 :Coordinate Geometry

Example Question #7 :Coordinate Geometry

Example Question #8 :Coordinate Geometry

Example Question #9 :Coordinate Geometry

Example Question #10 :Coordinate Geometry

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Find the Best Tutors

Email address:
Your name:
Feedback: