GMAT Math : Data-Sufficiency Questions

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 #5 : Dsq: Graphing A Logarithm

Define a function as 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:

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:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

Since only positive numbers have logarithms,

Bx+C > 0

Bx > -C

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

Therefore, the vertical asymptote must be the vertical line of the equation

$x = - \frac{C}{B}$ .

Assume both statements to be true. We need two numbers and whose 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 of and is 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 #1 : Dsq: Graphing A Logarithm

Define a function as follows:

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

for nonzero real numbers A,B,C,D .

Does the graph of have a -intercept?

Statement 1: C = 8 .

Statement 2: D = 9 .

Possible Answers:

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.

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 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 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 if is a positive value. Statement 1 gives as positive, so it follows that the graph indeed has a -intercept. Statement 2, which only gives , is irrelevant.

Report an Error

Example Question #7 : Dsq: Graphing A Logarithm

Define a function as follows:

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

for nonzero real numbers A,B,C,D .

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

Statement 1: and are both positive.

Statement 2: and are of opposite sign.

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.

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:

Since only positive numbers have logarithms,

Bx+C > 0

Bx > -C

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

Therefore, 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; since and are 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 #1 : Coordinate Geometry

Define a function as 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: and are of opposite sign.

Statement 2: A+C = 0

Possible Answers:

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.

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.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 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:

Since only positive numbers have logarithms,

Bx+C > 0

Bx > -C

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

Therefore, 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 that is 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 . This means that and are 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, both and are of the opposite sign from , and are 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 #1 : Dsq: Graphing A Logarithm

Define a function as follows:

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

for nonzero real numbers A,B,C,D .

Does the graph of have a -intercept?

Statement 1: A> D .

Statement 2: and have different signs.

Possible Answers:

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.

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:

The -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 if is a positive value. However, the two statements together do not give this information; the values of and from Statement 1 are irrelevant, and Statement 2 does not reveal which of and is positive and which is negative.

Report an Error

Example Question #2 : Graphing

Let and be 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:

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.

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.

Correct answer:

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

Explanation:

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

$(a + bi)(a - bi) = a^{2}+b^{2}$ .

Therefore, 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

Example Question #1 : Dsq: Graphing Complex Numbers

Let and be real numbers.

From the number a + bi , subtract its complex conjugate. What is the result?

Statement 1: a = 7

Statement 2: b = 12

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.

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.

Correct answer:

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

Explanation:

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

(a + bi)- (a - bi) = a -a +bi+bi = 2bi .

Therefore, it is necessary and sufficient to know in order to answer the question. Statement 1 does not give this value, and is unhelpful here; Statement 2 does give this value.

Report an Error

Example Question #2 : Dsq: Graphing Complex Numbers

Let and be real numbers.

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

Statement 1: a = 12

Statement 2: b= 18

Possible Answers:

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.

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:

The complex conjugate of an imaginary number a + bi is a - bi , and the sum of the two numbers is

(a + bi)+ (a - bi) = 2a .

Therefore, it is necessary and sufficient to know in order to answer the question. Statement 1 alone gives this information; Statement 2 does not, and it is unhelpful.

Report an Error

Example Question #531 : Geometry

Let be a positive integer.

True or false: $i^{N} = 1$

Statement 1: is a prime number.

Statement 2: is a two-digit number ending in a 7.

Possible Answers:

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 insufficient 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.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

If is a positive integer, then $i^{N} = 1$ if and only if is a multiple of 4.

It follows that if $i^{N} = 1$ , cannot be a prime number. Also, every multiple of 4 is even, so as an even number, cannot end in 7. Contrapositively, if Statement 1 is true and is prime, or if Statement 2 is true and if ends in 7, it follows that is not a multiple of 4, and $i^{N} \ne 1$ .

Report an Error

Example Question #4 : Dsq: Graphing Complex Numbers

Let and be real numbers.

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

Statement 1: a = 12

Statement 2: $b = \sqrt{2}$

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.

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.

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:

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

$(a + bi)(a - bi) = a^{2}+b^{2}$ .

Therefore, it is necessary and sufficient to know the values of both and in order to answer the problem. Each statement alone gives only one of these values, so each statement alone provides insufficient information; the two together give both, so the two statements together provide sufficient information.

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 Phoenix, Calculus Tutors in Washington DC, SAT Tutors in Denver, Spanish Tutors in Denver, MCAT Tutors in Phoenix, Reading Tutors in San Francisco-Bay Area, ACT Tutors in San Francisco-Bay Area, Calculus Tutors in Atlanta, GRE Tutors in Atlanta, Calculus Tutors in Houston

Popular Courses & Classes

ISEE Courses & Classes in Philadelphia, LSAT Courses & Classes in Denver, ACT Courses & Classes in Seattle, GRE Courses & Classes in Denver, MCAT Courses & Classes in Los Angeles, ISEE Courses & Classes in Boston, SSAT Courses & Classes in Atlanta, GRE Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Houston, SSAT Courses & Classes in Boston

Popular Test Prep

MCAT Test Prep in Dallas Fort Worth, SSAT Test Prep in Houston, SAT Test Prep in Atlanta, LSAT Test Prep in Houston, ACT Test Prep in Seattle, ACT Test Prep in Philadelphia, ISEE Test Prep in Boston, SSAT Test Prep in Phoenix, MCAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Washington DC

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 : Data-Sufficiency Questions

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #5 : Dsq: Graphing A Logarithm

Example Question #1 : Dsq: Graphing A Logarithm

Example Question #7 : Dsq: Graphing A Logarithm

Example Question #1 : Coordinate Geometry

Example Question #1 : Dsq: Graphing A Logarithm

Example Question #2 : Graphing

Example Question #1 : Dsq: Graphing Complex Numbers

Example Question #2 : Dsq: Graphing Complex Numbers

Example Question #531 : Geometry

Example Question #4 : Dsq: Graphing Complex Numbers

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details