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 #661 : Data Sufficiency Questions

True or false: (A,B) , (C,D) , and $\left ( E,F\right )$ are collinear points.

Statement 1: $\frac{A-C}{B-D} = \frac{C-E}{D-F}$

Statement 2: A < C< E and B < D < F

Possible Answers:

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 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:

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

Explanation:

Assume Statement 1 alone.

The proportion statement

$\frac{A-C}{B-D} = \frac{C-E}{D-F}$

can be rewritten by setting the reciprocals of the expressions equal:

$\frac{B-D}{A-C} = \frac{D-F}{C-E}$

The first expression is the slope of the line through (A,B) and (C,D) ; the second is the slope of the line through (C,D) and $\left ( E,F\right )$ . Since the slopes are equal, the three points are on the same line - collinear.

The three points cannot be assumed to be collinear from Statement 2 alone. For example, (1,1) , (2,2) , and (3,3) collectively fit the condition of Statement 2, and all three points are easily seen to be on the line of the equation y=x . However, (1,1) , (2,2) , and (3,4) collectively fit the condition of Statement 2, and while the line through the first two points is again y=x , (3,4) is off that line, so the three points are noncollinear.

Report an Error

Example Question #5 : Dsq: Graphing A Point

True or false: (A,B) and (C,D) are in the same quadrant of the rectangular coordinate plane.

Statement 1: and are of different sign.

Statement 2: and $D\;$ are of different 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:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

Two points in the same quadrant have -coordinates of the same sign and -coordinates of the same sign; however, from Statement 1 alone, we find that the -coordinates of the points have different signs, and from Statement 2 alone, we find that this holds for the $y\,$ -coordinates. Therefore, from either statement alone, the points can be proved to be in different quadrants.

Report an Error

Example Question #6 : Dsq: Graphing A Point

In which quadrant is the point (A,B) located: I, II, III, or IV?

Statement 1: B = 2A

Statement 2: $\left (A+5 \right )^{2}+ \left ( B+6\right )^{2}= 16$

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.

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:

Assume Statement 1 alone. The set of points that satisfy the equation is the set of all points on the line of the equation

y = 2x

which will pass through at least two quadrants on the coordinate plane. Therefore, Statement 1 provides insufficient information.

Now assume Statement 2 alone. The set of points that satisfy the equation is the set of all points of the circle of the equation

$\left (x+5 \right )^{2}+ \left ( y+6\right )^{2}= 16$

This circle has (-5,-6) as its center and $\sqrt{16} = 4$ as its radius. Since its center is (-5,-6) , which is 5 units away from its closest axis, and the radius is less than 5 units, the circle never intersects an axis, so it is contained entirely within the same quadrant as its center. The center has negative - and $y\:$ -coordinates, placing it, and the entire circle, in Quadrant III.

Report an Error

Example Question #7 : Dsq: Graphing A Point

In which quadrant is the point (A,B) located: I, II, III, or IV?

Statement 1: A > 0

Statement 2: A -B > 0

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:

Assume both statements. The points (6,4) and (6,-4) each satisfy the conditions of both statements, since 6 > 0 , 6 -4= 2> 0 , and 6-(-4) = 10 > 0 . The former is in Quadrant I, having a positive -coordinate and a positive $y\,$ -coordinate; the latter is in Quadrant IV, having a positive -coordinate and a negative $y\,$ -coordinate.

Report an Error

Example Question #8 : Dsq: Graphing A Point

True or false: (A,B) , (C,D) , and $\left ( E,F\right )$ are collinear points.

Statement 1: 2C= A +E and 2D= B + F

Statement 2: (A-C ) ( D-F) = (C-E)(B-D )

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:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

Assume Statement 1 alone. The equations can be rewritten as follows:

2C= A +E

$C= \frac{A +E}{2}$

2D= B + F

$D= \frac{B + F}{2}$

The - and $y \:$ -coordinates of (C,D) are the arithmetic means of those of (A,B) and $\left ( E,F\right )$ , so (C,D) is the midpoint of the segment with those endpoints. Therefore, the three points are collinear.

Assume Statement 2 alone. The statement can be rewritten as follows:

(A-C ) ( D-F) = (C-E)(B-D )

$\frac{(A-C ) ( D-F) }{(C-E)(A-C ) }=\frac{ (C-E)(B-D )}{(C-E)(A-C ) }$

$\frac{ D-F }{C-E }=\frac{ B-D }{ A-C }$

The first expression is the slope of the line through (C,D) and $\left ( E,F\right )$ ; the second expression is the slope of the line through (A,B) and (C,D) . Since the slopes are equal, the three points are collinear.

Report an Error

Example Question #661 : Data Sufficiency Questions

What quadrant contains the point (A,B) , where $A,B \neq 0$ ?

Statement 1: AB > 0

Statement 2: A - B > 0

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 insufficient to answer the question.

Explanation:

Statement 1 alone tells you that and are of the same sign, so the point is in Quadrant I (both positive) or Quadrant III (both negative).

Statement 2 tells you that any of the following hold:

is positive and is negative - example: 5-(-2) = 7

is negative and is negative - example: -2-(-5) = 3

is positive and is positive - example: 5-2 = 3

This places the point in any quadrant except Quadrant II (where is negative and is positive).

The two statements together only eliminate two quadrants and leave both Quadrant I and Quadrant III as possibilities.

Report an Error

Example Question #2 : Dsq: Graphing An Ordered Pair

Graph the point (a,b) .

I) (a,b) is in quadrant IV.

II) a^2=49 b^2=36 .

Possible Answers:

Either statement is sufficient to answer the question.

Both statements are needed to answer the question.

Neither statement is sufficient to answer the question. More information is needed.

Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.

Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.

Correct answer:

Both statements are needed to answer the question.

Explanation:

Graph the point (a,b)

I) (a,b) is in quadrant 4

II)

To graph (a,b) we need to know a and b

I) Tells us which quadrant the point is in. In quadrant 4, the x value is positive and the y value must be negative.

II) Lets us find the following:

$a=\pm7$

$b=\pm6$

So the only possible location of (a,b) is (7,-6) .

Therefore, both statements are needed to answer the question.

Report an Error

Example Question #1 : Dsq: Graphing An Exponential Function

Graph the exponential function g(x) .

I) g(x) is a monomial.

II) g(x) has a base of 4.

Possible Answers:

Either statement is sufficient to answer the question.

Statement I is sufficient to answer the question, but Statement II is not sufficient to answer the question.

Both statements are needed to answer the question.

Statement II is sufficient to answer the question, but Statement I is not sufficient to answer the question.

Neither statement is sufficient to answer the question. More information is needed.

Correct answer:

Neither statement is sufficient to answer the question. More information is needed.

Explanation:

An exponential function follows the general form of

y=n^x+c

Statement I tells us that there is only one term, so the part of the equation isn't needed for this exponential function.

Statement II tells us that in this case, n=4 .

However, we could have nearly anything as our exponent. We are unable to make an accurate graph of this function, so more information is needed.

Report an Error

Example Question #662 : Data Sufficiency Questions

The graph of the function $f(x) = Ax^{2} + Bx +C$ is a parabola. Is this parabola concave upward or is it concave downward?

Statement 1: A = -3

Statement 2: $B^{2} - 4AC = 16$

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:

Whether the parabola of a quadratic function $f(x) = Ax^{2} + Bx +C$ is concave upward or concave downward depends on one thing and one thing only - whether quadratic coefficient is positive or negative. Statement 1 gives you this information; Statement 2 does not.

Report an Error

Example Question #663 : Data Sufficiency Questions

What is the equation of the line of symmetry of a vertical parabola on the coordinate plane?

Statement 1: The -intercept of the parabola is (0, 6) .

Statement 2: The only -intercept of the parabola is at (3,0) .

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.

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:

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

Explanation:

The line of symmetry of a vertical parabola is the vertical line passing through the vertex. Statement 1 alone is not helpful, since it only gives the -intercept.

Statement 2 alone, however, answers the question. In a parabola with only one -intercept, that -intercept, given in Statement 2 as (3,0) , doubles as the vertex. The vertical line through the vertex, which here is the line with equation x= 3 , is the line of symmetry.

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 Dallas Fort Worth, MCAT Tutors in Seattle, LSAT Tutors in Houston, Chemistry Tutors in New York City, Reading Tutors in Philadelphia, GMAT Tutors in New York City, Statistics Tutors in Houston, English Tutors in Boston, ACT Tutors in Seattle, Reading Tutors in Seattle

Popular Courses & Classes

Spanish Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in San Diego, SSAT Courses & Classes in Atlanta, MCAT Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Washington DC, SAT Courses & Classes in Houston, GRE Courses & Classes in Philadelphia, MCAT Courses & Classes in Atlanta, GMAT Courses & Classes in Denver, SAT Courses & Classes in San Diego

Popular Test Prep

ACT Test Prep in San Francisco-Bay Area, GRE Test Prep in Houston, GRE Test Prep in Boston, GRE Test Prep in Dallas Fort Worth, MCAT Test Prep in Atlanta, MCAT Test Prep in Denver, LSAT Test Prep in Atlanta, LSAT Test Prep in Chicago, GMAT Test Prep in Phoenix, GMAT Test Prep in Denver

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 #661 : Data Sufficiency Questions

Example Question #5 : Dsq: Graphing A Point

Example Question #6 : Dsq: Graphing A Point

Example Question #7 : Dsq: Graphing A Point

Example Question #8 : Dsq: Graphing A Point

Example Question #661 : Data Sufficiency Questions

Example Question #2 : Dsq: Graphing An Ordered Pair

Example Question #1 : Dsq: Graphing An Exponential Function

Example Question #662 : Data Sufficiency Questions

Example Question #663 : Data Sufficiency Questions

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details