GMAT Math : GMAT Quantitative Reasoning

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 #11 : Algebra

is a number not in the set $\left\{-1, 0, 1 \right\}$ .

Of the elements $\left \{ x^{2}, x^{3}, x^{4}\right \}$ , which is the greatest?

Statement 1: is a negative number.

Statement 2: $\left | x\right |>\frac{1}{2}$

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.

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 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:

Assume both statements are known. The greatest of the three numbers must be $x^{2}$ or $x^{4}$ , since even powers of negative numbers are positive and odd powers of negative numbers are negative.

Case 1: $x = -\frac{2}{3}$

$x^{2} = \left ( -\frac{2}{3} \right )^{2} = \frac{4}{9} = \frac{36}{81}$

$x^{4} = \left ( -\frac{2}{3} \right )^{4} = \frac{16}{81}$

$x^{2} > x^{4}> x^{3}$

Case 2: x = -2 ,

then

$x^{2} = \left ( -2 \right )^{2} =4$

$x^{4} = \left (-2 \right )^{4} = 16$

$x^{4} > x^{2} > x^{3}$

In both cases, is negative and $\left | x\right |>\frac{1}{2}$ , but in one case, $x^{2}$ is the greatest number, and in the other, $x^{4}$ is. The two statements together are inconclusive.

Report an Error

Example Question #12 : Algebra

Philip has been assigned to write one number in the circle and one number in the square in the diagram below in order to produce a number in scientifc notation.

$\bigcirc \times 10^{\square }$ .

Did Philip succeed?

Statement 1: Philip wrote -7.5 in the circle.

Statement 2: Philip wrote in the square.

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

Explanation:

A number in scientific notation takes the form

$a \times 10 ^{n}$

where $1 \le |a| < 10$ and is an integer of any sign.

Statement 1 alone proves that Philip entered a correct number into the circle, since $1 \le |-7.5| = 7.5 < 10$ . Statement 2 alone proves that he entered a correct number into the square, since is an integer. But each statement alone is insufficient, since each leaves uinclear whether the other number is valid. The two statements together, however, prove that Philip put correct numbers in both places, thereby writing a number in scientific notation.

Report an Error

Example Question #801 : Data Sufficiency Questions

is an integer. Is there a real number such that $x^{A}=B$ ?

Statement 1: is negative

Statement 2: is even

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.

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.

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:

The equivalent question is "does have a real $A \textrm{th }$ root?"

If you know only that is negative, you need to know whether is even or odd; negative numbers have real odd-numbered roots, but not real even-numbered roots.

If you know only that is even, you need to know whether is negative or nonnegative; negative numbers do not have real even-numbered roots, but nonnegative numbers do.

If you know both, however, then you know that the answer is no, since as stated before, negative numbers do not have real even-numbered roots.

Therefore, the answer is that both statements together are sufficient to answer the question, but neither statement alone is sufficient to answer the question.

Report an Error

Example Question #1 : Inequalities

Data sufficiency question- do not actually solve the question

Is $\small xy< 12$ ?

1. $\small x^2=64; 1\leq y\leq 1.5$

2. $\small x+y=6$

Possible Answers:

Statement 1 alone is sufficient, but statement 2 along is not sufficient to answer the question

Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question

Statements 1 and 2 together are not sufficient, and additional information is needed to answer the question

Each statement alone is sufficient

Both statements taken together are sufficient to answer the question but neither statement alone is sufficient

Correct answer:

Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question

Explanation:

From statement 1, we can conclude that $\small xy\leq 12$ but not $\small xy< 12$ . From the second statement, we can conclude that the greatest product will result from $\small 3+3=6$ or 9, which is less than 12.

Report an Error

Example Question #2 : Inequalities

How many solutions does the equation $\left | x - A \right | = B$ have?

Statement 1: A = 8

Statement 2: B = -8

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.

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.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT 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 only know that A = 8 , then the above statement becomes $\left | x - 8 \right | = B$ , and it can have zero, one, or two solutions depending on the value of . For example:

If B = -5 , the equation is $\left | x - 8 \right | = -5$ , which has no solution, as an absolute value cannot be negative.

If B = 0 , the equation is $\left | x - 8 \right | = 0$ , which requires that x - 8=0 , or x = 8 , since only 0 has absolute value 0; this means the equation has one solution.

If we only know that B = -8 , then the equation becomes $\left | x - A \right | = -8$ , which has no solution regardless of the value of ; this is because, as stated before, an absolute value cannot be negative.

Report an Error

Example Question #13 : Algebra

True or false: is a positive number.

Statement 1: $N = \left | N \right |$

Statement 2: $N > N^{2}$

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

Explanation:

If is negative, then |N| = -N and $N ^{2} > 0 > N$ . Therefore, either Statement 1 or Statement 2 alone proves nonnegative. However, if N = 0 , then $N = \left | N \right |$ , but $N > N^{2}$ is false.

Therefore, Statement 2 proves positive, but Statement 1 only proves nonnegative.

Report an Error

Example Question #14 : Algebra

True or false: x < 5

Statement 1: |x| > 5

Statement 2: $x^{2}> 25$

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.

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.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

x= 6 makes both statements true, since |6|= 6 > 5 and $6^{2}= 36 > 25$ .

x= - 6 makes both statements true, since |-6|= 6 > 5 and $(-6)^{2}= 36 > 25$ .

One of the two values is less than 5, and one is greater than 5. The statements together provide insufficient information.

Report an Error

Example Question #15 : Algebra

is a whole number.

True or false: is odd.

Statement 1: $2^{x} > 0$

Statement 2: $(-2)^{x} > 0$

Possible Answers:

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.

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.

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 alone is a superfluous statement, since a positive number raised to any power must yield a positive result.

Statement 2 alone answers the question, since a negative number raised to a whole number exponent yields a positive result if and only if the exponent is even. Since Statement 2 states that $(-2)^{x}$ is positive, is even, not odd.

Report an Error

Example Question #16 : Algebra

True or false: x < 9

Statement 1: |x| < 9

Statement 2: $x^{2}< 81$

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:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

Assume Statement 1 alone. |x| < 9 can be rewritten as -9 < x < 9 .

Assume Statement 2 alone. It can be rewritten as

$x^{2}< 81$

the solution set of which is -9 < x < 9

From either statement alone, it follows that x < 9 .

Report an Error

Example Question #17 : Algebra

True or false: x > 0

Statement 1: $2^{x}<4^{x}$

Statement 2: $x^{3}> 0$

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 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.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

Assume Statement 1 alone. Since $2^{x}$ and $4^{x}$ are both positive, we can divide both sides by $2^{x}$ to yield the statement

$2^{x}<4^{x}$

$4^{x} > 2^{x}$

$\frac{ 4^{x}}{2^{x}} >\frac{ 2^{x}}{2^{x}}$

$\left (\frac{ 4}{2} \right )^{x} >1$

$2^{x}> 1$

Since $f(x) = 2^{x}$ increases as increases, and since $2^{0}= 1$ , it follows that x > 0 .

Assume Statement 2 alone. Since the cube root of a number assumes the same sign as the number itself, $x^{3}> 0$ implies that x>0 .

From either statement alone it follows that x>0 .

Report an Error

All GMAT Math Resources

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

Popular Subjects

ACT Tutors in San Diego, GRE Tutors in Los Angeles, Statistics Tutors in Washington DC, ACT Tutors in Denver, Reading Tutors in New York City, Chemistry Tutors in San Diego, Algebra Tutors in Denver, Algebra Tutors in Seattle, MCAT Tutors in San Diego, Chemistry Tutors in Denver

Popular Courses & Classes

ACT Courses & Classes in Miami, Spanish Courses & Classes in Atlanta, SSAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Phoenix, ISEE Courses & Classes in New York City, MCAT Courses & Classes in Washington DC, GMAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Chicago, SSAT Courses & Classes in Philadelphia, ACT Courses & Classes in Boston

Popular Test Prep

LSAT Test Prep in Boston, ISEE Test Prep in New York City, ISEE Test Prep in San Francisco-Bay Area, LSAT Test Prep in Chicago, MCAT Test Prep in Miami, SAT Test Prep in Washington DC, LSAT Test Prep in Denver, ACT Test Prep in Boston, ACT Test Prep in Miami, GMAT Test Prep in Seattle

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 #11 : Algebra

Example Question #12 : Algebra

Example Question #801 : Data Sufficiency Questions

Example Question #1 : Inequalities

Example Question #2 : Inequalities

Example Question #13 : Algebra

Example Question #14 : Algebra

Example Question #15 : Algebra

Example Question #16 : Algebra

Example Question #17 : Algebra

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details