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 #6 : Fractions

is a real number. True or false: is an integer.

Statement 1: $\frac{14}{11} N$ is an integer.

Statement 2: $\frac{3}{7} + N$ is an integer.

Possible Answers:

STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.

EITHER STATEMENT ALONE provides sufficient information to answer the question.

BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.

STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.

BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.

Correct answer:

STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.

Explanation:

Statement 1 alone does not prove is or is not an integer.

For example, if N = 11 , then

$\frac{14}{11} N = \frac{14}{11} \cdot 11 = 14$ .

If $N = \frac{11}{14}$ , then

$\frac{14}{11} N = \frac{14}{11} \cdot \frac{11} {14}= 1$ .

is an integer in only one scenario, but Statement 1 is true in both.

Now assume Statement 2 alone, and let $M = \frac{3}{7} + N$ . Then is an integer by Statement 2, and

$M -N= \frac{3}{7}$

Suppose is an integer. Then M -N , the difference of integers, is itself an integer. But we know that this is equal to $\frac{3}{7}$ , which is not an integer, so, by contradiction, is not an integer.

Report an Error

Example Question #1 : Dsq: Understanding Decimals

$\frac{A}{B}$ is a fraction in lowest terms. Is its decimal representation a terminating decimal or a repeating decimal?

Statement 1: is a power of 5.

Statement 2: is a multiple of 7.

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:

A fraction in lowest terms can be expressed as a terminating decimal if and only if its denominator has no prime factors other than 2 or 5; the numerator is irrelevant. Statement 1 is unhelpful since it only gives information about the numerator. If Statement 2 is assumed - that is, if we know the denominator has 7 as a prime factor - we know that the decimal representation of $\frac{A}{B}$ is repeating.

Report an Error

Example Question #1 : Decimals

and are fractions in lowest terms.

True or false: The result a+b can be represented by an integer or a terminating decimal.

Statement 1: Both fractions have powers of 5 in their denominators.

Statement 2: Both fractions have powers of 3 in their numerators.

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:

Assume Statement 1 alone. A necessary and sufficient condition for a lowest-terms fraction to be equivalent to a terminating decimal is that its only prime factors are 2 and 5. Statement 1 says this about both fractions; the sum of terminating decimals is itself an integer or a terminating decimal.

Statement 2 alone provides insuffiicient information. Examine these examples:

$\frac{3}{5} + \frac{9}{5} = \frac{12}{5} = 2.4$

$\frac{3}{7} + \frac{9}{7} = \frac{12}{7} = 1.\overline{714285}$

Both fit the conditions of the main premise and Statement 2, but in only one case is the sum equal to a terminating decimal.

Report an Error

Example Question #2 : Dsq: Understanding Decimals

and are fractions in lowest terms.

True or false: The result a+b can be represented by an integer or a terminating decimal.

Statement 1: Both denominators are even.

Statement 2: Both denominators are multiples of 3.

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.

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 insufficient to answer the question.

Explanation:

Assume both statements to be true. A multiple of both 2 and 3 is also a multiple of 6, so both denominators are multiples of 6. Examine these two examples:

$\frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3} = 0.\overline{3}$

$\frac{1}{6} + \frac{5}{6} = \frac{6}{6} = 1$

In both examples, the conditions of the problem, including both statements, are met, but in only one is the sum equivalent to a terminating decimal or integer.

Report an Error

Example Question #3 : Dsq: Understanding Decimals

and are fractions in lowest terms.

True or false: The result a b can be represented by an integer or a terminating decimal.

Statement 1: Neither denominator is a multiple of 5.

Statement 2: Both denominators are powers of 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.

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:

Assume Statement 1 alone. Examine these two examples:

$\frac{1}{3} \times \frac{1}{3} = \frac{1}{9} = 0.\overline{1}$

$\frac{1}{2} \times \frac{1}{4} = \frac{1}{8} = 0.125$

Both fit the main condition and that of Statement 1, but in only one case is the sum equal to a terminating decimal or integer.

Assume Statement 2 alone. A necessary and sufficient condition for a lowest-terms fraction to be equivalent to a terminating decimal is that its only prime factors are 2 and 5. By Statement 2, both denominators have 2 as their only prime factor, so both can be represented by terminating decimals; their product must be terminating as well.

Report an Error

Example Question #4 : Dsq: Understanding Decimals

and are fractions in lowest terms.

True or false: The result a b can be represented by an integer or a terminating decimal.

Statement 1: The denominator of is a power of 7.

Statement 2: The denominator of is a power of 3.

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.

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. Examine these two examples; both fit the main condition and those given in both statements.

$\frac{1}{7} \times \frac{1}{3} = \frac{1}{21} = 0.\overline{037}$

$\frac{3}{7} \times \frac{7}{3} = \frac{21}{21} = 1$

In only one case is the product equivalent to an integer or a terminating decimal.

Report an Error

Example Question #243 : Arithmetic

and are fractions in lowest terms.

True or false: The result a b can be represented by an integer or a terminating decimal.

Statement 1: The denominator of is three times the numerator of .

Statement 2: The denominator of is six times the numerator of .

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:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

Assume Statement 1 alone. Rewrite the fractions as follows:

$a = \frac{M}{N}, b= \frac{P}{Q}$ , where GCF(M,N)= GCF (P,Q)= 1 - that is, their lowest-terms representations.

By Statement 1, N = 3P , so $a = \frac{M}{3P}$ . Therefore,

$ab = \frac{M}{3P} \cdot \frac{P}{Q} = \frac{M}{3 } \cdot \frac{1}{Q} = \frac{M}{3Q }$

Since $\frac{M}{3P}$ is in lowest terms, is not a multiple of 3, so the 3 must remain in the denominator, even if the and the can be reduced. Since a fraction which, in lowest terms, has a denominator with any prime factor other than 2 or 5 cannot be represented by an integer or a terminating decimal, Statement 1 proves that has a repeating decimal as its equivalent.

A similar argument can be used to demonstrate that Statement 2 proves the same of .

Report an Error

Example Question #2 : Decimals

and are fractions in lowest terms.

True or false: The result a b can be represented by an integer or a terminating decimal.

Statement 1: The denominator of is five times the numerator of .

Statement 2: The denominator of is eight times the numerator of .

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.

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

Explanation:

Assume Statement 1 alone. Examine these examples:

$\frac{1}{2} \times \frac{1}{5} = \frac{1}{10} = 0.1$

$\frac{1}{3} \times \frac{1}{5} = \frac{1}{15} = 0.0\overline{6}$

In both cases, the main conditon and that of Statement 1 are satisfied, but in only one case can the result be represented by a terminating decimal or integer.

A similar argument shows Statement 2 alone to be insufficient:

$\frac{1}{8} \times \frac{1}{5} = \frac{1}{40} = 0.025$

$\frac{1}{8} \times \frac{1}{3} = \frac{1}{24} = 0.041\overline{6}$

Assume both statements. Then rewrite the fractions as follows:

$a = \frac{M}{N}, b= \frac{P}{Q}$ , where GCF(M,N)= GCF (P,Q)= 1 - that is, their lowest-terms representations.

By Statement 1, Q = 5M ; by Statement 2, N = 8P . Therefore,

$a = \frac{M}{8P}, b= \frac{P}{5M}$ ,

and their product is

$a b= \frac{M}{8P} \cdot \frac{P}{5M} =\frac{MP}{40MP} = \frac{1}{40} = 0.025$ ,

a terminating decimal.

Report an Error

Example Question #245 : Arithmetic

Solve for in the following equation.

6y-13x=-54

I) is equivalent to seventy nine hundredths.

II) The slope of the line parallel to this equation is ${}\frac{13}{6}$ .

Possible Answers:

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.

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.

Correct answer:

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

Explanation:

We have one equation and two unknowns. To find x, we need to find y.

I) Tells us that y is .79 therefore we can plug this value into our equation and solve for x.

6y-13x=-54

Plugging in the y value from Statement I and using algebraic operations to solve for x.

6(0.79)-13x=-54

Multiply first term.

4.74-13x=-54

Subtract 4.74 from both sides.

-13x=-58.74

Divide by -13.

x=4.518

II) Is irrelevant.

Therefore Statement I) alone is sufficient to answer the question but Statement II) alone is not.

Report an Error

Example Question #1 : Real Numbers

Is z a negative number?

(1) $\dpi{100} \small 13z>14z$

(2) $\dpi{100} \small 4+z$ is positive

Possible Answers:

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

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

EACH statement ALONE is sufficient.

Correct answer:

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

Explanation:

(1) Subtracting $\dpi{100} \small 13z$ from both sides of $\dpi{100} \small 13z>14z$ shows that $\dpi{100} \small 0>z$ , so $\dpi{100} \small z$ must be negative $\dpi{100} \small \rightarrow$ SUFFICIENT

(2) Subtracting 4 from both sides of $\dpi{100} \small 4+z>0$ gives $\dpi{100} \small z>-4$ . Therefore, for this statement, $\dpi{100} \small z$ can be negative but is not necessarily negative. $\dpi{100} \small \rightarrow$ NOT SUFFICIENT.

Report an Error

All GMAT Math Resources

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

Popular Subjects

French Tutors in Phoenix, Chemistry Tutors in Phoenix, ACT Tutors in Denver, Biology Tutors in Seattle, ACT Tutors in Seattle, SAT Tutors in Denver, MCAT Tutors in San Francisco-Bay Area, GMAT Tutors in Houston, Statistics Tutors in New York City, MCAT Tutors in Atlanta

Popular Courses & Classes

ISEE Courses & Classes in Phoenix, SAT Courses & Classes in Phoenix, Spanish Courses & Classes in Miami, SSAT Courses & Classes in Denver, ISEE Courses & Classes in Boston, SAT Courses & Classes in Seattle, ISEE Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Washington DC, Spanish Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Washington DC

Popular Test Prep

GRE Test Prep in Miami, GRE Test Prep in Houston, SAT Test Prep in Chicago, GRE Test Prep in Chicago, MCAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Phoenix, SAT Test Prep in San Diego, ISEE Test Prep in Chicago, ISEE Test Prep in Denver, MCAT Test Prep in Atlanta

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 #6 : Fractions

Example Question #1 : Dsq: Understanding Decimals

Example Question #1 : Decimals

Example Question #2 : Dsq: Understanding Decimals

Example Question #3 : Dsq: Understanding Decimals

Example Question #4 : Dsq: Understanding Decimals

Example Question #243 : Arithmetic

Example Question #2 : Decimals

Example Question #245 : Arithmetic

Example Question #1 : Real Numbers

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details