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 #9 : Real Numbers

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

Statement 1: $N^{3} - 4N^{2}+ 4N -16 = 0$

Statement 2: $N^{3} - 4N^{2}- 4N +16 = 0$

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.

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

EITHER STATEMENT ALONE provides sufficient information to answer the question.

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

Correct answer:

EITHER STATEMENT ALONE provides sufficient information to answer the question.

Explanation:

Assume Statement 1 alone. The polynomial expression in

$N^{3} - 4N^{2}+ 4N -16 = 0$

can be factored as follows:

$N^{2} (N - 4)+ 4 (N - 4) = 0$

$\LARGE (N^{2} + 4) (N - 4) = 0$

Either $\normal { N - 4 = 0 }$ , in which case N = 4 , or

$N^{2}+ 4 = 0$ - which is impossible for any real value of , since

$N^{2} \ge 0$ , and

$N^{2}+ 4 \ge 4 > 0$

Therefore, is an integer.

Assume Statement 2 alone. Again, we factor:

$N^{3} - 4N^{2}- 4N +16 = 0$

$N^{2} (N - 4)- 4 (N - 4) = 0$

$(N^{2} - 4)\: (N - 4) = 0$

(N+2)(N-2)(N-4) = 0

Similarly to the polynomial in Statement 1, N = -2 , N = 2 , or N = 4 . All three possible values of are integers.

Report an Error

Example Question #10 : Real Numbers

Evaluate $A \cdot B + C \cdot D$ .

Statement 1: $A \cdot B + D \cdot C = 100$

Statement 2: $A \cdot B = C \cdot D$

Possible Answers:

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.

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

Explanation:

Assume Statmemt 1 alone. By the commutative property of multiplication:

$C \cdot D = D \cdot C$

By the addition property of equality,

$A \cdot B + C \cdot D = A \cdot B + D \cdot C$

By substitution,

$A \cdot B + C \cdot D = 100$

Statement 2 alone, however, does not answer the question. If $A \cdot B = C \cdot D$ , then by substitution,

$A \cdot B + C \cdot D = A \cdot B + A \cdot B = 2 \cdot A \cdot B$ ;

however, without further information, we cannot evaluate this expression.

Report an Error

Example Question #11 : Dsq: Understanding Real Numbers

Evaluate AB + CD .

Statement 1: is the multiplicative inverse of .

Statement 2: is the multiplicative inverse of .

Possible Answers:

STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 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 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 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:

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

Explanation:

The multiplicative inverse of a number is the number that can be multiplied by that number to yield product 1.

Assume Statement 1 alone. is the multiplicative inverse of , so AB = 1 , and

AB + CD = 1+ CD .

However, we know nothing about or , so we cannot evaluate the expression. For similar reasons, Statement 2 alone is also insufficient.

Now assume both statements to be true. By Statement 1, AB = 1 , and by Statement 2, CD = 1 , so

AB + CD = 1+ 1= 2 .

Report an Error

Example Question #252 : Arithmetic

is a real number, with $N^{2}$ a positive integer. True or false: is a rational number.

Statement 1: $N^{2}$ is a multiple of 9.

Statement 2: $N^{2}$ is a multiple of 12.

Possible Answers:

BOTH STATEMENTS TOGETHER do 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.x

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

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.

Correct answer:

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

Explanation:

The two statements together provide insufficient information to answer the question. For example, 36 and 72 are both multiples of both 9 and 12. However, the positive square root of 36 is 6, making an integer and, consequently, rational. However, the positive square root of 72 is not an integer, since 72 falls between consecutive perfect squares 64 and 81 (the squares of 8 and 9, respectively), and any square root of an integer that is not itself an integer must be irrational.

Report an Error

Example Question #11 : Dsq: Understanding Real Numbers

Evaluate $A \cdot B + C \cdot D$ .

Statement 1: $C \cdot D + A \cdot B = 66$

Statement 2: $B \cdot A + D \cdot C= 66$

Possible Answers:

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

EITHER STATEMENT ALONE provides sufficient information to answer the question.

STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 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.

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

Correct answer:

EITHER STATEMENT ALONE provides sufficient information to answer the question.

Explanation:

Assume Statement 1 alone. By the commutative property of addition,

$A \cdot B + C \cdot D = C \cdot D + A \cdot B$ .

By substitution,

$A \cdot B + C \cdot D = 66$ .

Assume Statement 2 alone. By the commutative property of multiplication,

$A \cdot B = B \cdot A$ and $C \cdot D = D \cdot C$

By two substitutions,

$A \cdot B + C \cdot D = B \cdot A + D \cdot C$

$A \cdot B + C \cdot D = 66$

Report an Error

Example Question #254 : Arithmetic

Evaluate AB+C .

Statement 1: is the multiplicative inverse of .

Statement 2: is the additive inverse of .

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.

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

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

EITHER STATEMENT ALONE provides 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.

Correct answer:

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

Explanation:

Assume both statements to be true. The multiplicative inverse of a number is the number that can be added to that number to yield product 1; the additive inverse of a number is the number that can be added to that number to yield sum 0. Therefore,

AB = 1 , or, equivalently, $A = \frac{1}{B}$ , and

B + C = 0 , or, equivalently, C = -B .

The expression can be restated in terms of :

$AB+C = \frac{1}{B} \cdot B + (-B) = 1 - B$ .

However, we do not know , and we have no way of finding it out, so we cannot evaluate the expression. Therefore, the question cannot be answered.

Report an Error

Example Question #15 : Dsq: Understanding Real Numbers

Evaluate (A+B)+ C .

Statement 1: B = 0

Statement 2: is the additive inverse of .

Possible Answers:

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

STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does 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.

EITHER STATEMENT ALONE provides 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:

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

Explanation:

Assume Statement 1 alone. Since B = 0 , then by substitution,

(A+B)+ C = (A+0)+ C = A + C .

But without further information, the expression cannot be evaluated.

Assume Statement 2 alone. is the additive inverse of , so, by definition, C+A= 0 . Applying the commutative, then associative, properties,

(A+B)+ C = C + (A+B) = (C+A)+ B = 0 + B = B

But without further information, the expression cannot be evaluated.

Now assume both statements to be true. From Statement 2 and Statement 1 combined,

(A+B)+ C = B = 0 .

Report an Error

Example Question #16 : Dsq: Understanding Real Numbers

Evaluate A (B + C) .

Statement 1: AB =128

Statement 2: AC = - 37

Possible Answers:

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

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

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

EITHER STATEMENT ALONE provides 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:

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

Explanation:

By the distributive property of multiplication over addition,

$A (B + C) = A \cdot B + A \cdot C$

Assume Statement 1 alone. $A \cdot B = 128$ , so, by substitution,

$A (B + C) = 128+ A \cdot C$ .

But, without knowing , , or their product, it is impossible to determine the value of the expression. Statement 2 provides insufficient information, for similar reasons.

Now assume both statements to be true. Then

$A (B + C) = A \cdot B + A \cdot C$

Since $A \cdot B = 128$ and $A \cdot C = - 37$ , by substitution,

A (B + C) = 128 + (-37 ) = 91 .

Report an Error

Example Question #17 : Dsq: Understanding Real Numbers

is a real number. True or false: is a rational number.

Statement 1: $N^{3}-2N^{2}-2N + 4 = 0$

Statement 2: $N^{4} - 4 = 0$

Possible Answers:

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

EITHER STATEMENT ALONE provides sufficient information to answer the question.

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

Assume Statement 1 alone. The polynomial expression in

$N^{3}-2N^{2}-2N + 4 = 0$

can be factored as follows:

$N^{2} (N-2)-2 (N-2) = 0$

$(N^{2}-2 ) (N-2) = 0$

Either N - 2 = 0 , in which case N = 2 , which, as an integer is also rational, or

$N ^{2}- 2 = 0$ , in which case:

$N^{2} = 2$

or either $N = - \sqrt{2}$ or $N = \sqrt{2}$ , both irrational.

Therefore, Statement 1 provides insufficient information.

Assume Statement 2 alone. If $N^{4} - 4 = 0$ , then $N^{4} = 4$ , making a fourth root of 4. A rational root of an integer must itself be an integer, and there is no integer which, when taken to the fourth power, is equal to 4. Therefore, must be irrational.

Report an Error

Example Question #261 : Arithmetic

Evaluate $A^{B}$ .

Statement 1: A = 1

Statement 2: B = 0

Possible Answers:

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

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

EITHER STATEMENT ALONE provides sufficient information to answer the question.

Correct answer:

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

Explanation:

From Statement 1 alone, since 1 raised to the power of any real number is equal to 1, we know that

$A^{B} = 1 ^{B} = 1$ .

However, we cannot determine the value of $A^{B}$ knowing only that B = 0 . If is a nonzero number, then $A^{B} = A^{0} = 1$ . However, if A = 0 , then

$A^{B} = 0^{0}$ ,

which is an undefined expression.

Report an Error

All GMAT Math Resources

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

Popular Subjects

LSAT Tutors in Chicago, SSAT Tutors in New York City, Biology Tutors in Chicago, English Tutors in Boston, Biology Tutors in Boston, Calculus Tutors in Houston, Biology Tutors in Denver, Chemistry Tutors in Seattle, Chemistry Tutors in Phoenix, Spanish Tutors in Phoenix

Popular Courses & Classes

ACT Courses & Classes in Seattle, SSAT Courses & Classes in Los Angeles, ISEE Courses & Classes in Seattle, GRE Courses & Classes in Houston, Spanish Courses & Classes in Washington DC, LSAT Courses & Classes in Seattle, SSAT Courses & Classes in San Diego, MCAT Courses & Classes in Houston, GRE Courses & Classes in Atlanta, GMAT Courses & Classes in Miami

Popular Test Prep

ISEE Test Prep in San Diego, GMAT Test Prep in Miami, SAT Test Prep in Los Angeles, LSAT Test Prep in Seattle, ACT Test Prep in Atlanta, GRE Test Prep in New York City, ISEE Test Prep in Chicago, ISEE Test Prep in Washington DC, ACT Test Prep in Seattle, SSAT Test Prep in Los Angeles

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 #9 : Real Numbers

Example Question #10 : Real Numbers

Example Question #11 : Dsq: Understanding Real Numbers

Example Question #252 : Arithmetic

Example Question #11 : Dsq: Understanding Real Numbers

Example Question #254 : Arithmetic

Example Question #15 : Dsq: Understanding Real Numbers

Example Question #16 : Dsq: Understanding Real Numbers

Example Question #17 : Dsq: Understanding Real Numbers

Example Question #261 : Arithmetic

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details