GMAT Math : Arithmetic

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 #7 : Understanding Real Numbers

If and are composite integers, which of the following can be prime?

Possible Answers:

x^2+y^2

x^2-y^2

None of these can be prime.

$x\cdot y$

x^2y+2y

Correct answer:

x^2+y^2

Explanation:

x^2-y^2 = (x-y)(x+y) so this is a composite number for all and .

$x\cdot y$ is by definition a composite number.

$x^2y+2y = y\cdot (x^2+2)$ the product of 2 numbers.

This leaves just x^2+y^2 . For a number to be prime, it must be odd (except for 2) so we need to have either or be odd (but not both). The first composite odd number is 9. 9^2 = 81 . The smallest composite number is 4. 4^2 = 16 .

81+16 = 97 is a prime number.

So the answer is x^2+y^2

Report an Error

Example Question #1 : Understanding Real Numbers

If $\frac{122}{x-3}$ is a real number, which of the following CANNOT be a value for x?

Possible Answers:

122

-122

-3

125

Correct answer:

Explanation:

The definition of the set of real numbers is the set of all numbers that can fit into a/b where a and b are both integers and b does not equal 0.

So, since we see a fraction here, we know a non-real number occurs if the denominator is 0. Therefore we can find where the denominator is 0 by setting x-3 =0 and solving for x. In this case, x=3 would create a non-real number. Thus our answer is that x CANNOT be 3 for our expression to be a real number.

Report an Error

Example Question #1 : Understanding Real Numbers

Let be the product of integers from 18 to 33, inclusive. If g=2x , how many more unique prime factors does have than ?

Possible Answers:

Not enough information given.

Greater than

Correct answer:

Explanation:

This question does not require any calculation. Given that 32 (an even number) is a factor of , then 2 must be a prime factor. If is then multiplied by 2 (to get ) then has no additional unique prime factors (its only additional prime factor, 2, is NOT unique).

Report an Error

Example Question #2 : Real Numbers

If $\dpi{100} \small x\ and\ y$ are both negative, then $\dpi{100} \small \frac{x+y}{-xy}$ could NOT be equal to....

Possible Answers:

$\dpi{100} \small -5$

$\dpi{100} \small \frac{3}{4}$

$\dpi{100} \small 5$

$\dpi{100} \small \frac{\sqrt{8}}{4}$

Correct answer:

$\dpi{100} \small -5$

Explanation:

$\dpi{100} \small x+y$ is negative and $\dpi{100} \small xy$ is positive

$\dpi{100} \small \frac{Negative}{-Positive} = \frac{Negative}{Negative} = Positive$

Therefore, the solution cannot be negative.

Report an Error

Example Question #411 : Arithmetic

If $\frac{873}{x^3-8}$ is a real number, which one of these cannot be a value of ?

Possible Answers:

Correct answer:

Explanation:

For the expression to be defined, the denominator needs to be different from 0. Therefore:

$x^{3}-8=0$

$x^3 = 8 \Leftrightarrow x = \sqrt[3]{8} \Leftrightarrow x = (2^{3})^{\frac{1}{3}} = 2$

So the correct answer is 2.

Report an Error

Example Question #1961 : Problem Solving Questions

If x<y , and 2y<10 , and x<1 , what can we say for sure about x+y ?

Possible Answers:

x+y>4

x+y is positive

x+y is negative

None of the other answers.

x+y=0

Correct answer:

None of the other answers.

Explanation:

To show the other answers aren't always true, we need to choose 2 numbers that satisfy the given inequalities but also contradict each answer one-by-one.

Let x =0, y =4 this choice shows that sometimes x +y = 4 , which rules out the answers x +y>4 , x+y is negative, and x+y = 0

Now Let x=-3, y=-2 , this will still satisfy the given inequalities, but now x+y = -5 . This means that the answer " x+y is positive" isn't always true either.

Report an Error

Example Question #412 : Arithmetic

Which of the following is equal to the sum of thirty-three one-thousandths and three hundred three ten-thousandths?

Possible Answers:

Six hundred thirty-three ten-thousandths

Three hundred thirty-six ten-thousandths

Three hundred sixty-six ten-thousandths

Six hundred six ten-thousandths

Six hundred three ten-thousandths

Correct answer:

Six hundred thirty-three ten-thousandths

Explanation:

The one-thousandths and ten-thousandths places are the third places and the fourth places, respectively, to the right of the decimal point. Therefore:

Thirty-three one-thousandths = 0.033

Three hundred three ten-thousandths = 0.0303

Add:

$\begin{matrix} \: \: \: 0.0330\\ +\underline{0.0303}\\ \: \: \: 0.0633 \end{matrix}$

The last nonzero digit ends at the ten-thousandths place, so this is $\frac{633}{10,000}$ , or

six hundred thirty-three ten-thousandths.

Report an Error

Example Question #1961 : Gmat Quantitative Reasoning

Which of the following is equal to 0.0407?

Possible Answers:

Four hundred seven ten-thousandths

Four hundred seventy ten-thousandths

Four hundred seven one-thousandths

Forty-seven ten-thousandths

Four hundred seventy one-thousandths

Correct answer:

Four hundred seven ten-thousandths

Explanation:

The last nonzero digit is located in the fourth place right of the decimal point - the ten-thousandths place. Put the number, without decimal point or leading zeroes, over 10,000. This number is $\frac{407}{10,000}$ , or four hundred seven ten-thousandths.

Report an Error

Example Question #12 : Understanding Real Numbers

Which of the following is equal to three one-hundredths subtracted from one fourth?

Possible Answers:

Twenty-three one-hundredths

Thirty-seven one-hundredths

Five one-hundredths

Twenty-two one-hundredths

Forty-seven one-hundredths

Correct answer:

Twenty-two one-hundredths

Explanation:

The one-hundredths place is the second place to the right of the decimal point; therefore, three one-hundredths is equal to 0.03. One fourth can be converted to decimal form as follows:

$\frac{1}{4} = \frac{1 \cdot 25}{4\cdot 25} = \frac{25}{100}$ ,

which is twenty-five one-hundredths, or 0.25. Subtract:

0.25 - 0.03 = 0.22 ,

or twenty-two one-hundredths.

Report an Error

Example Question #15 : Understanding Real Numbers

13 -a = 9 - b

15 - c = 8 -d

10-a = 18-d

Order $\small a,b, c,d$ from least to greatest.

Possible Answers:

$\small \small a,b,d,c$

$\small a,b ,c,d$

$\small \small b,a,c,d$

$\small b,a,d,c$

$\small a,c,b,d$

Correct answer:

$\small b,a,d,c$

Explanation:

We can find each in terms of .

13 -a = 9 - b

13 -a+b + a -13= 9 - b +b + a -13

b = a-4

10-a = 18-d

10-a + d + a - 10 = 18-d + d + a - 10

d = a+8

15 - c = 8 -d

15 - c = 8 -(a+8)

15 - c = -a

-a +c + a = 15 -c +c + a

c= a+ 15

In ascending order, the numbers are:

b = a-4

d = a+8

c= a+ 15

The correct choice is $\small b,a,d,c$ .

Report an Error

All GMAT Math Resources

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

Popular Subjects

Physics Tutors in New York City, SAT Tutors in San Diego, SAT Tutors in Houston, Statistics Tutors in Seattle, GMAT Tutors in Phoenix, Reading Tutors in Chicago, GMAT Tutors in Philadelphia, Chemistry Tutors in Los Angeles, ACT Tutors in New York City, Algebra Tutors in Boston

Popular Courses & Classes

SAT Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Philadelphia, ISEE Courses & Classes in Houston, ISEE Courses & Classes in Atlanta, SSAT Courses & Classes in Houston, ACT Courses & Classes in San Diego, LSAT Courses & Classes in Atlanta, ISEE Courses & Classes in San Diego, GMAT Courses & Classes in Chicago, Spanish Courses & Classes in Phoenix

Popular Test Prep

LSAT Test Prep in Philadelphia, MCAT Test Prep in Denver, SAT Test Prep in Phoenix, MCAT Test Prep in Los Angeles, GRE Test Prep in New York City, SAT Test Prep in Miami, SSAT Test Prep in Chicago, GMAT Test Prep in Miami, SSAT Test Prep in Washington DC, GRE Test Prep in San Francisco-Bay Area

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 : Arithmetic

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #7 : Understanding Real Numbers

Example Question #1 : Understanding Real Numbers

Example Question #1 : Understanding Real Numbers

Example Question #2 : Real Numbers

Example Question #411 : Arithmetic

Example Question #1961 : Problem Solving Questions

Example Question #412 : Arithmetic

Example Question #1961 : Gmat Quantitative Reasoning

Example Question #12 : Understanding Real Numbers

Example Question #15 : Understanding Real Numbers

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details