GMAT Math : Understanding arithmetic sets

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

← Previous 1 2 3 Next →

Example Question #1 : Arithmetic

Which set is NOT equal to the other sets?

Possible Answers:

$\left \{ 4,1,4,3 \right \}$

$\left \{ 3,4,3,1 \right \}$

$\left \{ 4,3,1,4 \right \}$

$\left \{ 1,3,4 \right \}$

$\left \{ 1,3,1,1 \right \}$

Correct answer:

$\left \{ 1,3,1,1 \right \}$

Explanation:

Order and repetition do NOT change a set. Therefore, the set we want to describe contains the numbers 1, 3, and 4. The only set that doesn't contain all 3 of these numbers is $\left \{ 1,3,1,1 \right \}$ , so it is the set that does not equal the rest of the sets.

Report an Error

Example Question #1 : Arithmetic

Given the sets A = {2, 3, 4, 5} and B = {3, 5, 7}, what is $A \bigcup B$ ?

Possible Answers:

$\left \{ 3,5,7 \right \}$

$\left \{ 2,3,4,5 \right \}$

$\left \{ 2,3,4,5,7 \right \}$

$\left \{ 2,3,4,5,6,7 \right \}$

$\left \{ 3,5 \right \}$

Correct answer:

$\left \{ 2,3,4,5,7 \right \}$

Explanation:

We are looking for the union of the sets. That means we want the elements of A OR B.

So $A \bigcup B$ = {2, 3, 4, 5, 7}.

Report an Error

Example Question #1 : Sets

Given the set = {2, 3, 4, 5}, what is the value of 3+A ?

Possible Answers:

$\left \{ 6,9,12,15 \right \}$

$\left \{ 5 \right \}$

cannot be added together

$\left \{ 12,20,28 \right \}$

$\left \{ 5,6,7,8 \right \}$

Correct answer:

$\left \{ 5,6,7,8 \right \}$

Explanation:

We need to add 3 to every element in .

Then:

$3+A=\left \{ 3+2,3+3,3+4,3+5 \right \}=\left \{ 5,6,7,8 \right \}.$

Report an Error

Example Question #1 : Arithmetic

There exists two sets and . = {1, 4} and = {3, 4, 6}. What is A+B ?

Possible Answers:

$\left \{ 3,8 \right \}$

$\left \{ 1,3,4,4,6 \right \}$

$\left \{ 6,7,9,8,10,12 \right \}$

$\left \{ 2,5,8 \right \}$

$\left \{ 4,5,7,8,10 \right \}$

Correct answer:

$\left \{ 4,5,7,8,10 \right \}$

Explanation:

Add each element of to each element of .

A+B = {1 + 3, 1 + 4, 1 + 6, 4 + 3, 4 + 4, 4 + 6} = {4, 5, 7, 8, 10}

Report an Error

Example Question #2 : Arithmetic

How many functions map from $X=\left \{ a,b \right \}$ to $Y=\left \{ 1,2,3 \right \}$ ?

Possible Answers:

Correct answer:

Explanation:

There are three choices for (1, 2, and 3), and similarly there are three choices for (also 1, 2, and 3). Together there are $3\cdot 3=9$ possible functions from to . Remember to multiply, NOT add.

Report an Error

Example Question #6 : Understanding Arithmetic Sets

How many elements are in a set from which exactly 768 unique subsets can be formed?

Possible Answers:

It is not possible to form exactly 768 unique subsets.

Correct answer:

It is not possible to form exactly 768 unique subsets.

Explanation:

The number of subsets that can be formed from a set with elements is $2^{N}$ . However, $2^{9} = 512$ and $2^{10} = 1024$ , so there is no integer for which $2^{N} = 768$ . Therefore, a set with exactly 768 elements cannot exist.

Report an Error

Example Question #3 : Arithmetic

Let the univeraal set be the set of all positive integers.

Define the sets

$A = \left \{ 1,6,11,16,21,26,...\right\}$ ,

$B = \left \{1, 5, 9, 13,17,21,25,...\right \}$ ,

$C = \left\{1,4,7,10,13,16,19,...\right \}$ .

If the elements in $A \cap B \cap C$ were ordered in ascending order, what would be the fourth element?

Possible Answers:

181

481

421

241

Correct answer:

181

Explanation:

A,B,C are the sets of all positive integers that are one greater than a multiple of five, four, and three, respectively. Therefore, for a number to be in all three sets, and subsequently, $A \cap B \cap C$ , the number has to be one greater than a number that is a multiple of five, four, and three. Since LCM (5,4,3) = 60 , the number has to be one greater than a multiple of 60. The first four numbers that fit this description are 1, 61, 121, and 181, the last of which is the correct choice.

Report an Error

Example Question #1 : Sets

A six-sided die is rolled, and a coin is flipped. If the coin comes up heads, the roll is considered to be the number that appears face up on the die; if the coin comes up tails, the outcome is considered to be twice that number. What is the sample space of the experiment?

Possible Answers:

$\left \{ 2,3,4,5,6, 7,8,9,10,11,12\right \}$

$\left \{ 1,2,3,4,5,6, 7,8,9,10,11,12\right \}$

$\left \{ 2,4,6,8,10,12\right \}$

$\left \{ 2,3,4,5,6 ,8,10,12\right \}$

$\left \{ 1,2,3,4,5,6 ,8,10,12\right \}$

Correct answer:

$\left \{ 1,2,3,4,5,6 ,8,10,12\right \}$

Explanation:

If heads comes up on the coin, the number on the die is recorded. This can be any element of the set $\left \{ 1,2,3,4,5,6\right \}$ .

If tails comes up on the coin, twice the number on the die is recorded. This can be twice any element of the set $\left \{ 1,2,3,4,5,6\right \}$ - that is, any element of the set $\left \{ 2,4,6,8,10,12\right \}$ .

The sample space is the union of these two sets:

$\left \{ 1,2,3,4,5,6 ,8,10,12\right \}$

Report an Error

Example Question #4 : Arithmetic

A six-sided die is rolled, and a coin is flipped. If the coin comes up heads, the roll is considered to be the number that appears face up on the die; if the coin comes up tails, the outcome is considered to be half that number, with any fraction simply thrown out. What is the sample space of the experiment?

Possible Answers:

$\left \{ 0,1,2,3,4,5,6\right \}$

$\left \{ \frac{1}{2}, 1, 1\frac{1}{2}, 2,2 \frac{1}{2}, 3,4,5,6\right \}$

$\left \{ 1, 1\frac{1}{2}, 2,2 \frac{1}{2}, 3 ,4,5,6\right \}$

$\left \{ \frac{1}{2}, 1, 1\frac{1}{2}, 2,2 \frac{1}{2}, 3,3\frac{1}{2}, 4,4\frac{1}{2},5,5\frac{1}{2}, 6\right \}$

$\left \{ 1,2,3,4,5,6\right \}$

Correct answer:

$\left \{ 0,1,2,3,4,5,6\right \}$

Explanation:

If heads comes up on the coin, the number on the die is recorded. This can be any element of the set $\left \{ 1,2,3,4,5,6\right \}$ .

If tails comes up on the coin, half the number on the die is recorded, and any fraction is thrown out. Half the elements of the set $\left \{ 1,2,3,4,5,6\right \}$ comprise the set $\left \{ \frac{1}{2}, 1, 1\frac{1}{2}, 2,2 \frac{1}{2}, 3\right \}$ , but since we are throwing out the fractional parts, this becomes the set $\left \{ 0, 1,2,3\right \}$ .

The sample space is the union of these two sets, which is $\left \{ 0,1,2,3,4,5,6\right \}$ .

Report an Error

Example Question #1 : Arithmetic

Temperature

Refer to the above graph, which shows the peak temperature in Smithville for each of seven days in a one-week period.

Between which two consecutuve days did the peak temperature see its greatest decrease?

Possible Answers:

Friday to Saturday

Tuesday to Wednesday

Wednesday to Thursday

Thursday to Friday

Monday to Tuesday

Correct answer:

Friday to Saturday

Explanation:

You only need to look for the portion of the line with the greatest negative slope, which is that which represents Friday to Saturday.

Report an Error

← Previous 1 2 3 Next →

All GMAT Math Resources

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

Popular Subjects

Calculus Tutors in Los Angeles, Chemistry Tutors in San Francisco-Bay Area, Chemistry Tutors in Washington DC, LSAT Tutors in Los Angeles, GMAT Tutors in Phoenix, MCAT Tutors in Miami, LSAT Tutors in Miami, Biology Tutors in Washington DC, ISEE Tutors in Houston, ACT Tutors in New York City

Popular Courses & Classes

LSAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Los Angeles, ISEE Courses & Classes in San Diego, ACT Courses & Classes in Washington DC, SAT Courses & Classes in Boston, SSAT Courses & Classes in New York City, SAT Courses & Classes in Seattle, GRE Courses & Classes in Houston, MCAT Courses & Classes in Phoenix, LSAT Courses & Classes in Phoenix

Popular Test Prep

GRE Test Prep in Houston, ACT Test Prep in Washington DC, SSAT Test Prep in Dallas Fort Worth, MCAT Test Prep in Chicago, GRE Test Prep in Los Angeles, SSAT Test Prep in Houston, SAT Test Prep in Seattle, ISEE Test Prep in Dallas Fort Worth, LSAT Test Prep in Chicago, MCAT Test Prep in Boston

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 : Understanding arithmetic sets

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Arithmetic

Example Question #1 : Arithmetic

Example Question #1 : Sets

Example Question #1 : Arithmetic

Example Question #2 : Arithmetic

Example Question #6 : Understanding Arithmetic Sets

Example Question #3 : Arithmetic

Example Question #1 : Sets

Example Question #4 : Arithmetic

Example Question #1 : Arithmetic

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details