Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Quantitative : How to find the missing part of a list

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

Create An Account

All ISEE Upper Level Quantitative Resources

8 Diagnostic Tests 234 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Sets

A class has 25 students. If 60% of them are boys, how many students are girls?

Possible Answers:

Correct answer:

Explanation:

If 60% of the students are boys, 40% are girls (100 – 60 = 40). Multiply 25 by 40% (25 * 0.4 = 10); therefore, 10 students are girls.

Report an Error

Example Question #1 : How To Find The Missing Part Of A List

We can divide the natural numbers into four sets:

$A = \left \{ 1, 5, 9, 13, 17, ... \right \}$

$B= \left \{ 2, 6, 10, 14, 18...\right \}$

$C = \left \{ 3, 7, 11, 15, 19...\right \}$

$D = \left \{ 4, 8, 12, 16, 20...\right \}$

In which of these sets would 197 be a member?

Possible Answers:

It cannot be determined from the information given.

Correct answer:

Explanation:

The sets are divided according to the remainder obtained when each element is divided by 4. 197 divided by 4 yields a remainder of 1; all of the elements of match this description, so $197 \in A$ .

Report an Error

Example Question #1 : How To Find The Missing Part Of A List

Define the universal set, , as follows:

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

Also, let

$A = \left \{ 1, 2, 3, 6, 9\right \}$ and $B = \left \{ 3, 5, 7, 9, 10\right \}$

Which of these sets represents the complement of $A \cup B$ ?

Possible Answers:

$\left \{ 3,9\right \}$

$\left \{ 1, 2, 3, 5, 6, 7, 9, 10\right \}$

$\left \{ 3, 4, 8 ,9\right \}$

$\left \{ 4, 8\right \}$

$\left \{ 1, 2, 5, 6, 7, 10\right \}$

Correct answer:

$\left \{ 4, 8\right \}$

Explanation:

$A \cup B$ , the union of and is the set of all elements in , , or both. Merge the two sets to get:

$A \cup B = \left \{ 1, 2, 3, 5, 6, 7, 9, 10\right \}$

The complement of a set is the set of all elements in the universal set that are not in the set. The only elements in not in $A \cup B$ are 4 and 8, so

$\overline{ \left (A \cup B \right )}= \left \{ 4,8\right \}$

Report an Error

Example Question #2 : How To Find The Missing Part Of A List

Which of the following is an example of two sets and such that $A \cap B = \varnothing$ ?

Possible Answers:

$A = \left \{ \textrm{John, Mary, Fred, Stan, Harry } \right \}$

$B = \left \{ \textrm{Greg, Larry, Phil, Andy, Joanne }\right \}$

$A = \left \{ a,v,r, w,s,y\right \}$

$B = \left \{ k, p, r, q,x\right \}$

$A = \left \{ 2, 8, 4, 1, 10\right \}$

$B = \left \{ 5, 9, 7, 2, 0\right \}$

$A = \left \{ \Delta , \Gamma , \Theta , \Lambda , \Sigma \right \}$

$B = \left \{ \Omega , \Psi , \Phi , \Pi , \Lambda \right \}$

$A = \left \{ \textrm{Lincoln, Washington, Jefferson, Jackson, Madison}\right \}$

$B = \left \{ \textrm{ Monroe, Kennedy, Madison, McKinley , Taft} \right \}$

Correct answer:

$A = \left \{ \textrm{John, Mary, Fred, Stan, Harry } \right \}$

$B = \left \{ \textrm{Greg, Larry, Phil, Andy, Joanne }\right \}$

Explanation:

$\varnothing$ refers to the empty set, the set with no elements; $A \cap B = \varnothing$ if and only if the two sets have no elements in common. In four of these cases, and share an element, which in each of these four choices is underlined:

$A = \left \{ \Delta , \Gamma , \Theta , \underline{\Lambda} , \Sigma \right \}$

$B = \left \{ \Omega , \Psi , \Phi , \Pi , \underline{\Lambda} \right \}$

$A = \left \{ \textrm{Lincoln, Washington, Jefferson, Jackson, \underline{Madison}}\right \}$

$B = \left \{ \textrm{ Monroe, Kennedy, \underline{Madison}, McKinley , Taft} \right \}$

$A = \left \{ a,v,\underline{r}, w,s,y\right \}$

$B = \left \{ k, p, \underline{r}, q,x\right \}$

$A = \left \{ \underline{2}, 8, 4, 1, 10\right \}$

$B = \left \{ 5, 9, 7, \underline{2}, 0\right \}$

$A = \left \{ \textrm{John, Mary, Fred, Stan, Harry } \right \}$ and $B = \left \{ \textrm{Greg, Larry, Phil, Andy, Joanne }\right \}$ do not have an element in common, so this is the right choice.

Report an Error

Example Question #3 : How To Find The Missing Part Of A List

Define set $A = \left \{ 1, 3, 5, 6, 7, 8, 10 \right \}$ . How could we define set so that $A \cap B = \left \{ 1, 5, 6, 8\right \}$ ?

Possible Answers:

$B = \left \{ 1, 2, 5, 6, 9, 12, 13, 15\right \}$

$B = \left \{ 1,5, 10\right \}$

$B = \left \{ 1, 2, 4, 5, 6, 10, 11, 12\right \}$

$B = \left \{ 1, 2, 5, 6, 8, 9, 11, 12\right \}$

$B = \left \{5, 6,8, 9, 16\right \}$

Correct answer:

$B = \left \{ 1, 2, 5, 6, 8, 9, 11, 12\right \}$

Explanation:

$A \cap B$ is the set of all elements in both and .

We can test each set and determine which elements are shared by that set and :

If $B = \left \{ 1, 2, 5, 6, 9, 12, 13, 15\right \}$ :

then

$A \cap B$

$= \left \{ \underline{1}, 3, \underline{5}, \underline{6}, 7, 8, 10 \right \} \cap \left \{ \underline{1}, 2,\underline{ 5}, \underline{6}, 9, 12, 13, 15\right \}$

$= \left \{ 1,5,6\right \}$

If $B = \left \{ 1, 2, 4, 5, 6, 10, 11, 12\right \}$ :

then

$A \cap B$

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

$= \left \{ 1,5,6, 10\right \}$

If $B = \left \{ 1,5, 10\right \}$ :

then

$A \cap B$

$= \left \{ \underline{1}, 3, \underline{5},6, 7, 8, \underline{10} \right \} \cap \left \{ \underline{1}, \underline{5}, \underline{10}\right \}$

$= \left \{ 1,5, 10\right \}$

If $B = \left \{5, 6,8, 9, 16\right \}$ :

then

$A \cap B$

$= \left \{ 1, 3, \underline{5}, \underline{6}, 7, \underline{8}, 10 \right \} \cap\left \{\underline{5}, \underline{6},\underline{8},9, 16\right \}$

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

If $B = \left \{ 1, 2, 5, 6, 8, 9, 11, 12\right \}$ :

then

$A \cap B$

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

$= \left \{ 1,5,6, 8\right \}$

This is the correct choice.

Report an Error

Example Question #1 : How To Find The Missing Part Of A List

A pair of fair dice are rolled. Which is the greater quantity?

(a) The probability that at least one die comes up 5 or 6

(b) $\frac{1}{2}$

Possible Answers:

(a) is greater

(b) is greater

(a) and (b) are equal

It is impossible to tell from the information given.

Correct answer:

(a) is greater

Explanation:

For the roll to be unfavorable to the event that at least one of the dice is 5 or 6, both dice would have to be 1, 2, 3, or 4. There are $4 \times 4 = 16$ ways out of 36 that this can happen, so there are 36-16 = 20 ways for either or both of the two dice to be 5 or 6. Since half of 36 is 18, the probability of this event is greater than $\frac{1}{2}$ .

Report an Error

Example Question #2 : How To Find The Missing Part Of A List

A pair of fair dice are tossed. Which is the greater quantity?

(a) The probability that the product of the two dice will be an even number

(b) $\frac{1}{2}$

Possible Answers:

(a) and (b) are equal

(b) is greater

It is impossible to tell from the information given

(a) is greater

Correct answer:

(a) is greater

Explanation:

The product of the two dice will be an odd number only if both dice are odd; the rolls favorable to that event are:

$\left \{ (1,1) , (1,3), (1,5), (3,1) , (3,3), (3,5),(5,1) , (5,3), (5,5) \right \}$ ,

or nine out of the thirty-six possible rolls. This makes twenty-seven of the thirty-six equally probable rolls favorable to getting an even product. Since half of 36 is 18, the probability of getting an even product is greater than $\frac{1}{2}$ .

This makes (a) the greater quantity

Report an Error

Example Question #3 : How To Find The Missing Part Of A List

Which quantity is greater?

(a) The number of even integers that satisfy the inequality 0 < x < 1,000

(b) The number of multiples of 4 that satisfy the inequality 0 < y < 2,000

Possible Answers:

(a) and (b) are equal

It is impossible to tell from the information given.

(b) is greater

(a) is greater

Correct answer:

(a) and (b) are equal

Explanation:

The easiest way to answer this is to try to match each element in the first set to one the second set as follows:

$2 \rightarrow 4$

$4 \rightarrow 8$

$6 \rightarrow 12$

...

$998 \rightarrow 1,996$

In other words, each element in the set in (a) is paired with the element in the set in (b) that is its double. Since there is a one-to-one correspondence, the two sets are of equal aize, and (a) and (b) are equal quantities.

Report an Error

Example Question #9 : Sets

Which quantity is greater?

(a) The number of even integers that satisfy the inequality $0 < x \leq 1,000$

(b) The number of odd integers that satisfy the inequality $0 < x \leq 1,000$

Possible Answers:

(a) and (b) are equal.

It is impossible to tell from the information given.

(b) is greater.

(a) is greater.

Correct answer:

(a) and (b) are equal.

Explanation:

The easiest way to answer this is to try to match each element in the first set to one in the second set as follows:

$2 \rightarrow 1$

$4 \rightarrow3$

$6\rightarrow 5$

...

$1,000 \rightarrow 999$

Since there is a one-to-one correspondence between the elements of the two sets, (a) and (b) are equal.

Report an Error

Example Question #3 : How To Find The Missing Part Of A List

A pair of fair dice are tossed. Which is the greater quantity?

(a) The probability that the product of the numbers will be at least .

(b) $\frac {1}{3}$

Possible Answers:

(b) is greater.

(a) is greater.

(a) and (b) are equal.

It is impossible to tell from the information given.

Correct answer:

(b) is greater.

Explanation:

Out of a possible thirty-six rolls, the following result in a product of or greater:

(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6,3), (6, 4), (6, 5), (6, 6)

This is ten equally probable rolls out of thirty-six, resulting in a probability of

$\frac {10}{36} = \frac{5}{18}$ .

Since $\frac {1}{3} = \frac {6} {18} > \frac {5} {18}$ , (b) is the greater quantity.

Report an Error

View Tutors

Kaitlyn
Certified Tutor

Fairfield University, Bachelor of Science, Biology, General. NUI Galway Ireland, Master of Science, Neuroscience.

View Tutors

Gabby
Certified Tutor

University of Oregon, Bachelor in Arts, Journalism. University of Oregon, Current Grad Student, Communication, General.

View Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

All ISEE Upper Level Quantitative Resources

8 Diagnostic Tests 234 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Computer Science Tutors in Phoenix, Biology Tutors in San Diego, SAT Tutors in Miami, Statistics Tutors in Phoenix, French Tutors in Washington DC, English Tutors in San Diego, Calculus Tutors in Phoenix, MCAT Tutors in Los Angeles, Biology Tutors in Atlanta, Reading Tutors in Boston

Popular Courses & Classes

SSAT Courses & Classes in Atlanta, ACT Courses & Classes in Philadelphia, Spanish Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Seattle, SAT Courses & Classes in Denver, GMAT Courses & Classes in Chicago, LSAT Courses & Classes in Chicago, MCAT Courses & Classes in Philadelphia, ISEE Courses & Classes in Denver, SSAT Courses & Classes in Houston

Popular Test Prep

ACT Test Prep in Atlanta, SAT Test Prep in Seattle, GRE Test Prep in Seattle, LSAT Test Prep in Los Angeles, ISEE Test Prep in Denver, SAT Test Prep in Denver, ISEE Test Prep in Seattle, LSAT Test Prep in Seattle, GMAT Test Prep in New York City, MCAT Test Prep in Washington DC

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)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

ISEE Upper Level Quantitative : How to find the missing part of a list

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #1 : Sets

Example Question #1 : How To Find The Missing Part Of A List

Example Question #1 : How To Find The Missing Part Of A List

Example Question #2 : How To Find The Missing Part Of A List

Example Question #3 : How To Find The Missing Part Of A List

Example Question #1 : How To Find The Missing Part Of A List

Example Question #2 : How To Find The Missing Part Of A List

Example Question #3 : How To Find The Missing Part Of A List

Example Question #9 : Sets

Example Question #3 : How To Find The Missing Part Of A List

All ISEE Upper Level Quantitative Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: