Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Quantitative : How to factor a number

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 #30 : Numbers And Operations

If we consider the factors of as a set of numbers, which one is greater?

(a) The range of the set

(b) Sum of the median and the mean of the set

Possible Answers:

(a) and (b) are equal

(b) is greater

(a) is greater

It is not possible to tell based on the information given.

Correct answer:

(a) is greater

Explanation:

Factors of are $1,3,5,9,15\ and\ 45$ . So we have:

$\left \{ 1,3,5,9,15,45\right \}$

The range is the difference between the lowest and the highest values. So we have:

Range=45-1=44

The mean of a set of data is given by the sum of the data, divided by the total number of values in the set.

$Mean=\frac{1+3+5+9+15+45}{6}=13$

The median is the average of the two middle values of a set of data with an even number of values:

$Median=\frac{5+9}{2}=7$

So we have:

Mean+Median=13+7=20

So (a) is greater than (b)

Report an Error

Example Question #31 : Numbers And Operations

If we consider the factors of 1369 as a set of numbers, which one is greater?

(a) Product of the the median and the mean of the set

(b) The range of the set

Possible Answers:

(a) and (b) are equal

It is not possible to tell based on the information given.

(a) is greater

(b) is greater

Correct answer:

(a) is greater

Explanation:

Factors of 1369 are $1,37\ and\ 1369$ . So we have:

$\left \{ 1,37,1369\right \}$

The range is the difference between the lowest and the highest values. So we have:

Range=1369-1=1368

The mean of a set of data is given by the sum of the data, divided by the total number of values in the set.

$Mean=\frac{1+37+1369}{3}=469$

The median is the middle value of a set of data containing an odd number of values:

Median=13

So we have:

$Mean\times Median=469\times 13=6097$

So (b) is greater than (a)

Report an Error

Example Question #32 : Numbers And Operations

If we consider the factors of as a set of numbers, which one is greater?

(a) The mean of the set

(b) Ratio of the range and the median of the set

Possible Answers:

(a) and (b) are equal

It is not possible to tell based on the information given.

(a) is greater

(b) is greater

Correct answer:

(a) is greater

Explanation:

Factors of are $1,5\ and\25$ . So we have:

$\left \{ 1,5,25\right \}$

The range is the difference between the lowest and the highest values. So we have:

Range=25-1=24

The median is the middle value of a set of data containing an odd number of values, which is in this problem. So the ratio of the range and the median is:

$\frac{Range}{Median}=\frac{24}{5}=4.8$

The mean of a set of data is given by the sum of the data, divided by the total number of values in the set.

$Mean=\frac{1+5+25}{3}\approx 10.33$

So (a) is greater than (b)

Report an Error

Example Question #33 : Numbers And Operations

Which one is greater?

(a) The total number of factors of

$(b)\ 10$

Possible Answers:

(a) is greater

(a) and (b) are equal

(b) is greater

it is not possible to tell based on the information given.

Correct answer:

(b) is greater

Explanation:

Factors of are:

$1,2,3,4,6,9,12, 18\ and\ 36$ . So it has factors, which is less than .

Report an Error

Example Question #34 : Numbers And Operations

Which one is the greater quantity:

(a) Sum of the factors of 125

(b) Sum of the factors of

Possible Answers:

it is not possible to tell based on the information given.

(a) and (b) are equal

(a) is greater

(b) is greater

Correct answer:

(b) is greater

Explanation:

Factors of 125 are:

$1,5,25\ and\ 125$ and their summation is:

1+5+25+125=156

and the factors of are:

$1,2,4,5,8,10,16,20,40\ and\ 80$ and their summation is:

1+2+4+5+8+10+16+20+40+80=186

So (b) is greater than (a) .

Report an Error

Example Question #35 : Numbers And Operations

If we consider the factors of 100 as a set of numbers, compare the mean and the median of the set.

Possible Answers:

The mean and the median are equal

The mean is greater

The median is greater

It is not possible to tell based on the information given.

Correct answer:

The mean is greater

Explanation:

Factors of 100 are $1,2,4,5,10,20,25,50\ and\ 100$ . So we should compare the mean and the median of the following set of numbers:

$\left \{ 1,2,4,5,10,20,25,50,100 \right \}$

The mean of a set of data is given by the sum of the data, divided by the total number of values in the set:

$Mean=\frac{1+2+4+5+10+20+25+50+100}{9}=\frac{217}{9}\approx24$

The median is the middle value of a set of data containing an odd number of values which is in this problem. So the mean is greater than the median.

Report an Error

Example Question #36 : Numbers And Operations

Which one is greater?

(a) The product of the factors of .

(b) The median of the following set:

$\left \{ 40,42,48,54,70 \right \}$

Possible Answers:

(b) is greater

(a) and (b) are equal

It is not possible to tell based on the information given.

(a) is greater

Correct answer:

(a) is greater

Explanation:

Factors of are: $1,2,4\ and \8$ . So the product of the factors of are:

$1\times 2\times 4\times 8=64$

The median is the middle value of a set of data containing an odd number of values, which is in this problem. So (a) is greater than (b) .

Report an Error

Example Question #37 : Numbers And Operations

Which one is greater?

(a) The sum of the factors of

(b) The product of the factors of

Possible Answers:

It is not possible to tell based on the information given.

(b) is greater

(a) and (b) are equal

(a) is greater

Correct answer:

(b) is greater

Explanation:

Factors of are $1,2,3,4,5,6,10,12,15,20,30\ and\ 60$

$\Rightarrow Sum \ of\ the \ factors=1+2+3+4+5+6+10+12+15+20+30+60=168$

Factors of are $1,2,7\ and\14$

$\Rightarrow Product \ of\ the\ factors=1\times 2\times 7\times 14=196$

So (b) is greater thaan (a) .

Report an Error

Example Question #29 : How To Factor A Number

and are positive integers; x > y ; x+ y is an even number. Which of the following also must be even?

Possible Answers:

x - y + 1

x - y

x + 2 y

xy + 1

Correct answer:

x - y

Explanation:

If x+ y is even, then and are either both even or both odd. The difference of two even numbers is even, and so is the difference of two odd numbers, so x - y must be even. Let's check the other choices, however:

x - y must be even, so x - y + 1 must be odd.

is either the product of two even numbers, which is even, or the product of two odd numbers, which is odd. Therefore, is of indeterminate sign. Similarly, xy + 1 is as well.

is even for any integer , so x + 2 y takes the same sign as ; but this is not given to us.

x - y is the correct choice.

Report an Error

Example Question #21 : How To Factor A Number

Which is the greater quantity?

(A)

(B) The sum of the factors of 28 except for 28 itself.

Possible Answers:

(A) and (B) are equal

(B) is greater

(A) is greater

It is impossible to determine which is greater from the information given

Correct answer:

(A) and (B) are equal

Explanation:

Leaving out 28 itself, the factors of 28 are $\left \{ 1, 2, 4, 7, 14\right \}$ . The sum of all of these factors is 1 + 2 + 4 + 7 + 14 = 28 , making the quantities equal.

Report an Error

View Tutors

Robert
Certified Tutor

University of North Carolina at Chapel Hill, Bachelor in Arts, English. North Carolina Central University, Master of Arts, En...

View Tutors

Gregory
Certified Tutor

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

View Tutors

Gabby
Certified Tutor

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

All ISEE Upper Level Quantitative Resources

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

Popular Subjects

English Tutors in New York City, Biology Tutors in Chicago, Computer Science Tutors in Philadelphia, SSAT Tutors in San Francisco-Bay Area, Biology Tutors in Philadelphia, Math Tutors in Boston, ISEE Tutors in San Diego, GMAT Tutors in Phoenix, ACT Tutors in Boston, Chemistry Tutors in San Diego

Popular Courses & Classes

LSAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Philadelphia, MCAT Courses & Classes in Chicago, ISEE Courses & Classes in Washington DC, LSAT Courses & Classes in Seattle, LSAT Courses & Classes in Denver, LSAT Courses & Classes in Boston, SAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Washington DC, MCAT Courses & Classes in Washington DC

Popular Test Prep

LSAT Test Prep in Philadelphia, SSAT Test Prep in San Francisco-Bay Area, GRE Test Prep in Washington DC, SSAT Test Prep in Atlanta, ACT Test Prep in Phoenix, GRE Test Prep in Seattle, SAT Test Prep in Dallas Fort Worth, GMAT Test Prep in Washington DC, GRE Test Prep in San Francisco-Bay Area, MCAT Test Prep in Miami

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 factor a number

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #30 : Numbers And Operations

Example Question #31 : Numbers And Operations

Example Question #32 : Numbers And Operations

Example Question #33 : Numbers And Operations

Example Question #34 : Numbers And Operations

Example Question #35 : Numbers And Operations

Example Question #36 : Numbers And Operations

Example Question #37 : Numbers And Operations

Example Question #29 : How To Factor A Number

Example Question #21 : How To Factor A Number

All ISEE Upper Level Quantitative Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: