We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Quantitative : Variables

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 : Operations

Multiply:

(0.6x-0.4y)(0.6x+0.4y)

Possible Answers:

$0.36x^{2}-0.48xy+ 0.16y^{2}$

$0.36x^{2}+0.16y^{2}$

$0.36x^{2}-0.48xy- 0.16y^{2}$

$0.36x^{2}- 0.16y^{2}$

$0.36x^{2}-0.24xy+ 0.16y^{2}$

Correct answer:

$0.36x^{2}- 0.16y^{2}$

Explanation:

This can be solved using the pattern for the sum times difference of two terms:

(0.6x-0.4y)(0.6x+0.4y)

$=\left ( 0.6x \right )^{2} -\left ( 0.4y \right ) ^{2}$

$=0.6^{2}x^{2}- 0.4^{2}y^{2}$

$=0.36x^{2}- 0.16y^{2}$

Report an Error

Example Question #1 : Operations

Multiply:

$\left (\frac{4}{3}x + \frac{5}{3} \right )\left (\frac{4}{3}x - \frac{5}{3} \right )$

Possible Answers:

$\frac{16}{9} x ^{2}+ \frac{25}{9}$

$\frac{16}{9} x ^{2} - \frac{40}{9} x- \frac{25}{9}$

$\frac{16}{9} x ^{2} - \frac{20}{9} x- \frac{25}{9}$

$\frac{16}{9} x ^{2}- \frac{25}{9}$

$\frac{16}{9} x ^{2} - \frac{40}{9} x+ \frac{25}{9}$

Correct answer:

$\frac{16}{9} x ^{2}- \frac{25}{9}$

Explanation:

This can be solved using the pattern for the sum times difference of two terms:

$\left (\frac{4}{3}x + \frac{5}{3} \right )\left (\frac{4}{3}x - \frac{5}{3} \right )$

$=\left (\frac{4}{3}x \right ) ^{2}- \left (\frac{5}{3} \right )^{2}$

$=\frac{4 ^{2}}{3 ^{2}}\cdot x ^{2}- \frac{5^{2}}{3^{2}}$

$=\frac{16}{9} x ^{2}- \frac{25}{9}$

Report an Error

Example Question #3 : Operations

Simplify:

$\left (\frac{4}{3}x - \frac{5}{3} \right )^{2}$

Possible Answers:

$\frac{16}{9}x^{2} - \frac{20}{9}x +\frac{25}{9}$

$\frac{16}{9}x^{2} - \frac{25}{9}$

$\frac{16}{9}x^{2} - \frac{20}{9}x -\frac{25}{9}$

$\frac{16}{9}x^{2} - \frac{40}{9}x +\frac{25}{9}$

$\frac{16}{9}x^{2} - \frac{40}{9}x -\frac{25}{9}$

Correct answer:

$\frac{16}{9}x^{2} - \frac{40}{9}x +\frac{25}{9}$

Explanation:

This can be solved using the pattern for the square of a binomial:

$\left (\frac{4}{3}x - \frac{5}{3} \right )^{2}$

$=\left (\frac{4}{3}x \right ) ^{2} -2 \cdot \frac{4}{3}x \cdot \frac{5}{3} + \left ( \frac{5}{3} \right ) ^{2}$

$=\frac{4^{2}}{3^{2}}\cdot x^{2} -2 \cdot \frac{4}{3}\cdot \frac{5}{3} \cdot x +\frac{5^{2}}{3^{2}}$

$=\frac{16}{9}x^{2} - \frac{40}{9}x +\frac{25}{9}$

Report an Error

Example Question #2 : Operations

N is a positive integer; N > 1 . Which is greater?

(a) $N^{2} - 2N + 1$

(b) 0

Possible Answers:

(a) is greater

(a) and (b) are equal

(b) is greater

It is impossible to tell from the information given

Correct answer:

(a) is greater

Explanation:

$N^{2} - 2N + 1 = (N - 1)^{2}$ . Since N > 1 , N - 1 > 0 , and $N^{2} - 2N + 1 = (N - 1)^{2} > 0$ . This makes (a) greater.

Report an Error

Example Question #3 : Operations

N is a positive integer; N > 1 . Which is greater?

(a) $N^{2} - 4N + 4$

(b)

Possible Answers:

(a) is greater.

(b) is greater.

(a) and (b) are equal.

It is impossible to tell from the information given.

Correct answer:

It is impossible to tell from the information given.

Explanation:

If N = 2 , then $N^{2} - 4N + 4 = 2 ^{2} - 4 \cdot 2 + 4= 4 - 8 + 4 = 0$ .

If N = 3 , then $N^{2} - 4N + 4 = 3 ^{2} - 4 \cdot 3 + 4= 9 - 12 + 4 = 1$ .

Therefore, at least two possibilities can be demonstrated.

Report an Error

Example Question #4 : How To Multiply Variables

Which is the greater quantity?

(a) $-8 (x^{2}-x-6 )$

(b) $-8 x^{2}+8x-48$

Possible Answers:

(a) is greater.

(a) and (b) are equal.

It is impossible to tell from the information given.

(b) is greater.

Correct answer:

(a) is greater.

Explanation:

$-8 (x^{2}-x-6 )$

$=( -8 ) x^{2}-( -8 )x-( -8 )6$

$=-8 x^{2}-( -8x )-( -48 )$

$=-8 x^{2}+ 8x + 48$

Since 48 > -48 ,

$-8 x^{2}+ 8x + 48 > -8 x^{2}+ 8x - 48$ .

Report an Error

Example Question #5 : Operations

Assume is nonzero. Which expression is not equivalent to $16 y^{4}$ ?

Possible Answers:

All four expressions given in the other choices are equivalent to $16 y^{4}$ .

$\frac{32y^{8}}{2y^{4}}$

$\left ( 4y^{4}\right )^{4}$

$4y^{4} + 4y^{4} +4y^{4} + 4y^{4}$

$8 y^{2} \cdot 2y^{2}$

Correct answer:

$\left ( 4y^{4}\right )^{4}$

Explanation:

Each expression can be simplified using the properties of exponents, among others:

$\frac{32y^{8}}{2y^{4}} = \frac{32 }{2 } \cdot \frac{ y^{8}}{ y^{4}} = 16 y^{8-4} =16y^{4}$

$8 y^{2} \cdot 2y^{2} = 8 \cdot 2 \cdot y^{2} \cdot y^{2} = 16 y ^{2+2}= 16 y ^{4}$

$4y^{4} + 4y^{4} +4y^{4} + 4y^{4} = (4+4+4+4)y^{4} = 16y^{4}$

$\left ( 4y^{4}\right )^{4} = \left ( 4 \right )^{4} \cdot \left ( y^{4}\right )^{4} = 256y^{4 \cdot 4} = 256y^{16}$

The correct choice is $\left ( 4y^{4}\right )^{4}$ , as it is the only choice not equivalent to $16 y^{4}$ .

Report an Error

Example Question #5 : How To Multiply Variables

Let be negative. Which of the following is the greater quantity?

(A) -4y

(B) -5y

Possible Answers:

(A) and (B) are equal

(A) is greater

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

(B) is greater

Correct answer:

(B) is greater

Explanation:

-4 > -5 ,

So by the multiplication property of inequality, when each is multiplied by the negative number ,

-4y < -5y

and (B) is greater.

Report an Error

Example Question #1 : How To Multiply Variables

is a positive number. Which is greater?

(A) One ninth of 117% of

(B) One eleventh of 143% of

Possible Answers:

(A) and (B) are equal

(A) is greater

(B) is greater

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

Correct answer:

(A) and (B) are equal

Explanation:

117% of is equal to 1.17 N .

One-ninth of this is $\frac{1}{9} \cdot 1.17 N = \frac{1.17 }{9} \cdot N = 0.13N$

143% of is equal to 1.43N

One-eleventh of this is $\frac{1}{11} \cdot 1.43 N = \frac{1.43 }{11} \cdot N = 0.13N$

Regardless of the value of , the quanitites are equal.

Report an Error

Example Question #5 : Variables

Which of the following expressions is equivalent to

$\left ( 11x - \sqrt {11x}\right )\left ( 11x +\sqrt {11x}\right )$ ?

Possible Answers:

11x

121x^2 - 121x

100x^2

121x^2 - 11x

110x

Correct answer:

121x^2 - 11x

Explanation:

Use the difference of squares pattern as follows:

$\left ( 11x - \sqrt {11x}\right )\left ( 11x +\sqrt {11x}\right )$

$=\left ( 11x \right) ^{2} - \left ( \sqrt {11x}\right ) ^{2}$

$=11^{2}x^{2} - 11x$

$=121x^{2} - 11x$

Report an Error

View Tutors

Ana
Certified Tutor

Grand Canyon University, Bachelors, Education. Grand Canyon University, Masters, Education.

View Tutors

Gregory
Certified Tutor

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

View Tutors

Ericka
Certified Tutor

Southern Nazarene University, Bachelors, Network Engineering and Management . Oklahoma State University-Main Campus, Master o...

All ISEE Upper Level Quantitative Resources

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

Popular Subjects

GMAT Tutors in Phoenix, English Tutors in Houston, MCAT Tutors in Denver, SAT Tutors in Houston, ISEE Tutors in Boston, SSAT Tutors in New York City, Calculus Tutors in Houston, Computer Science Tutors in Los Angeles, GMAT Tutors in Dallas Fort Worth, Physics Tutors in Washington DC

Popular Courses & Classes

GRE Courses & Classes in San Diego, GMAT Courses & Classes in Miami, GMAT Courses & Classes in Boston, GRE Courses & Classes in Atlanta, LSAT Courses & Classes in San Diego, MCAT Courses & Classes in Denver, ISEE Courses & Classes in Los Angeles, MCAT Courses & Classes in Seattle, Spanish Courses & Classes in Phoenix, ISEE Courses & Classes in Washington DC

Popular Test Prep

LSAT Test Prep in Phoenix, MCAT Test Prep in Denver, ACT Test Prep in Seattle, SSAT Test Prep in Denver, GRE Test Prep in Boston, SAT Test Prep in Atlanta, ISEE Test Prep in Washington DC, GMAT Test Prep in Miami, SAT Test Prep in Washington DC, ISEE 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)

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 : Variables

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #1 : Operations

Example Question #1 : Operations

Example Question #3 : Operations

Example Question #2 : Operations

Example Question #3 : Operations

Example Question #4 : How To Multiply Variables

Example Question #5 : Operations

Example Question #5 : How To Multiply Variables

Example Question #1 : How To Multiply Variables

Example Question #5 : Variables

All ISEE Upper Level Quantitative Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: