Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Middle Level Quantitative : How to add variables

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

Create An Account

All ISEE Middle Level Quantitative Resources

6 Diagnostic Tests 110 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Define an operation on the real numbers as follows:

For all real values of $\displaystyle a$ and $\displaystyle b$,

$a \bigstar b = ab-a+b$ $\displaystyle a \bigstar b = ab-a+b$

$\displaystyle N$ is a positive number. Which is the greater quantity?

(a) $N \bigstar N$ $\displaystyle N \bigstar N$

(b) $(-N) \bigstar (-N)$ $\displaystyle (-N) \bigstar (-N)$

Possible Answers:

(a) and (b) are equal

(a) is the greater quantity

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

(b) is the greater quantity

Correct answer:

(a) and (b) are equal

Explanation:

$a \bigstar b = ab-a+b$ $\displaystyle a \bigstar b = ab-a+b$

$N \bigstar N =N \cdot N -N+N = N^{2}-N+N = N^{2}$ $\displaystyle N \bigstar N =N \cdot N -N+N = N^{2}-N+N = N^{2}$

and

$(-N) \bigstar (-N) = (-N) \cdot (-N) - (-N) + (-N)$ $\displaystyle (-N) \bigstar (-N) = (-N) \cdot (-N) - (-N) + (-N)$

$= (-1) \cdot N \cdot (-1) \cdot N+N - N$ $\displaystyle = (-1) \cdot N \cdot (-1) \cdot N+N - N$

$= N^{2}+N-N$ $\displaystyle = N^{2}+N-N$

$= N^{2}$ $\displaystyle = N^{2}$

The two are equal regardless of the value of $\displaystyle N$.

Report an Error

Example Question #11 : Variables

$\displaystyle x$ and $\displaystyle y$ are both negative numbers. Which is the greater quantity?

(a) $(x \div 5) + 0.1 y$ $\displaystyle (x \div 5) + 0.1 y$

(b) $0.2 x + (y \div 10)$ $\displaystyle 0.2 x + (y \div 10)$

Possible Answers:

(a) and (b) are equal

(b) is the greater quantity

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

(a) is the greater quantity

Correct answer:

(a) and (b) are equal

Explanation:

The two quantities are equal regardless of the values of $\displaystyle x$ and $\displaystyle y$. To see this, we note that

$0.2 x = \frac{2}{10} x = \frac{1}{5} x = \frac{x}{5} = x \div 5$ $\displaystyle 0.2 x = \frac{2}{10} x = \frac{1}{5} x = \frac{x}{5} = x \div 5$

and

$0.1y = \frac{1}{10} y = \frac{y}{10} = y \div 10$ $\displaystyle 0.1y = \frac{1}{10} y = \frac{y}{10} = y \div 10$

Therefore, by the addition property of equality,

$0.2 x + (y \div 10) =( x \div 5 )+ 0.1 y$ $\displaystyle 0.2 x + (y \div 10) =( x \div 5 )+ 0.1 y$

Report an Error

Example Question #13 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

$\displaystyle 5 < A < 7$

$\displaystyle 5 < B < 7$

5 <C < 7 $\displaystyle 5 < C < 7$

Which is the greater quantity?

(a) $\displaystyle A + B + C$

(b) 18

Possible Answers:

(a) is the greater quantity

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

(a) and (b) are equal

(b) is the greater quantity

Correct answer:

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

Explanation:

The information is insufficient, as we see by exploring two cases:

Case 1: $A = B = C = 5\frac{1}{3}$ $\displaystyle A = B = C = 5\frac{1}{3}$

$A+ B + C = 5\frac{1}{3}+ 5\frac{1}{3} + 5\frac{1}{3} = 16 < 18$ $\displaystyle A+ B + C = 5\frac{1}{3}+ 5\frac{1}{3} + 5\frac{1}{3} = 16 < 18$

Case 2: $A = B = C = 6\frac{1}{3}$ $\displaystyle A = B = C = 6\frac{1}{3}$

$A+ B + C = 6\frac{1}{3}+ 6\frac{1}{3} + 6\frac{1}{3} =19 > 18$ $\displaystyle A+ B + C = 6\frac{1}{3}+ 6\frac{1}{3} + 6\frac{1}{3} =19 > 18$

Remember, the three variables need not stand for whole numbers.

Report an Error

View Tutors

Yongmao
Certified Tutor

Nankai University, Bachelor of Science, Chemistry. Washington University in St Louis, Doctor of Philosophy, Organic Chemistry.

View Tutors

Gabby
Certified Tutor

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

View Tutors

Jacqueline
Certified Tutor

Yale University, Bachelor of Science, German Studies. Cornell University, Master of Science, German Studies.

All ISEE Middle Level Quantitative Resources

6 Diagnostic Tests 110 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Spanish Tutors in Atlanta, MCAT Tutors in Dallas Fort Worth, GMAT Tutors in Atlanta, Chemistry Tutors in Los Angeles, Statistics Tutors in Seattle, Computer Science Tutors in Seattle, SSAT Tutors in Dallas Fort Worth, GMAT Tutors in San Diego, GMAT Tutors in Houston, Calculus Tutors in Houston

Popular Courses & Classes

LSAT Courses & Classes in Atlanta, SAT Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Houston, GMAT Courses & Classes in Miami, ACT Courses & Classes in Chicago, GRE Courses & Classes in Chicago, ACT Courses & Classes in San Diego, SSAT Courses & Classes in Denver, ISEE Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Washington DC

Popular Test Prep

ACT Test Prep in Chicago, SAT Test Prep in Philadelphia, GRE Test Prep in San Diego, MCAT Test Prep in Denver, SSAT Test Prep in Seattle, SAT Test Prep in San Diego, SSAT Test Prep in Chicago, SSAT Test Prep in Atlanta, GMAT Test Prep in Philadelphia, ACT Test Prep in San Diego

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 Middle Level Quantitative : How to add variables

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

All ISEE Middle Level Quantitative Resources

Example Questions

Example Question #11 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #11 : Variables

Example Question #13 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

All ISEE Middle Level Quantitative Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: