Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Middle Level Quantitative : 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 #8 : How To Subtract Variables

5 < A < 7

5 < B < 7

5 <C < 7

Which is the greater quantity?

(a) A - B + C

(b) 9

Possible Answers:

(a) is the greater quantity

(b) is the greater quantity

(a) and (b) are equal

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

Correct answer:

(b) is the greater quantity

Explanation:

5 < A < 7

5 <C < 7

also, since 5 < B < 7 , it follows that

-7 < -B < -5

A - B + C = A + (-B)+ C , and by the inequality properties,

A + (-B)+ C < 7 + (-5) + 7

A -B + C < 7 -5 + 7

A -B + C < 9

making 9 the greater quantity.

Report an Error

Example Question #21 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

What is the value of $9\div0.1$ ?

Possible Answers:

4.5

Correct answer:

Explanation:

$9\div 0.1=\frac{9}{0.1}=\frac{90}{1}=90$

(The numerator and the denominator are both multiplied by 10 in order to convert the fraction to whole numbers.)

Therefore, 90 is the correct answer.

Report an Error

Example Question #1 : How To Divide Variables

What is the value of $6\div0.2$ ?

Possible Answers:

300

Correct answer:

Explanation:

$6\div 0.2=\frac{6}{0.2}=\frac{60}{2}=30$

(The numerator and the denominator are both multiplied by 10 in order to convert the fraction to whole numbers.)

Therefore, 30 is the correct answer.

Report an Error

Example Question #3 : How To Divide Variables

Simplify:

$\frac{4x^2y}{12xy^3z}$

Possible Answers:

$\frac{xy^2z}{3}$

$\frac{4x^3}{12y^4z}$

3xy^3z

$\frac{1x^2y}{4xy^3z}$

$\frac{1x}{3y^2z}$

Correct answer:

$\frac{1x}{3y^2z}$

Explanation:

Since all of the variables are positive powers, this is easy. Start by reducing the numeric coefficient:

$\frac{4x^2y}{12xy^3z} = \frac{1x^2y}{3xy^3z}$

Next, cancel out the variables. Subtract the smaller power from the larger one. Remember that if there is no power listed, it is 1:

$\frac{1x^2y}{3xy^3z} = \frac{1x}{3y^2z}$

Report an Error

Example Question #3 : How To Divide Variables

Simplify:

$\frac{45a^2tz^2}{3tz^3}$

Possible Answers:

$\frac{15a^2}{z}$

$\frac{15a^2t}{z^2}$

$\frac{a^2}{15tz}$

$\frac{15z^2}{at}$

$\frac{45a^2t}{a^2z^2}$

Correct answer:

$\frac{15a^2}{z}$

Explanation:

Since all of the variables are positive powers, this is easy. Start by reducing the numeric coefficient:

$\frac{45a^2tz^2}{3tz^3} = \frac{15a^2tz^2}{tz^3}$

Next, cancel out the variables. Subtract the smaller power from the larger one. Remember that if there is no power listed, it is 1:

$\frac{15a^2tz^2}{tz^3} = \frac{15a^2}{z}$

Report an Error

Example Question #4 : How To Divide Variables

Simplify:

$\frac{5a^{-2}x}{ax^2}$

Possible Answers:

$\frac{a}{25a^2x}$

$\frac{1}{5a^3x}$

$\frac{x^2}{25a}$

$\frac{5}{a^3x}$

$\frac{5a}{x}$

Correct answer:

$\frac{5}{a^3x}$

Explanation:

The easiest way to begin with questions like this one is to "flip" the negative exponents to the top or bottom of the fraction. When you do this, you make the exponent's sign positive:

$\frac{5a^{-2}x}{ax^2} = \frac{5x}{a^2ax^2}$

Now, since all of the variables are positive powers, this is easy. Normally, you would begin by reducing the numeric coefficient. This is not necessary since there is only a 5 in the numerator. Therefore, combine the like variables first:

$\frac{5x}{a^2ax^2} = \frac{5x}{a^3x^2}$

Next, cancel out the variables. Subtract the smaller power from the larger one. Remember that if there is no power listed, it is 1:

$\frac{5x}{a^3x^2} = \frac{5}{a^3x}$

Report an Error

Example Question #23 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Simplify:

$\frac{35x^{-3}y^2z^{-1}}{105ax^2y^{-2}{}z^{-5}}$

Possible Answers:

$\frac{y^4z^4}{3ax^5}$

$\frac{3y^4z^4}{35ax^5}$

$\frac{xyz^4}{3a}$

$\frac{y^2z^4}{35ax^5z^1}$

$\frac{xy}{3az^4}$

Correct answer:

$\frac{y^4z^4}{3ax^5}$

Explanation:

The easiest way to begin with questions like this one is to "flip" the negative exponents to the top or bottom of the fraction. When you do this, you make the exponent's sign positive:

$\frac{35x^{-3}y^2z^{-1}}{105ax^2y^{-2}z^{-5}} = \frac{35y^2y^2z^5}{105ax^3x^2z^1}$

Next, go ahead and reduce the numeric coefficient:

$\frac{35y^2y^2z^5}{105ax^3x^2z^1} = \frac{1y^2y^2z^5}{3ax^3x^2z^1}$

Then, combine the like variables first:

$\frac{1y^2y^2z^5}{3ax^3x^2z^1} = \frac{1y^4z^5}{3ax^5z^1}$

Finally, cancel out the variables. Subtract the smaller power from the larger one. Remember that if there is no power listed, it is 1:

$\frac{1y^4z^5}{3ax^5z^1} = \frac{1y^4z^4}{3ax^5} = \frac{y^4z^4}{3ax^5}$

Report an Error

Example Question #3 : How To Divide Variables

Solve for :

ax+4a = 3a^2

$a \ne 0$

Possible Answers:

3a^2 - 4a

3a^2+4a-x

4-3a

3a-4

3-4a

Correct answer:

3a-4

Explanation:

To start, notice that the left side of the equation has a common factor of . You can factor this out:

ax+4a = 3a^2

becomes

a(x+4) = 3a^2

Next, you can divide both sides by since you know that it does not equal :

$x+4 = \frac{3a^2}{a}$

Simplifying the right side, you get:

x+4 = 3a

Finally, subtract from both sides:

x = 3a-4

Report an Error

Example Question #21 : Variables

Solve for :

5xb-25x=450x^3

$x \ne 0$

Possible Answers:

90x^3+5x

No possible answer

$\frac{450x^3}{5x-25}$

$\frac{-45x^2}{2}$

90x^2+5

Correct answer:

90x^2+5

Explanation:

To start, notice that the left side of the equation has common factors of and . You can factor these out:

5xb-25x=450x^3

becomes...

5x(b-5)=450x^3

Next, you can divide both sides by since you know that it does not equal :

$(b-5)=\frac{450x^3}{5x}$

Simplify the right side by canceling the and reducing the :

(b-5)=90x^2

Finally, add to both sides:

b=90x^2+5

Report an Error

Example Question #23 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

is the multiplicative inverse of . Which is the greater quantity?

(a) $\frac{a}{b}$

(b)

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:

is the multiplicative inverse of , so, by definition, ab= 1 . We show that this is insufficient information, however, with two cases.

Case 1: $a = 2, b= \frac{1}{2}$

$ab = 2 \cdot \frac{1}{2} = 1$

$\frac{a}{b} = a \div b = 2 \div \frac{1}{2} = 2 \cdot 2 = 4 > 1$

Case 2: $a= \frac{1}{2}, b = 2$

$ab = \frac{1}{2} \cdot 2 = 1$

$\frac{a}{b} = a \div b = \frac{1}{2} \div 2 = \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4} < 1$

Therefore,it is not clear which, if either, is the greater, $\frac{a}{b}$ or 1.

Report an Error

View Tutors

Aaron
Certified Tutor

Portland State University, Bachelors, Economics. Portland State University, Masters, Environmental and Resource Management.

View Tutors

Yongmao
Certified Tutor

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

View Tutors

Gregory
Certified Tutor

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

All ISEE Middle Level Quantitative Resources

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

Popular Subjects

Algebra Tutors in Philadelphia, SSAT Tutors in San Francisco-Bay Area, Algebra Tutors in Atlanta, Computer Science Tutors in Miami, Reading Tutors in Boston, Spanish Tutors in Denver, Chemistry Tutors in Houston, GRE Tutors in Seattle, ISEE Tutors in New York City, Spanish Tutors in Miami

Popular Courses & Classes

Spanish Courses & Classes in Houston, ACT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Seattle, MCAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Phoenix, GMAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Seattle, Spanish Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Miami, GMAT Courses & Classes in Washington DC

Popular Test Prep

MCAT Test Prep in Seattle, ISEE Test Prep in Seattle, GMAT Test Prep in Dallas Fort Worth, ACT Test Prep in Dallas Fort Worth, GMAT Test Prep in Washington DC, SSAT Test Prep in San Diego, GMAT Test Prep in Seattle, ISEE Test Prep in Atlanta, GMAT Test Prep in Chicago, SAT Test Prep in New York City

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 : Variables

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

All ISEE Middle Level Quantitative Resources

Example Questions

Example Question #8 : How To Subtract Variables

Example Question #21 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #1 : How To Divide Variables

Example Question #3 : How To Divide Variables

Example Question #3 : How To Divide Variables

Example Question #4 : How To Divide Variables

Example Question #23 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #3 : How To Divide Variables

Example Question #21 : Variables

Example Question #23 : 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: