We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Middle Level Quantitative : Algebraic Concepts

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 #22 : Equations

How many elements of the set $\left \{ -2, -1, 0, 1, 2 \right \}$ can be substituted for to make the inequality $-9y \geq 18$ a true statement?

Possible Answers:

One

None

Four

Two

Five

Correct answer:

One

Explanation:

$-9y \geq 18$

$-9y \div (-9) \leq 18\div (-9)$ (Note that the inequality symbol switches here)

$y\leq -2$

Of the elements of $\left \{ -2, -1, 0, 1, 2 \right \}$ , only fits this criterion.

Report an Error

Example Question #21 : Equations

If y = 4 , then how many integers can be substituted for to make the equation 4xy = 0 a true statement?

Possible Answers:

Infinitely many

It cannot be determined from the information given

Zero

One

Two

Correct answer:

One

Explanation:

If y = 4 , the equation can be rewritten and solved as follows:

4xy = 0

$4x \cdot 4 = 0$

16x = 0

$16x \div 16 = 0 \div 16$

x = 0

This is the only number that makes this statement true, so the correct choice is "one".

Report an Error

Example Question #153 : Algebraic Concepts

If x = -8 , then how many integers can be substituted for to make the equation $x^{2} + y^{3} = 0$ a true statement?

Possible Answers:

One

Two

Zero

Six

Three

Correct answer:

One

Explanation:

If x = -8 , then the equation can be rewritten and solved as follows:

$x^{2} + y^{3} = 0$

$(-8)^{2} + y^{3} = 0$

$64 + y^{3} = 0$

$64 + y^{3} -64 = 0-64$

$y^{3} = -64$

The only integer that can be cubed to yield the result is , so the correct response is "one".

Report an Error

Example Question #152 : Algebraic Concepts

If y = 12 , then how many integers can be substituted for to make the equation $x^{2} - y^{2} = 0$ a true statement?

Possible Answers:

One

Two

Zero

It cannot be determined from the information given

Infinitely many

Correct answer:

Two

Explanation:

If y = 12 , the equation can be restated and solved as follows:

$x^{2} - y^{2} = 0$

$x^{2} - 12^{2} = 0$

$x^{2} -144 = 0$

$x^{2} -144 + 144 = 0 + 144$

$x^{2} = 144$

Both x = 12 and x = -12 make this true, so both make the original statement true. "Two" is the correct choice.

Report an Error

Example Question #24 : How To Find The Solution To An Equation

How many elements of the set $\left \{ -2, -1, 0, 1, 2 \right \}$ can be substituted for to make the inequality $y + 3\frac{1}{2} < 2 \frac{1}{4}$ a true statement?

Possible Answers:

Five

One

Two

Three

Four

Correct answer:

One

Explanation:

$y + 3\frac{1}{2} < 2 \frac{1}{4}$

$y + 3\frac{1}{2} - 3\frac{1}{2} < 2 \frac{1}{4} - 3\frac{1}{2}$

$y < 2 \frac{1}{4} - 3\frac{1}{2}$

$y < -\left ( 3\frac{1}{2} - 2 \frac{1}{4} \right )$

$y <- 1 \frac{1}{4}$

Of the elements of the set $\left \{ -2, -1, 0, 1, 2 \right \}$ , only fits this criterion, making "one" the correct choice.

Report an Error

Example Question #155 : Algebraic Concepts

$\frac{c}{-6 } = 25$

$\frac{d}{-9} = 20$

Which is the greater quantity?

(A)

(B)

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) is greater

Explanation:

$\frac{c}{-6 } = 25$

$\frac{c}{-6 }\times (-6) = 25 \times (-6)$

c= -150

$\frac{d}{-9} = 20$

$\frac{d}{-9}\times (-9) = 20 \times (-9)$

d = -180

Since 150 < 180 , -150 > -180 .

c > d , so (A) is greater.

Report an Error

Example Question #22 : Equations

If x = 0 , then how many integers can be substituted for to make the equation 9xy = 0 a true statement?

Possible Answers:

One

Four

Zero

Two

Infinitely many

Correct answer:

Infinitely many

Explanation:

If x = 0 , this can be rewritten as

9xy = 0

$9 \cdot 0 \cdot y =0$

0 y =0

However, since zero multiplied by any number yields a product of zero, this is a true statement for all values of . This makes "infinitely msny" correct.

Report an Error

Example Question #31 : How To Find The Solution To An Equation

4A + 30 = 76 - 4B

Evaluate A + B .

Possible Answers:

$-11 \frac{1}{2}$

It is impossible to evaluate A + B from the information given

$-26 \frac{1}{2}$

$26 \frac{1}{2}$

$11 \frac{1}{2}$

Correct answer:

$11 \frac{1}{2}$

Explanation:

We will not be able to solve for the values of and ; instead, we need to group them together by reorganizing the equation.

4A + 30 = 76 - 4B

Start by adding and subtracting on each side. This will allow both variables to be on the left and both whole numbers to be on the right.

4A + 30 + 4B - 30 = 76 - 4B + 4B - 30

4A + 4B = 76 - 30

4A + 4B = 46

can be factored out of the left side.

$4\left ( A + B \right )= 46$

Divide both sides by .

$4\left ( A + B \right ) \div 4 = 46\div 4$

$A + B = 11 \frac{1}{2}$

Report an Error

Example Question #151 : Algebraic Concepts

Divide 1,000 by 30. The quotient is ; the remainder is . Which is the greater quantity?

(A)

(B)

Possible Answers:

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

(A) and (B) are equal

(B) is greater

(A) is greater

Correct answer:

(A) is greater

Explanation:

First, divide:

$1,000 \div 30 = 33 \textrm{ R } 10$

Q = 33 and R = 10 , so Q > R .

(A) is greater.

Report an Error

Example Question #32 : Equations

A + 9 = B - 7

Evaluate A + B .

Possible Answers:

It is impossible to evaluate A + B from the information given

{2}

Correct answer:

It is impossible to evaluate A + B from the information given

Explanation:

We cannot solve for and on their own. Instead, we need to reorganize the equation to find A + B .

A + 9 = B - 7

A+9-B-9=B-7-B-9

A-B=-7-9

It quickly becomes clear that we cannot solve for A + B with certainty.

If A = 2 and B = 18 , then

A + 9 = B - 7 , since

2 + 9 = 18 - 7 = 11

This makes A + B = 2 + 18= 20

If A = 3 and B = 19 , then

A + 9 = B - 7 , since

3 + 9 = 19 - 7 = 12

This makes A + B = 3+ 19 = 22

Therefore, A + B cannot be evaluated with certainty.

Report an Error

View Tutors

Crystal
Certified Tutor

SUNY at Binghamton, Bachelor of Science, Mechanical Engineering.

View Tutors

Eva
Certified Tutor

Technicka Univerzita Liberec, Bachelor of Education, Education.

View Tutors

Kara
Certified Tutor

University of Central Missouri, Bachelor of Science, Science Teacher Education. University of Central Missouri, Certificate, ...

All ISEE Middle Level Quantitative Resources

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

Popular Subjects

Chemistry Tutors in Chicago, Math Tutors in Denver, French Tutors in San Francisco-Bay Area, Biology Tutors in Miami, Chemistry Tutors in New York City, Math Tutors in Phoenix, SSAT Tutors in Washington DC, ISEE Tutors in Atlanta, Physics Tutors in Atlanta, French Tutors in Los Angeles

Popular Courses & Classes

ISEE Courses & Classes in Seattle, Spanish Courses & Classes in Denver, MCAT Courses & Classes in Seattle, GRE Courses & Classes in Philadelphia, LSAT Courses & Classes in Houston, Spanish Courses & Classes in Chicago, GRE Courses & Classes in Miami, SSAT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Phoenix, GRE Courses & Classes in Atlanta

Popular Test Prep

GRE Test Prep in Washington DC, GRE Test Prep in Chicago, GMAT Test Prep in Seattle, ISEE Test Prep in Houston, SAT Test Prep in Atlanta, MCAT Test Prep in Dallas Fort Worth, LSAT Test Prep in New York City, LSAT Test Prep in Houston, ACT Test Prep in Chicago, GRE Test Prep in Denver

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 : Algebraic Concepts

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

All ISEE Middle Level Quantitative Resources

Example Questions

Example Question #22 : Equations

Example Question #21 : Equations

Example Question #153 : Algebraic Concepts

Example Question #152 : Algebraic Concepts

Example Question #24 : How To Find The Solution To An Equation

Example Question #155 : Algebraic Concepts

Example Question #22 : Equations

Example Question #31 : How To Find The Solution To An Equation

Example Question #151 : Algebraic Concepts

Example Question #32 : Equations

All ISEE Middle Level Quantitative Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: