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 #53 : How To Find The Solution To An Equation

m + (-45) = 77

n +45 = - 77

Which is the greater quantity?

(a)

(b)

Possible Answers:

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

(b) is the greater quantity

(a) is the greater quantity

(a) and (b) are equal

Correct answer:

(a) is the greater quantity

Explanation:

m + (-45) = 77

m + (-45) - (-45) = 77 - (-45)

m = 77 + 45 = 122

n +45 = - 77

n +45 - 45 = - 77 - 45

n = - 77 +( - 45) = -(77+45) = -122

m > n

Report an Error

Example Question #54 : How To Find The Solution To An Equation

Solve for :

$- \frac{1}{4}r - (-3)=34$

Possible Answers:

r = -148

r = 124

r = 148

r = -124

Correct answer:

r = -124

Explanation:

$- \frac{1}{4}r - (-3)=34$

$- \frac{1}{4}r - (-3) + (-3) =34 + (-3)$

$- \frac{1}{4}r =34 -3$

$- \frac{1}{4}r =31$

$- \frac{1}{4}r \div \left ( - \frac{1}{4} \right ) =31 \div \left ( - \frac{1}{4} \right )$

$r =31 \cdot \left ( - 4 \right )$

r = -124

Report an Error

Example Question #55 : How To Find The Solution To An Equation

Solve the equation:

18 + 8t = 132

Possible Answers:

t = 14.75

t = 14.25

t = 15 .25

t= 15.75

Correct answer:

t = 14.25

Explanation:

To solve to the equation isolate the variable on one side of the equation with all other constants on the other side. To accomplish this perform opposite operations to manipulate the equations.

18 + 8t = 132

First subtract 18 from both sides.

18 + 8t- 18 = 132 - 18

8t = 114

Now divide by 8 on both sides.

$8t \div 8 = 114 \div 8$

t = 14.25

Report an Error

Example Question #56 : How To Find The Solution To An Equation

A + 25 = -B + 75

Which is the greater quantity?

(a) A + B

(b) A - B

Possible Answers:

(a) and (b) are equal

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

(a) is the greater quantity

(b) is the greater quantity

Correct answer:

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

Explanation:

A + 25 = -B + 75

A + 25 + B - 25 = -B + 75 + B - 25

A + B = 50

However, without further information, we cannot determine whether this is greater than A -B . For example,

A = 25 , B = 25 is consistent with the information, and A -B = 25 - 25 = 0 < 50 .

A = 75, B = - 25 is consistent with the information, and 75 -B = 75 -( - 25 )= 100 >50 .

Report an Error

Example Question #57 : How To Find The Solution To An Equation

A + (-45) = -30 + B

A + 45= 30 - B

Which is the greater quantity?

(a) A + B

(b) A - B

Possible Answers:

(b) is the greater quantity

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

(a) is the greater quantity

(a) and (b) are equal

Correct answer:

(b) is the greater quantity

Explanation:

It is not necessary to find and to answer this question.

A + (-45) = -30 + B

A + (-45) - B + 45 = -30 + B - B + 45

A - B = -30 + 45 = + (45-30) = 15

A + 45= 30 - B

A + 45+ B - 45 = 30 - B + B - 45

A + B = 30 - 45 = 30 + (-45) = - (45-30 )= -15

A - B > A + B .

Report an Error

Example Question #58 : Equations

is positive.

A+ B =100

A + C = 200

Which is the greater quantity?

(a)

(b)

Possible Answers:

(a) is the greater quantity

(a) and (b) are equal

(b) is the greater quantity

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

Correct answer:

(b) is the greater quantity

Explanation:

A+ B =100 ,

B = 100 - A

and

$2 B = 2\left (100 - A \right ) = 200 - 2A$

A + C = 200 ,

C= 200 - A

If A > 0 , then, since 1 < 2 ,

A < 2 A

-A > - 2 A

200 -A >200 - 2 A

and

C > 2B .

Report an Error

Example Question #58 : How To Find The Solution To An Equation

m - (-28) = -57

n - (-27) = -58

Which is the greater quantity?

(a)

(b)

Possible Answers:

(b) is the greater quantity

(a) is the greater quantity

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

(a) and (b) are equal

Correct answer:

(a) and (b) are equal

Explanation:

m - (-28) = -57

m - (-28) + (-28) = -57 + (-28)

m = -(57+28) = -85

n - (-27) = -58

n - (-27) + (-27) = -58 + (-27)

n = -(58+27) = -85

m = n

Report an Error

Example Question #61 : Equations

Solve for :

- 0.05 t + (-7) = -44

Possible Answers:

t = 1,020

t = - 740

t = - 1,020

t = 740

Correct answer:

t = 740

Explanation:

Apply the properties of equality to both sides of the equation as follows in order to isolate on the left side, keeping in mind the rules for signed integer arithmetic:

- 0.05 t + (-7) = -44

- 0.05 t + (-7) - (-7) = -44 - (-7)

- 0.05 t = -44+7

- 0.05 t = -(44-7)

- 0.05 t = -37

$- 0.05 t \div (- 0.05) = -37 \div (- 0.05)$

$t = 37 \div 0.05$

Move the decimal points two places right in each of the two numbers, then divide:

$t = 3,700 \div 5$

t = 740

Report an Error

Example Question #62 : Equations

- 0.04 t = 0.005

- 0.05 u= 0.004

Which is the greater quantity?

(a)

(b)

Possible Answers:

(a) and (b) are equal

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

(a) is the greater quantity

(b) is the greater quantity

Correct answer:

(b) is the greater quantity

Explanation:

Isolate on one side of the first equation by dividing both sides by the coefficient of :

- 0.04 t = 0.005

$- 0.04 t \div (- 0.04) = 0.005 \div (- 0.04)$

$t = - \left ( 0.005 \div 0.04 \right )$

Divide by moving the decimal points right two places in order to make the divisor an integer:

$t = - \left ( 0.5 \div4 \right )$

t = -0.125

Similarly:

- 0.05 u= 0.004

$- 0.05 u\div (- 0.05 ) = 0.004 \div (- 0.05 )$

$u=-( 0.004 \div 0.05 )$

$u= -( 0. 4 \div 5 )$

u= - 0.08

0.08 < 0.125 , so

-0.08 >- 0.125 ;

that is, u > t .

Report an Error

Example Question #62 : Equations

is a positive number; is the additive inverse of .

Which is the greater quantity?

(a) 7a + 7b

(b) 7ab

Possible Answers:

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

(a) and (b) are equal

(b) is the greater quantity

(a) is the greater quantity

Correct answer:

(b) is the greater quantity

Explanation:

If is the additive inverse of , then, by definition,

a+ b = 0 .

Therefore, after distribution,

$7a + 7b = 7(a+b) = 7 \cdot 0 = 0$ .

If is a positive number, then its additive inverse, , must be negative. Therefore, , as the product of two numbers of unlike sign, is negative. Multiply this by the positive number 7 and the result is also negative, so

7ab < 0 ,

and

7(a+b) > 7ab .

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

Biology Tutors in Chicago, Math Tutors in Houston, Statistics Tutors in Houston, GMAT Tutors in New York City, Spanish Tutors in Chicago, French Tutors in Seattle, English Tutors in Atlanta, English Tutors in Boston, English Tutors in Philadelphia, SSAT Tutors in Phoenix

Popular Courses & Classes

SSAT Courses & Classes in Phoenix, SAT Courses & Classes in Seattle, ACT Courses & Classes in Miami, MCAT Courses & Classes in Miami, Spanish Courses & Classes in Philadelphia, Spanish Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Miami, Spanish Courses & Classes in New York City, ISEE Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Philadelphia

Popular Test Prep

ISEE Test Prep in Los Angeles, MCAT Test Prep in Miami, SAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in San Diego, LSAT Test Prep in Philadelphia, GRE Test Prep in Dallas Fort Worth, LSAT Test Prep in Phoenix, MCAT Test Prep in Denver, ACT Test Prep in San Diego, ACT Test Prep in Houston

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 #53 : How To Find The Solution To An Equation

Example Question #54 : How To Find The Solution To An Equation

Example Question #55 : How To Find The Solution To An Equation

Example Question #56 : How To Find The Solution To An Equation

Example Question #57 : How To Find The Solution To An Equation

Example Question #58 : Equations

Example Question #58 : How To Find The Solution To An Equation

Example Question #61 : Equations

Example Question #62 : Equations

Example Question #62 : 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: