We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Quantitative : Equations

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

← Previous 1 2 3 4 5 6 7 8 9 … 16 17 Next →

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

x + 3y = 28

3x + 2y = 35

Which is the greater quantity?

(a)

(b)

Possible Answers:

It is impossible to tell from the information given

(b) is greater

(a) is greater

(a) and (b) are equal

Correct answer:

(a) and (b) are equal

Explanation:

Multiply both sides of the top equation by 3, and subtract both sides of the second equation.

x + 3y = 28

$3\left ( x + 3y \right )= 3 \cdot 28$

$3 x + 9y \right )= 84$

$\underline{3x + 2y = 35}$

7y = 49

$7y \div 7= 49 \div 7$

y = 7

Now substitute to find :

x + 3y = 28

$x + 3 \cdot 7 = 28$

x + 21= 28

x + 21-21= 28-21

x = 7

The two are equal.

Report an Error

Example Question #32 : Equations

4x +y = 20

2x + 3y = 30

Which is the greater quantity?

(a)

(b)

Possible Answers:

(a) and (b) are equal

(b) is greater

(a) is greater

It is impossible to tell from the information given

Correct answer:

(b) is greater

Explanation:

Triple both sides of the top equation, and subtract both sides of the bottom equation:

4x +y = 20

$3 \left ( 4x +y \right ) = 3\left ( 20\right )$

12x +3y = 60

$\underline{2x + 3y = 30}$

10x =30

$10x \div 10 = 30 \div 10$

x = 3

Now substitute to find :

4x +y = 20

$4 \cdot 3 +y = 20$

12 +y = 20

12 +y -12= 20 -12

y = 8

This makes y > x

Report an Error

Example Question #33 : Equations

t = |u - 1|

Which is the greater quantity?

(a)

(b)

Possible Answers:

(a) is greater

(a) and (b) are equal

It is impossible to tell from the information given

(b) is greater

Correct answer:

It is impossible to tell from the information given

Explanation:

We show that it cannot be determined which of and , if either, is greater, by showing one case in which t > u and one case in which t < u .

Case 1: u = 0 . Then

t = |u - 1| = |0 - 1| = | - 1| = 1

and t > u .

Case 2: u = 1 . Then

t = |u - 1| = |1 - 1| = | 0| = 0

and t < u .

Report an Error

Example Question #34 : Equations

t = |u + 1|

Which is the greater quantity?

(a)

(b)

Possible Answers:

(a) and (b) are equal

(b) is greater

(a) is greater

It is impossible to tell from the information given

Correct answer:

(a) is greater

Explanation:

If u < 0 , then, since is nonnegative, t > u .

If $u \geq 0$ , then $u + 1 \geq 1 > 0$ , so the equation becomes t = u + 1 . Therefore, t > u .

Either way, (a) is greater.

Report an Error

Example Question #31 : Algebraic Concepts

x + y = 10

Which is the greater quantity?

(a) 5y + 5x

(b) 50

Possible Answers:

(b) is greater

It is impossible to tell from the information given

(a) is greater

(a) and (b) are equal

Correct answer:

(a) and (b) are equal

Explanation:

x + y = 10

By the commutative property,

y + x = 10

By the multiplication property of equality,

$5 \left ( y + x \right )= 5\cdot 10$

By distribution,

5y + 5x = 5 0

Report an Error

Example Question #36 : Equations

is a positive number. Which is the greater quantity?

(a) $N ^{2}$

(b) $N ^{3} + N$

Possible Answers:

It is impossible to tell from the information given

(b) is greater

(a) and (b) are equal

(a) is greater

Correct answer:

(b) is greater

Explanation:

If N > 1 , then $N ^{3}+ N > N ^{3}= N ^{2} \cdot N > N ^{2} \cdot 1 = N ^{2}$

If N = 1 , then $N ^{3}+ N = 1 ^{3}+1 = 2 > 1 = 1^{2} = N ^{2}$

If 0 < N < 1 , then $N ^{3}+ N > N = N \cdot 1 > N \cdot N = N ^{2}$

Therefore, regardless of the value of , as long as is positive, $N ^{3} + N > N ^{2}$ , and (b) is greater.

Report an Error

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

$100 x + 100 y = \frac{1}{5}$

Which is the greater quantity?

(a) x + y

(b) 0.005

Possible Answers:

(a) and (b) are equal.

(b) is greater.

It is impossible to tell from the information given.

(a) is greater.

Correct answer:

(b) is greater.

Explanation:

$100 x + 100 y = \frac{1}{5}$

From the multiplication property of equality,

$\frac{1}{100} \cdot \left ( 100 x + 100 y \right ) = \frac{1}{100} \cdot \frac{1}{5}$ .

By distribution,

$x + y = \frac{1}{500} = 0.002 < 0.005$ .

Report an Error

Example Question #32 : How To Find The Solution To An Equation

5t = 6u

Which is the greater quantity?

(a) | t |

(b) |u|

Possible Answers:

(a) and (b) are equal.

(b) is greater.

It is impossible to tell from the information given.

(a) is greater.

Correct answer:

(a) is greater.

Explanation:

5t = 6u

$5t \div 5= 6u\div 5$

$t = \frac{6}{5} u$

Take the absolute value of both sides:

$\left |t \right|= \left | \frac{6}{5} u \right |$

$\left |t \right|= \frac{6}{5} \left | u \right | > \left | u \right |$

This makes (a) greater.

Report an Error

Example Question #39 : Equations

$4 A + 4 B = \frac{1}{25}$

10 C +10 D = 0.1

Which is the greater quantity?

(a) A + B

(b) C + D

Possible Answers:

(a) is greater.

It is impossible to tell from the information given.

(a) and (b) are equal.

(b) is greater.

Correct answer:

(a) and (b) are equal.

Explanation:

(a) $4 A + 4 B = \frac{1}{25}$

$\frac{1}{4} \cdot \left ( 4 A + 4 B \right ) = \frac{1}{4} \cdot \frac{1}{25}$

$A + B = \frac{1}{100 }$

(b) 10 C +10 D = 0.1

Rewrite as a fraction:

$10 C +10 D = \frac{1}{10 }$

$\frac{1}{10 } \cdot \left ( 10 C +10 D \right ) = \frac{1}{10 } \cdot \frac{1}{10 }$

$C + D= \frac{1}{100 }$

A + B = C + D

Report an Error

Example Question #34 : How To Find The Solution To An Equation

Define f(x) as follows:

$f(x) = \left\{\begin{matrix} x -3 \textrm{ if }x > 0 \\ x + 3 \textrm{ if }x \leq 0 \end{matrix}\right.$

Which is the greater quantity?

(a) f(5) + f(-5)

(b) f(0)

Possible Answers:

It is impossible to tell from the information given.

(b) is greater.

(a) is greater.

(a) and (b) are equal.

Correct answer:

(b) is greater.

Explanation:

(a) f(5) can be evaluated by using the definition of for positive :

f (x) = x - 3

f (5) =5 - 3 = 2

f(-5) can be evaluated by using the definition of for nonpositive :

f (x) = x + 3

f (-5) =-5 + 3 = -2

Add: f(5) + f(-5) = 2 + (-2) = 0

(b) f(0) can be evaluated by using the definition of for nonpositive :

f (0) = 0 + 3 = 3

f (0) > f(5) + f(-5)

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 … 16 17 Next →

View Tutors

Aaron
Certified Tutor

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

View Tutors

Chase
Certified Tutor

Western Governors University, Bachelor of Science, Mathematics.

View Tutors

Andrew
Certified Tutor

Swarthmore College, Bachelor in Arts, Philosophy.

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 Washington DC, Computer Science Tutors in Denver, Physics Tutors in San Diego, Spanish Tutors in Los Angeles, SSAT Tutors in Phoenix, ISEE Tutors in Atlanta, LSAT Tutors in Dallas Fort Worth, Physics Tutors in Atlanta, Computer Science Tutors in Miami, Reading Tutors in Atlanta

Popular Courses & Classes

MCAT Courses & Classes in Chicago, MCAT Courses & Classes in Houston, Spanish Courses & Classes in New York City, ISEE Courses & Classes in Los Angeles, Spanish Courses & Classes in Chicago, SSAT Courses & Classes in Los Angeles, ACT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Denver, MCAT Courses & Classes in San Diego, LSAT Courses & Classes in Boston

Popular Test Prep

MCAT Test Prep in New York City, SAT Test Prep in San Diego, SAT Test Prep in Chicago, GMAT Test Prep in Houston, ISEE Test Prep in Denver, MCAT Test Prep in Philadelphia, MCAT Test Prep in Los Angeles, GRE Test Prep in Atlanta, MCAT Test Prep in San Diego, ISEE Test Prep in Phoenix

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 : Equations

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

All ISEE Upper Level Quantitative Resources

Example Questions

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

Example Question #32 : Equations

Example Question #33 : Equations

Example Question #34 : Equations

Example Question #31 : Algebraic Concepts

Example Question #36 : Equations

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

Example Question #32 : How To Find The Solution To An Equation

Example Question #39 : Equations

Example Question #34 : How To Find The Solution To An Equation

All ISEE Upper Level Quantitative Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: