We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Quantitative : Algebraic Concepts

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

Example Question #696 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

$\left \lceil N\right \rceil$ refers to the least integer greater than or equal to .

and are integers. C = A - 0.01; D = B + 0.01

Which is the greater quantity?

(a) $\left \lceil C \right \rceil + \left \lceil D\right \rceil$

(b) $\left \lceil C+ D \right \rceil$

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:

(a) Since is an integer, $\left \lceil C\right \rceil = \left \lceil A - 0.01 \right \rceil = A$ .

Since is an integer, $\left \lceil D\right \rceil = \left \lceil B+ 0.01 \right \rceil = B + 1$ .

$\left \lceil C \right \rceil + \left \lceil D\right \rceil = A + (B + 1) = (A+B)+ 1$

(b) By closure, A + B is an integer, so

$\left \lceil C+ D \right \rceil = \left \lceil (A - 0.01) + (B + 0.01)\right \rceil = \left \lceil A + B\right \rceil = A + B$ .

(a) is the greater quantity.

Report an Error

Example Question #22 : How To Find The Solution To An Equation

$\left \lfloor N\right \rfloor$ refers to the greatest integer less than or equal to .

and are integers.

a = x + 0.5, b= y + 0.5

Which is greater?

(a) $\left \lfloor a\right \rfloor + \left \lfloor b \right \rfloor$

(b) $\left \lfloor a+ b \right \rfloor$

Possible Answers:

(a) is greater.

(a) and (b) are equal.

(b) is greater.

It is impossible to tell from the information given.

Correct answer:

(b) is greater.

Explanation:

(a) Since is an integer, $\left \lfloor a \right \rfloor = \left \lfloor x + 0.5 \right \rfloor = x$ .

Since is an integer, $\left \lfloor b \right \rfloor = \left \lfloor y + 0.5 \right \rfloor = y$ .

$\left \lfloor a\right \rfloor + \left \lfloor b \right \rfloor = x + y$

(b) By closure, x+y is an integer, so

$\left \lfloor a+b \right \rfloor = \left \lfloor x + 0.5 +y+0.5 \right \rfloor = \left \lfloor x +y+1 \right \rfloor = x +y+1$ .

This makes (b) greater.

Report an Error

Example Question #22 : Algebraic Concepts

$x + 7 \sqrt{x} - 30 = 0$

Which is the greater quantity?

(a)

(b)

Possible Answers:

(a) and (b) are equal.

It cannot be determined from the information given.

(b) is greater.

(a) is greater.

Correct answer:

(a) and (b) are equal.

Explanation:

Substitute $t = \sqrt {x}$ and, subsequently, $t^{2} = x$ :

$t^{2} + 7 t- 30 = 0$

Factor as (t + ?) (t + ?) , replacing the two question marks with integers whose product is and whose sum is . These integers are -3,10 .

(t-3)(t +10) = 0

Break this up into two equations, replacing $\sqrt{x}$ for :

t-3= 0

t = 3

$\sqrt{x} = 3$

$\left ( \sqrt{x} \right )^{2} = 3^{2}$

x=9

t +10 = 0

t = -10

$\sqrt{x} = -10$

This has no solution, since $\sqrt {x}$ must be nonnegative. x=9

is the only solution, so (a) and (b) must be equal.

Report an Error

Example Question #21 : Equations

Consider the line through points (3,4) and (7,2) .

Which is the greater quantity?

(a) The -coordinate of the -intercept of this line

(b) The -coordinate of the -intercept of this line

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) is greater.

Explanation:

The slope of this line is

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}= \frac{4-2}{3-7}= \frac{2}{-4} = -\frac{1}{2}$ .

We will use the point-slope form of the line, with this slope and point (3,4) :

$y - 4 = -\frac{1}{2} (x - 3)$

The -coordinate of the -intercept of this line can be found by substituting y = 0 and solving for :

$y - 4 = -\frac{1}{2} (x - 3)$

$0- 4 = -\frac{1}{2} \cdot x + \frac{1}{2} \cdot 3$

$- 4 = -\frac{1}{2} x + \frac{3}{2}$

$- 4- \frac{3}{2} = -\frac{1}{2} x + \frac{3}{2} - \frac{3}{2}$

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

$- \frac{11}{2}\cdot (-2) = -\frac{1}{2} x \cdot (-2)$

x = 11

The -coordinate of the -intercept of this line can be found by substituting x= 0 and solving for :

$y - 4 = -\frac{1}{2} (0 - 3)$

$y - 4 = -\frac{1}{2} (- 3)$

$y - 4 = \frac{3}{2}$

$y - 4 + 4 = \frac{3}{2} + 4$

$y = \frac{11}{2} = 5 \frac{1}{2}$

This makes (a) the greater quantity.

Report an Error

Example Question #701 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

The slope of a line is 2; the line does not pass through the origin.

Which is the greater quantity?

(a) The -coordinate of the -intercept

(b) The -coordinate of the -intercept

Possible Answers:

(a) and (b) are equal.

(a) is greater.

It is impossible to tell from the information given.

(b) is greater.

Correct answer:

It is impossible to tell from the information given.

Explanation:

Let (b,0),(0,a) be the - and -intercepts, respectively. We know that the line does not pass through the origin - so $a,b \neq 0$ .

Then the slope is:

$m = \frac{a-0}{0-b} = \frac{a}{-b} = - \frac{a}{b}$

$- \frac{a}{b} = 2$

a = -2b

Either or can be the greater. For example, if b = 1 , then a = -2 , and if b =- 1 , then a = 2 .

Report an Error

Example Question #702 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

$6^{3x}= 36 ^{x+ 3}$ .

Which is the greater quantity?

(a)

(b)

Possible Answers:

It is impossible to tell from the information given.

(a) is greater.

(b) is greater.

(a) and (b) are equal.

Correct answer:

(a) and (b) are equal.

Explanation:

$36 = 6^{2}$ , so substitute and use the power of a power rule.

$6^{3x}= 36 ^{x+ 3}$

$6^{3x}=\left ( 6^{2} \right )^{x+ 3}$

$6^{3x}= 6^{2(x+ 3)}$

$6^{3x}= 6^{2x + 6}$

3x = 2x + 6

3x -2x= 2x-2x + 6

x = 6

This makes (a) and (b) equal.

Report an Error

Example Question #21 : Algebraic Concepts

Which is the greater quantity?

(a) The slope of the line of the equation y = 5x + 4

(b) The slope of the line of the equation y = 4x + 5

Possible Answers:

It is impossible to tell from the information given.

(a) is greater.

(a) and (b) are equal.

(b) is greater.

Correct answer:

(a) is greater.

Explanation:

Both equations are in slope-intercept form, so compare the coefficients of . The coefficients in (a) and (b) are 5 and 4, respectively, so these are the slopes of the lines. The line in (a) has the greater slope.

Report an Error

Example Question #22 : How To Find The Solution To An Equation

y = 2x + 1

Which is the greater quantity?

(a)

(b)

Possible Answers:

(a) and (b) are equal.

It is impossible to tell from the information given.

(a) is greater.

(b) is greater.

Correct answer:

It is impossible to tell from the information given.

Explanation:

Using two different cases, we show that it is impossible to tell which is greater.

Case 1: x = 1 . Then $y = 2x + 1 = 2 \cdot 1+ 1 = 2 + 1 = 3$ , and y > x .

Case 2: x = -3 . Then $y = 2x + 1 = 2 \cdot (-3)+ 1 = -6+ 1 = -5$ , and y < x .

Report an Error

Example Question #26 : Algebraic Concepts

x + y = 10

2x - y = 14

Which is the greater quantity?

(a)

(b)

Possible Answers:

(a) and (b) are equal.

(a) is greater.

It is impossible to tell from the information given.

(b) is greater.

Correct answer:

(a) is greater.

Explanation:

To solve the system of equations, add the left and right sides of the equation separately:

x + y = 10

$\underline{2x - y = 14}$

$3x\; \; \; \; \; \; = 24$

Divide:

$3x \div 3 = 24\div 3$

x=8

Substitute to get :

x+y = 10

8+y = 10

8-8+y = 10-8

y = 2

is greater.

Report an Error

Example Question #22 : Equations

t + 1 = |u|

Which is the greater quantity?

(a)

(b)

Possible Answers:

(b) is greater

(a) and (b) are equal

(a) is greater

It is impossible to tell from the information given

Correct answer:

It is impossible to tell from the information given

Explanation:

We show that it is possible for either or to be the greater by giving one of each case.

Case 1: u = 1 . Then $t + 1 = \left | 1\right | = 1$ , so t = 0

Case 2: u = -1 . Then $t + 1 = \left | -1\right | = 1$ , so t = 0

In Case 1, t < u ; in Case 2, t > u

Report an Error

View Tutors

Gabby
Certified Tutor

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

View Tutors

Ana
Certified Tutor

Grand Canyon University, Bachelors, Education. Grand Canyon University, Masters, Education.

View Tutors

Crystal
Certified Tutor

SUNY at Binghamton, Bachelor of Science, Mechanical Engineering.

All ISEE Upper Level Quantitative Resources

8 Diagnostic Tests 234 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

LSAT Tutors in Philadelphia, GRE Tutors in Los Angeles, Math Tutors in Seattle, MCAT Tutors in Washington DC, Chemistry Tutors in San Diego, GRE Tutors in San Diego, Statistics Tutors in Seattle, French Tutors in Philadelphia, GRE Tutors in Chicago, Computer Science Tutors in Los Angeles

Popular Courses & Classes

ISEE Courses & Classes in Seattle, LSAT Courses & Classes in Washington DC, SSAT Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Chicago, Spanish Courses & Classes in Philadelphia, ACT Courses & Classes in Washington DC, SAT Courses & Classes in Los Angeles, LSAT Courses & Classes in Boston, GMAT Courses & Classes in Phoenix, SSAT Courses & Classes in Chicago

Popular Test Prep

SSAT Test Prep in San Diego, GMAT Test Prep in Boston, ISEE Test Prep in New York City, ACT Test Prep in Washington DC, LSAT Test Prep in San Diego, MCAT Test Prep in Seattle, GMAT Test Prep in Denver, GRE Test Prep in Washington DC, GMAT Test Prep in New York City, SSAT Test Prep in Atlanta

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 : Algebraic Concepts

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #696 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #22 : How To Find The Solution To An Equation

Example Question #22 : Algebraic Concepts

Example Question #21 : Equations

Example Question #701 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #702 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #21 : Algebraic Concepts

Example Question #22 : How To Find The Solution To An Equation

Example Question #26 : Algebraic Concepts

Example Question #22 : Equations

All ISEE Upper Level Quantitative Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: