Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Quantitative : Variables

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 #51 : Operations

Which is the greater quantity?

(b) $(-7) \cdot x+ (-4)$

Possible Answers:

(a) is the greater quantity

(a) and (b) are equal

It cannot be determined which of (a) and (b) is greater

(b) is the greater quantity

Correct answer:

(a) is the greater quantity

Explanation:

Suppose is nonnegative.

Then |x| = x .

Consequently,

which must be positive,

and

$(-7) \cdot x+ (-4) = -7x-4$ ,

which is the opposite of 7 x +4 and consequently must be negative. Therefore, (a) is greater.

Suppose is negative.

Then |x| = -x .

Consequently,

and

$(-7) \cdot x+ (-4) = -7x-4$ .

4 > -4 , so

-7x+4> -7x-4 ,

and (a) is greater.

(a) is the greater quantity either way.

Report an Error

Example Question #52 : Variables

Define f (x) = 3x . The graph of g(x) is a line with slope $\frac{1}{2}$ .

$(g \circ f) (2) = 6$ .

Which is the greater quantity?

(a) f(2)

(b) g(2)

Possible Answers:

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

(a) is the greater quantity

(b) is the greater quantity

(a) and (b) are equal

Correct answer:

(a) is the greater quantity

Explanation:

f (x) = 3x , so $f (2) = 3 \cdot 2 = 6$ .

$(g \circ f) (2) = 6$ , so, by definition, g[ f (2) ] = 6 , or g(6) = 6 .

The graph of g(x) is a line through the point with coordinates (6,6) and with slope $\frac{1}{2}$ . The equation of the line can be determined by setting $g(x) = x = 6 , m = \frac{1}{2}$ in the slope-intercept form:

g(x) = mx+ b

$6 = \frac{1}{2} \cdot 6+ b$

6= 3+ b

b = 3 .

The equation of the line is $g(x) = \frac{1}{2} x+ 3$ , which makes this the definition of g(x) . By setting x= 2 ,

$g(2) = \frac{1}{2} \cdot 2+ 3 = 1 + 3 = 4$ .

Therefore, f(2)> g(2)

Report an Error

Example Question #51 : Operations

x- y = 125 ; and are both positive.

Which is the greater quantity?

(a) | y - x|

(b) | y + x|

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:

(b) is the greater quantity

Explanation:

If x- y = 125 ,

then

y - x = - (x-y) = -125 .

The absolute value of a negative number is its (positive) opposite, so

|y - x |= | -125| = 125

Also, if and are both positive, then y + x is positive; the absolute value of a positive number is the number itself, so | y + x| = y+ x . Since x- y = 125 , it follows that x = 125 + y . Therefore,

| y + x| = y+ x = y + (125+y ) = 125 + 2y

Since is given to be positive,

125 + 2y > 125 .

and

| y + x| > |y - x|

Report an Error

Example Question #1 : Variables And Exponents

Simplify:

$5x^{2} y ^{2}+7 + 6x^{2}y^{2} + 11 xy$

Possible Answers:

$22x^{3}y^{3}+7$

$29x^{3}y^{3}$

$30x^{2}y^{2}+ 11 xy +7$

The expression cannot be simplified further

$11x^{2}y^{2}+ 11 xy +7$

Correct answer:

$11x^{2}y^{2}+ 11 xy +7$

Explanation:

Group and combine like terms $5x^{2} y ^{2},6x^{2}y^{2}$ :

$5x^{2} y ^{2}+7 + 6x^{2}y^{2} + 11 xy$

$= 5x^{2} y ^{2}+ 6x^{2}y^{2}+ 11 xy +7$

$=\left ( 5+ 6 \right )x^{2}y^{2}+ 11 xy +7$

$=11x^{2}y^{2}+ 11 xy +7$

Report an Error

Example Question #2 : Variables And Exponents

x > 0, y < 0

Which is the greater quantity?

(a) $(x + y)^{2}$

(b) $x^{2}+ y^{2}$

Possible Answers:

(a) is greater.

(b) is greater.

It is impossible to tell from the information given.

(a) and (b) are equal.

Correct answer:

(b) is greater.

Explanation:

$(x + y)^{2} = x^{2}+2xy + y^{2}$

Since and have different signs,

xy<0 , and, subsequently,

2xy < 0

Therefore,

$(x + y)^{2} = x^{2}+2xy + y^{2} < x^{2} + y^{2}$

This makes (b) the greater quantity.

Report an Error

Example Question #1 : How To Add Exponential Variables

Assume that and are not both zero. Which is the greater quantity?

(a) $\frac{(x+y)^{2} + (x - y)^{2}}{x^{2}+y^{2}}$

(b) 4xy

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:

Simplify the expression in (a):

$\frac{(x+y)^{2} + (x - y)^{2}}{x^{2}+y^{2}}$

$=\frac{(x^{2}+2xy + y^{2})+ (x^{2}-2xy + y^{2})}{x^{2}+y^{2}}$

$=\frac{ x^{2}+x^{2} +2xy -2xy+ y^{2}+ y^{2}}{x^{2}+y^{2}}$

$=\frac{ 2x^{2} +2 y^{2}}{x^{2}+y^{2}} =\frac{ 2(x^{2}+y^{2})}{x^{2}+y^{2}} = 2$

Therefore, whether (a) or (b) is greater depends on the values of and , neither of which are known.

Report an Error

Example Question #1 : Variables And Exponents

x > 0

Which is the greater quantity?

(a) $x^{2} + 3x$

(b)

Possible Answers:

It is impossible to tell from the information given

(b) is greater

(a) and (b) are equal

(a) is greater

Correct answer:

It is impossible to tell from the information given

Explanation:

We give at least one positive value of for which (a) is greater and at least one positive value of for which (b) is greater.

Case 1: x = 2

(a) $x^{2} + 3x = 2^{2} + 3 \cdot 2 = 4 + 6 = 10$

(b) $4x = 4 \cdot 2 = 8$

Case 2: $x = \frac{1}{2}$

(a) $x^{2} + 3x = \left ( \frac{1}{2} \right ) ^{2} + 3 \cdot \frac{1}{2} = \frac{1}{4} + \frac{3}{2} = \frac{7}{4}= 1 \frac{3}{4}$

(b) $4x = 4 \cdot \frac{1}{2} = 2$

Therefore, either (a) or (b) can be greater.

Report an Error

Example Question #1 : Variables And Exponents

Assume all variables to be nonzero.

Simplify: $\left (12x^{5}y ^{4}z^{3} \right )^{0} + \left (3x^{5}y ^{4}z^{3} \right )^{0}$

Possible Answers:

$15x^{10}y ^{8}z^{6}$

None of the answer choices are correct.

$36x^{10}y ^{8}z^{6}$

$36x^{5}y ^{4}z^{3}$

$15x^{5}y ^{4}z^{3}$

Correct answer:

None of the answer choices are correct.

Explanation:

Any nonzero expression raised to the power of 0 is equal to 1. Therefore,

$\left (12x^{5}y ^{4}z^{3} \right )^{0} + \left (3x^{5}y ^{4}z^{3} \right )^{0} = 1 + 1 = 2$ .

None of the given expressions are correct.

Report an Error

Example Question #2 : Variables And Exponents

Simplify:

$\left (\frac{x^{3}}{2y^{4}} \right ) ^{-3}$

Possible Answers:

$\frac{8x^{6} }{ y^{7}}$

$\frac{8x^{9} }{ y^{12}}$

$\frac{1}{2y}$

$\frac{8 y^{7} }{x^{6} }$

$\frac{8 y^{12} }{x^{9} }$

Correct answer:

$\frac{8 y^{12} }{x^{9} }$

Explanation:

$\left (\frac{x^{3}}{2y^{4}} \right ) ^{-3} = \left (\frac{2y^{4}}{x^{3}} \right ) ^{3} = \frac{2^{3} \left (y^{4}\right ) ^{3} }{\left (x^{3} \right )^{3}}= \frac{8 y^{4 \cdot 3} }{x^{3\cdot 3} }= \frac{8 y^{12} }{x^{9} }$

Report an Error

Example Question #2 : How To Find The Exponent Of Variables

y>1

Which is greater?

(a) $y ^{-2}$

(b) $y^{2}$

Possible Answers:

(a) is greater

(b) is greater

It is impossible to tell from the information given

(a) and (b) are equal

Correct answer:

(b) is greater

Explanation:

If y > 1 , then $y ^{2}> 1^{2} = 1$ and $y ^{-2}= \frac{1}{y ^{2}} < \frac{1}{1} = 1$

$y ^{2}> 1> y ^{-2}$ , so by transitivity, $y ^{2}> y ^{-2}$ , and (b) is greater

Report an Error

View Tutors

Kaitlyn
Certified Tutor

Fairfield University, Bachelor of Science, Biology, General. NUI Galway Ireland, Master of Science, Neuroscience.

View Tutors

Magda
Certified Tutor

Heritage College, Bachelor of Science, Education.

View Tutors

Mary
Certified Tutor

Oklahoma Wesleyan University, Bachelor of Science, Business Teacher Education. University of Phoenix-Oklahoma City Campus, Ma...

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 Los Angeles, SAT Tutors in Phoenix, Algebra Tutors in San Diego, Math Tutors in Dallas Fort Worth, Math Tutors in Miami, English Tutors in Chicago, Biology Tutors in Miami, Calculus Tutors in Washington DC, GMAT Tutors in Miami, Math Tutors in Los Angeles

Popular Courses & Classes

LSAT Courses & Classes in Atlanta, ACT Courses & Classes in Washington DC, GRE Courses & Classes in Atlanta, GRE Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Denver, MCAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Los Angeles, SAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in San Diego

Popular Test Prep

GRE Test Prep in Phoenix, LSAT Test Prep in Miami, GMAT Test Prep in San Diego, GRE Test Prep in Washington DC, ISEE Test Prep in San Diego, GRE Test Prep in Seattle, ACT Test Prep in Washington DC, LSAT Test Prep in Houston, SSAT Test Prep in Atlanta, SSAT Test Prep in Chicago

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 : Variables

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #51 : Operations

Example Question #52 : Variables

Example Question #51 : Operations

Example Question #1 : Variables And Exponents

Example Question #2 : Variables And Exponents

Example Question #1 : How To Add Exponential Variables

Example Question #1 : Variables And Exponents

Example Question #1 : Variables And Exponents

Example Question #2 : Variables And Exponents

Example Question #2 : How To Find The Exponent Of Variables

All ISEE Upper Level Quantitative Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: