Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Quantitative : How to find the solution to an equation

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 #41 : How To Find The Solution To An Equation

$\left \lfloor N \right \rfloor$ is defined as the greatest integer less than or equal to

$\left \lceil N \right \rceil$ is defined as the least integer greater than or equal to

N > 1 ; itself is not an integer.

Which is the greater quantity?

(a) $\left \lceil N \right \rceil \cdot \left \left \lfloor N+1 \right \rfloor$

(b) $\left \lceil N + 1 \right \rceil \cdot \left \left \lfloor N \right \rfloor$

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) is greater.

Explanation:

Let $x = \left \lfloor N \right \rfloor$ .

Then $\left \lfloor N + 1 \right \rfloor = x + 1$ .

Since is a noninteger, $\left \lceil N\right \rceil = x+ 1$ and $\left \lceil N + 1 \right \rceil = x+ 2$ .

(a) $\left \lceil N \right \rceil \cdot \left \left \lfloor N+1 \right \rfloor = \left ( x + 1 \right ) \left ( x + 1 \right ) = x^{2}+2x+1$

(b) $\left \lceil N + 1 \right \rceil \cdot \left \left \lfloor N \right \rfloor = (x+2) x = x ^{2}+ 2x$

(a) is greater than (b).

Report an Error

Example Question #711 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Define f (x) = 4 - 5x and g (x) = 5 - 4x .

can be any real number.

Which is the greater quantity?

(a) $(f \circ g) (x)$

(b) $(g \circ f) (x)$

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:

(a) $(f \circ g) (x) = (f ( g (x) ) = f (5-4x )$

Substitute 5-4x for :

f (x) = 4 - 5x

f (5-4x ) = 4 - 5 (5-4x )

$= 4 - 5 \cdot 5-\left ( -5 \right ) \cdot 4x$

= 4 -25+20x

= 20x-21

(b) $(g \circ f) (x) = g(f(x)) = g (4-5x)$

Substitute 4-5x for :

g (x) = 5 - 4x

g (x) = 5 - 4(4-5x)

$= 5 - 4 \cdot 4- \left ( - 4 \right ) \cdot 5x$

= 5 - 16 +20x

= 20x - 11

-11 > -21 , so regardless of the value of , 20x - 11 > 20x - 21 , and (b) is greater.

Report an Error

Example Question #42 : How To Find The Solution To An Equation

Veronica and Stephanie bought sweaters of the same type, but at different stores. Veronica bought hers for $\$60.00$ at Markham's; Stephanie bought hers for $\$75.00$ at Schuster's. Veronica got a better discount rate than Stephanie, and she has been bragging about it.

Which is the greater quantity?

(a) The price of the sweater at Markham's before discount

(b) The price of the sweater at Schuster's before discount

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:

We show that the question cannot be answered with certainty by taking two sample cases.

Case 1: The sweaters cost $\$100.00$ at both stores.

Veronica saved $\$100.00 - 60.00 = \$40.00$ and got a $40\%$ discount rate. Stephanie saved $\$100.00 - 75.00 = \$25.00$ and got a $25\%$ discount rate.

Case 2: The sweater cost $\$100.00$ at Markham's and $\$90.00$ at Schuster's.

In this case Veronica saved $\$100.00 - 60.00 = \$40.00$ and got a $40\%$ discount rate. Stephanie saved $\$90.00 - 75.00 = \$15.00$ and got a discount rate of $\frac{15}{90} \times 100 = 16 \frac{2}{3} \%$ .

Report an Error

Example Question #43 : How To Find The Solution To An Equation

Define $g (x) = x^{4} + 2x^{2} - 1$ .

Which is the greater quantity?

(a) g(5)

(b) g(-5)

Possible Answers:

(a) is greater.

(a) and (b) are equal.

(b) is greater.

It is impossible to tell from the information given.

Correct answer:

(a) and (b) are equal.

Explanation:

(a) $g (x) = x^{4} + 2x^{2} - 1$

$g (5) = 5^{4} + 2 \cdot 5^{2} - 1$

$= 625 + 2 \cdot 25 - 1$

= 625 + 50 - 1

= 674

(b) $g (x) = x^{4} + 2x^{2} - 1$

$g (-5) = (-5)^{4} + 2 \cdot (-5)^{2} - 1$

$= 625 + 2 \cdot 25 - 1$

= 674

g (5) = g (-5)

Report an Error

Example Question #44 : How To Find The Solution To An Equation

The distance between Vandalia and Clark is 250 miles and is represented by six inches on a map. The distance between Vandalia and Ferrell is 125 miles.

Which is the greater quantity?

(a) The distance between Clark and Ferrell on a map

(b) Two inches

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:

The actual distance between Clark and Ferrell is unknown, but it is at least 250 - 125 = 125 miles. If is the map distance between Clark and Ferrell, then its minimum can be calculated using a proportion:

$\frac{N}{125} = \frac{6}{250}$

$\frac{N}{125} \cdot 125 = \frac{6}{250}\cdot 125$

$N = \frac{750}{250} = 3$

At the very least, the two are three inches apart on the map, so (a) is greater regardless.

Report an Error

Example Question #45 : How To Find The Solution To An Equation

Carl starts working for a bicycle store today. He wants to buy a certain bicycle, but his $20\%$ employee discount doesn't take effect until ninety days from now. He finds out that the price of the bicycle is due to increase by $30\%$ in sixty days.

Which is the greater quantity?

(a) The price Carl would pay for the bicycle today

(b) The price Carl would pay for the bicycle in ninety days, assuming that the bicycle does not change in price again

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:

(a) Let be the current price of the bicycle. Without the discount and the markup, Carl would pay today.

(b) Now we examine what Carl would pay in ninety days. The increase would be $30\%$ of , or, equivalently, 0.3x , and the price of the bicycle is

x + 0.3x = 1.3x .

The employee discount will be $20\%$ of this, or $0.2 \cdot 1.3x = 0.26x$ , and the price Carl would pay is

1.3x - 0.26x = 1.04x .

Carl would pay more by waiting ninety days.

Report an Error

Example Question #46 : How To Find The Solution To An Equation

The distance between Vandalia and Clark is 250 miles and is represented by six inches on a map. The distance between Vandalia and Ferrell is 125 miles.

Which is the greater quantity?

(a) The distance between Clark and Ferrell on a map

(b) Ten inches

Possible Answers:

(b) is greater.

(a) is greater.

It is impossible to tell from the information given.

(a) and (b) are equal.

Correct answer:

(b) is greater.

Explanation:

The actual distance between Clark and Ferrell is unknown, but at most it is 250 + 125 = 375 miles. If is the map distance between Clark and Ferrell, then its maximum can be calculated using a proportion:

$\frac{N}{375} = \frac{6}{250}$

$\frac{N}{375} \cdot 375 = \frac{6}{250}\cdot 375$

$N = \frac{2,250}{250} = 9$

At the very most, the two are nine inches apart on the map, so (b) is greater regardless.

Report an Error

Example Question #47 : How To Find The Solution To An Equation

$f(x) = x^{2} - x + 12$

Which is the greater quantity?

(a) f(4)

(b) f(-3)

Possible Answers:

(b) is greater.

(a) and (b) are equal.

(a) is greater.

It is impossible to tell from the information given.

Correct answer:

(a) and (b) are equal.

Explanation:

Substitute to evaluate each expression:

(a) $f(x) = x^{2} - x + 12$

$f(4) = 4^{2} - 4 + 12 = 16 - 4 + 12 = 24$

(b) $f(x) = x^{2} - x + 12$

$f(-3) = (-3)^{2} - (-3) + 12 = 9 + 3 + 12 = 24$

f(4)= f(-3)

Report an Error

Example Question #48 : How To Find The Solution To An Equation

A set of tires costs $\$240.00$ after a $20\%$ discount.

Which is the greater quantity?

(a) The price of the tires before the discount

(b) $\$288.00$

Possible Answers:

(a) is greater.

It is impossible to tell from the information given.

(b) is greater.

(a) and (b) are equal.

Correct answer:

(a) is greater.

Explanation:

A $20\%$ discount means that the tires sell for $80\%$ of their original price. If that original price is $\$288.00$ , then after the discount, they will sell for $80\%$ of $\$288.00$ . This is

$\$288.00 \times 0.8 = \$230.40$ ,

which is less than $\$240.00$ . Therefore, the original purchase price must be greater than $\$288.00$ .

Report an Error

Example Question #49 : How To Find The Solution To An Equation

Define f (x) = 4x - 3 , g (x) = 3x + 5 .

Which is the greater quantity?

(a) $\left ( f \circ g \right )(0)$

(b) $\left ( g \circ f \right )(0)$

Possible Answers:

(a) is greater.

(b) is greater.

(a) and (b) are equal.

It is impossible to tell from the information given.

Correct answer:

(a) is greater.

Explanation:

(a) $\left ( f \circ g \right )(0) = f(g(0))$

First, evaluate g(0) :

g (x) = 3x + 5 ,

so $g (0) = 3 \cdot 0+ 5 = 5$ .

Now, evaluate f(g(0)) = f (5) :

f (x) = 4x - 3

so $f (5) = 4 \cdot 5 - 3 = 20 -3 = 17$ .

$\left ( f \circ g \right )(0) = 17$

(b) $\left ( g \circ f \right )(0) =g(f(0))$

First, evaluate f (0) :

f (x) = 4x - 3 ,

so $f (0) = 4 \cdot 0- 3 = -3$ .

Now evaluate g(f(0)) = g(-3)

g (x) = 3x + 5 ,

so $g (-3) = 3 \left ( -3 \right ) + 5 = -9 + 5 = -4$ .

$\left ( g \circ f \right )(0) = -4$

$\left ( f \circ g \right )(0) > \left ( g\circ f \right )(0)$

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

Eva
Certified Tutor

Technicka Univerzita Liberec, Bachelor of Education, Education.

View Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

All ISEE Upper Level Quantitative Resources

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

Popular Subjects

Physics Tutors in Philadelphia, Reading Tutors in San Francisco-Bay Area, Reading Tutors in New York City, Reading Tutors in Los Angeles, SAT Tutors in Dallas Fort Worth, GRE Tutors in New York City, ACT Tutors in San Diego, Calculus Tutors in Houston, MCAT Tutors in Los Angeles, LSAT Tutors in Washington DC

Popular Courses & Classes

MCAT Courses & Classes in Phoenix, GMAT Courses & Classes in Phoenix, ACT Courses & Classes in Seattle, SAT Courses & Classes in Denver, SSAT Courses & Classes in Houston, SAT Courses & Classes in Boston, GMAT Courses & Classes in Los Angeles, LSAT Courses & Classes in San Diego, ISEE Courses & Classes in Houston, SSAT Courses & Classes in Denver

Popular Test Prep

GMAT Test Prep in Los Angeles, LSAT Test Prep in Atlanta, MCAT Test Prep in Denver, LSAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Miami, ISEE Test Prep in San Francisco-Bay Area, SAT Test Prep in Washington DC, ISEE Test Prep in Chicago, ACT Test Prep in New York City, ACT 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 : How to find the solution to an equation

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #41 : How To Find The Solution To An Equation

Example Question #711 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #42 : How To Find The Solution To An Equation

Example Question #43 : How To Find The Solution To An Equation

Example Question #44 : How To Find The Solution To An Equation

Example Question #45 : How To Find The Solution To An Equation

Example Question #46 : How To Find The Solution To An Equation

Example Question #47 : How To Find The Solution To An Equation

Example Question #48 : How To Find The Solution To An Equation

Example Question #49 : 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: