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 #121 : How To Find The Solution To An Equation

If is negative and |4y - 27| = 80 , then what is ?

Possible Answers:

y = -428

The equation has no negative solution.

$y = - 26 \frac{3}{4}$

$y = -13 \frac{1}{4}$

y = -212

Correct answer:

$y = -13 \frac{1}{4}$

Explanation:

|4y - 27| = 80 , so either

4y - 27 = - 80 or 4y - 27 = 80

We solve both equations separately:

4y - 27 = - 80

4y - 27 + 27 = - 80 + 27

4y = -53

$\frac{4y}{4} = \frac{-53}{4}$

$y = -13 \frac{1}{4}$

4y - 27 = 80

4y - 27 + 27 = 80 + 27

4y = 107

$\frac{4y}{4} = \frac{107}{4}$

$y = 26 \frac{3}{4}$

Since the negative solution is being requested, we choose $y = -13 \frac{1}{4}$ .

Report an Error

Example Question #122 : How To Find The Solution To An Equation

Give the solution set of the equation:

|3t + 12| - 15 = 34

Possible Answers:

$\left \{-12\frac{1}{3},12\frac{1}{3} \right \}$

$\left \{-10\frac{1}{3},12\frac{1}{3} \right \}$

$\left \{-20 \frac{1}{3},12\frac{1}{3} \right \}$

$\left \{-10\frac{1}{3},10\frac{1}{3} \right \}$

$\left \{-20 \frac{1}{3},20\frac{1}{3} \right \}$

Correct answer:

$\left \{-20 \frac{1}{3},12\frac{1}{3} \right \}$

Explanation:

|3t + 12| - 15 = 34

|3t + 12| - 15 + 15 = 34 + 15

|3t + 12| =49

Either

3t + 12 = -49 or 3t + 12 = 49 ,

so we solve the equations separately:

3t + 12 = -49

3t + 12 - 12 = -49 - 12

3t = -61

$\frac{3t}{3} =\frac{ -61}{3}$

$t = -20 \frac{1}{3}$

3t + 12 = 49

3t + 12 - 12 = 49 - 12

3t = 37

$\frac{3t}{3} =\frac{37}{3}$

$t = 12\frac{1}{3}$

The solution set is $\left \{-20 \frac{1}{3},12\frac{1}{3} \right \}$

Report an Error

Example Question #791 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

|x + 5| = |x | - 5

Which of the folllowing is a true statement?

Possible Answers:

The equation has no solution.

The equation has infinitely many solutions.

The equation has three solutions.

The equation has one solution.

The equation has two solutions.

Correct answer:

The equation has infinitely many solutions.

Explanation:

Since the absolute value of a nonnegative number is the number itself, and the absolute value of a negative number is its (positive) opposite, we have to examine up to three cases: $x \ge 0$ , $-5 \le x < 0$ , and x < -5 .

However, let us examine that third case.

This makes and x+5 negative, so the equation can be rewritten:

|x + 5| = |x | - 5

-(x+5) = -x - 5

-x-5= -x - 5

This statement is identically true. Therefore, all values of less than work, and we have already proved that there are infinitely many solutions. We do not need to go further.

Report an Error

Example Question #124 : How To Find The Solution To An Equation

t+ 13 = u + 8

u + 4 = v - 7

v- 11 = w - 6

Which of the following is a true statement?

Possible Answers:

t = w -19

t = w -21

t = w -13

t = w -27

t = w -11

Correct answer:

t = w -11

Explanation:

t+ 13 = u + 8 ,

t+ 13- 13 = u + 8 - 13

t = u - 5

u + 4 = v - 7

u + 4 - 4 = v - 7 - 4

u = v-11

v- 11 = w - 6

v- 11 + 11= w - 6 + 11

v = w+5

Using two substitutions:

t = u - 5

t = v-11 - 5 = v-16

t = v-16 = w+5 -16 = w -11

The correct choice is t = w -11 .

Report an Error

Example Question #121 : Equations

3t = 7u

4u = 7v

9v = 2w

Which of the following is a true statement?

Possible Answers:

27t = 8w

6t = w

189t = 56w

54t = 49 w

147t = 8w

Correct answer:

54t = 49 w

Explanation:

3t = 7u

$\frac{3t}{3} =\frac{ 7u}{3}$

$t =\frac{ 7}{3}u$

Similarly,

4u = 7v

$u = \frac{7}{4}v$

9v = 2w

$v = \frac{2}{9}w$

By substitution:

$t =\frac{ 7}{3}u =\frac{ 7}{3} \cdot \frac{7}{4}v =\frac{ 7}{3} \cdot \frac{7}{4} \cdot \frac{2}{9}w$

$t = \frac{49}{54}w$

$54 \cdot t =54 \cdot \frac{49}{54}w$

54t = 49 w

Report an Error

Example Question #122 : Equations

$8 ^{3x- 8} = 4 ^{y}$

Express in terms of .

Possible Answers:

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

$y = \frac{9}{2}x- 12$

$y = 2x-\frac{16}{3}$

y = 6x- 16

y = 3x-8

Correct answer:

$y = \frac{9}{2}x- 12$

Explanation:

$8 ^{3x- 8} = 4 ^{y}$

$\left (2^{3} \right )^{3x- 8} = (2^{2}) ^{y}$

$2^{3(3x- 8)} = 2^{2y}$

2y = 3(3x-8)

2y = 9x-24

$\frac{2y }{2}= \frac{9x-24}{2}$

$y = \frac{9}{2}x- 12$

Report an Error

Example Question #123 : Equations

$6 ^{x} \cdot 36 ^{y} = 216 ^{t}$

Which of the following is true of ?

Possible Answers:

$t = \frac{2}{3}x+ \frac{1}{3}y$

$t = \frac{1}{3}x+ \frac{2}{3}y$

t = 6x+ 3y

t = 3x+6y

t = x+2y

Correct answer:

$t = \frac{1}{3}x+ \frac{2}{3}y$

Explanation:

$6 ^{x} \cdot 36 ^{y} = 216 ^{t}$

$6 ^{x} \cdot\left ( 6 ^{2} \right )^{y} = \left (6^{3} \right )^{t}$

$6 ^{x} \cdot 6 ^{2 y} = 6^{3 t}$

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

3t = x+2y

$\frac{3t }{3}= \frac{x+2y}{3}$

$t = \frac{1}{3}x+ \frac{2}{3}y$

Report an Error

Example Question #124 : Equations

$\frac{4 ^{x} }{8 ^{y} } = 16^{t}$

Which of the following is true of ?

Possible Answers:

t = 4x-2y

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

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

t = 8x-12y

None of the other responses gives a correct answer.

Correct answer:

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

Explanation:

$\frac{4 ^{x} }{8 ^{y} } = 16^{t}$

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

$\frac{ 2^{2x} }{ 2^{3y} } = 2^{4t}$

$2^{2x -3y} = 2^{4t}$

4t = 2x-3y

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

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

Report an Error

Example Question #125 : Equations

Function 4

Define to be the function graphed in the figure above, and g(x) = 4x+8 .

Evaluate $(g \circ f) (-3)$

Possible Answers:

$(g \circ f) (-3) = -4$

$(g \circ f) (-3) = 4$

$(g \circ f) (-3) = 8$

$(g \circ f) (-3) = 16$

is outside the domain of $g \circ f$

Correct answer:

$(g \circ f) (-3) = 16$

Explanation:

$(g \circ f) (-3) = g [f(-3)]$

From the diagram below, it can be seen that f(-3) = 2 .

Function 4a

$(g \circ f) (-3) = g [f(-3)] = g(2)$

g(x) = 4x+8 , so

g(x) = 4 (2)+8 = 8 + 8 = 16

Therefore,

$(g \circ f) (-3) = 16$ .

Report an Error

Example Question #126 : Equations

Function 4

Define to be the function graphed in the figure above, and g(x) = 4x+8 .

Evaluate $(f \circ g) (-3)$

Possible Answers:

$(f \circ g) (-3) = -4$

$(f \circ g) (-3) = 8$

$(f \circ g) (-3) = 16$

is outside the domain of $f \circ g$

$(f \circ g) (-3) = 4$

Correct answer:

$(f \circ g) (-3) = 4$

Explanation:

$\left (f \circ g \right ) (-3) = f \left [ g (-3)\right ]$

g(x) = 4x+8

g(-3) = 4 (-3)+8 = -12 + 8 = -4

$f \left [ g (-3)\right ] = f(-4)$ .

Examine the diagram below.

Function 4a

As can be seen, f(-4)= 4 . Therefore, $(f \circ g) (-3) = 4$ .

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

ACT Tutors in Dallas Fort Worth, Calculus Tutors in San Diego, Statistics Tutors in Philadelphia, LSAT Tutors in Philadelphia, GRE Tutors in Phoenix, Reading Tutors in Washington DC, SAT Tutors in Denver, French Tutors in Miami, ISEE Tutors in New York City, Reading Tutors in Denver

Popular Courses & Classes

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

Popular Test Prep

MCAT Test Prep in Boston, GRE Test Prep in Washington DC, GMAT Test Prep in Phoenix, SSAT Test Prep in Denver, SSAT Test Prep in Philadelphia, MCAT Test Prep in Seattle, SAT Test Prep in Miami, MCAT Test Prep in Phoenix, MCAT Test Prep in San Diego, GMAT Test Prep in Denver

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 #121 : How To Find The Solution To An Equation

Example Question #122 : How To Find The Solution To An Equation

Example Question #791 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #124 : How To Find The Solution To An Equation

Example Question #121 : Equations

Example Question #122 : Equations

Example Question #123 : Equations

Example Question #124 : Equations

Example Question #125 : Equations

Example Question #126 : 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: