Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Quantitative : ISEE Upper Level (grades 9-12) Quantitative Reasoning

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 #761 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Give the -coordinate of the point on the graph of the equation $3\sqrt{x} +2 \sqrt{y} = 23$ that has -coordinate 64.

Possible Answers:

No such point exists.

$-\frac{1}{4}$

$\frac{1}{4}$

Correct answer:

No such point exists.

Explanation:

The point $\left ( 64, y\right )$ is on the graph of the equation $3\sqrt{x} +2 \sqrt{y} = 23$ . Finding the -coordinate of this point is the same as evaluating for x=64 . Substitute, and we get:

$3\sqrt{x} +2 \sqrt{y} = 23$

$3\sqrt{64} +2 \sqrt{y} = 23$

$3 \cdot8 +2 \sqrt{y} = 23$

$24 +2 \sqrt{y} = 23$

$24 +2 \sqrt{y} -24 = 23 -24$

$2 \sqrt{y} = -1$

$2 \sqrt{y} \div 2 = -1 \div 2$

$\sqrt{y} = - \frac{1}{2}$

Since the square root of a number must be positive, there is no solution. Therefore, there is no point on this graph with -coordinate 64.

Report an Error

Example Question #84 : Algebraic Concepts

Give the -coordinate of the point on the graph of the equation $\frac{4}{x} + \frac{3}{y} = 12$ that has -coordinate $\frac{1}{3}$ .

Possible Answers:

$-\frac{1}{4}$

No such point exists.

$\frac{1}{4}$

Correct answer:

No such point exists.

Explanation:

The point $\left ( \frac{1}{3}, y\right )$ is on the graph of the equation $\frac{4}{x} + \frac{3}{y} = 12$ . Finding the -coordinate of this point is the same as evaluating for $x= \frac{1}{3}$ . Substitute, and we get:

$\frac{4}{x} + \frac{3}{y} = 12$

$\frac{4}{\frac{1}{3}} + \frac{3}{y} = 12$

$12+ \frac{3}{y} = 12$

$12+ \frac{3}{y}- 12 = 12 - 12$

$\frac{3}{y} = 0$

However, there is no number that can be divided into 3 to yield a quotient of 0, so there is no solution. Therefore, there is no point on this graph with -coordinate $\frac{1}{3}$ .

Report an Error

Example Question #84 : Equations

$y = \frac{1}{3} x + \frac{4}{3}$

2x - 3y = 4

What is ?

Possible Answers:

$\frac{8}{3}$

$\frac{4}{3}$

Correct answer:

Explanation:

Substitute $\frac{1}{3} x + \frac{4}{3}$ for in the second equation:

2x - 3y = 4

$2x - 3 \left ( \frac{1}{3} x + \frac{4}{3} \right ) = 4$

2x - x -4 = 4

x -4 = 4

x -4+ 4 = 4 + 4

x = 8

Report an Error

Example Question #85 : Algebraic Concepts

$y = \frac{1}{3} x + \frac{4}{3}$

2x - 3y = 4

What is ?

Possible Answers:

$\frac{4}{3}$

$\frac{8}{3}$

Correct answer:

Explanation:

Solve for in the top equation:

$y = \frac{1}{3} x + \frac{4}{3}$

$3 \cdot y = 3 \cdot \left ( \frac{1}{3} x + \frac{4}{3} \right )$

3 y = x +4

3 y-4 = x +4 -4

x = 3 y-4

Substitute 3 y-4 for in the second equation:

2x - 3y = 4

$2 \left ( 3 y-4 \right )- 3y = 4$

6 y-8- 3y = 4

3 y-8 = 4

3 y-8 + 8 = 4 + 8

3 y = 12

$3 y \div 3 = 12 \div 3$

y = 4

Report an Error

Example Question #81 : Algebraic Concepts

If $\frac{x}{4}+2y=16$ , then what is an expression for x in terms of y?

Possible Answers:

x=64-8y

x=24-2y

x=8y-64

x=4y

x=16-2y

Correct answer:

x=64-8y

Explanation:

To solve this problem, isolate for x. First, move the y term over to the left side. This gives you $\frac{x}{4}=16-2y$ . Then, multiply both sides by 4. This gives you x=(16-2y)4 . Then, distribute the four to the terms inside the parantheses. This gives you a final answer of x=64-8y .

Report an Error

Example Question #86 : Equations

y = 0.5x + 1.4

1.5x-0.5y = 9.8

Evaluate .

Possible Answers:

x = 8.4

x = 7.28

x = 5.6

x = 5.2

The answer cannot be determined from the information given.

Correct answer:

x = 8.4

Explanation:

Substitute 0.5x + 1.4 for in the second equation as follows:

1.5x-0.5y = 9.8

$1.5x-0.5 \left ( 0.5x + 1.4 \right ) = 9.8$

1.5x-0.25 x - 0.7 = 9.8

1.25 x - 0.7 = 9.8

1.25 x - 0.7 + 0.7= 9.8 + 0.7

1.25 x =10.5

$1.25 x\div 1.25 =10.5 \div 1.25$

x = 8.4

Report an Error

Example Question #91 : How To Find The Solution To An Equation

A hat costs $70.80 after a 20% discount. How much did the hat cost before the discount?

Possible Answers:

$\$56.64$

$\$88.50$

It is impossible to tell from the information given.

$\$84.96$

$\$90.80$

Correct answer:

$\$88.50$

Explanation:

Since $70.80 is the price after a 20% discount off the original price, it is 80% of that original price. The problem is equivalent to asking:

$70.80 is 80% of what amount?

Let be the price before discount.

0.80 x = 70.80

$0.80 x \div 0.80 = 70.80 \div 0.80$

$x = \$88.50$

Report an Error

Example Question #91 : How To Find The Solution To An Equation

x + y = 14

2x + 3y = 36

Which is the greater quantity?

(A)

(B)

Possible Answers:

(B) is greater

(A) is greater

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

(A) and (B) are equal

Correct answer:

(B) is greater

Explanation:

x + y = 14 , so x = 14-y .

Substitute for in the other equation:

2x + 3y = 36

2 (14-y)+ 3y = 36

28-2y + 3y = 36

$28 +\left ( 3-2 \right ) y = 36$

28 + y = 36

28 + y -28 = 36-28

y = 8

x = 14-y = 14-8 = 6

y > x , so (B) is greater.

Report an Error

Example Question #93 : How To Find The Solution To An Equation

A line includes the points (3,6) and (4,9) . Which is the greater quantity?

(A) The -coordinate of the -intercept.

(B) The -coordinate of the -intercept.

Possible Answers:

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

(A) and (B) are equal

(A) is greater

(B) is greater

Correct answer:

(A) is greater

Explanation:

We can figure out the equation of the line as follows:

Set $x_{1} = 3, y_{1} = 6,x_{2} =4, y_{2} = 9$ . Substitute in the slope formula.

The slope is

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{9-6}{4-3} = \frac{3}{1} = 3$

In the slope-intercept formula, we set

x = 3, y = 6,m = 3 and solve for :

y = mx + b

$6 = 3 \cdot 3 + b$

6 = 9+ b

6 - 9 = 9+ b - 9

-3= b

The equation is y = 3x -3

The -intercept is (0, -3) . To find the -intercept, we substitute 0 for :

0 = 3x -3

0+ 3 = 3x -3 + 3

3 = 3x

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

x= 1

The -intercept is (1,0) .

This makes (A), the -coordinate of the -intercept, greater.

Report an Error

Example Question #91 : How To Find The Solution To An Equation

Define $f (x) = \sqrt{4-x}$ and $g(x) = \sqrt{x+3}$ .

What is the domain of the function f + g ?

Possible Answers:

$\left [ - 4, 3\right ]$

$(- \infty, -3]$

$\left [ -3, 4\right ]$

$(- \infty,\infty )$

$[4,\infty )$

Correct answer:

$\left [ -3, 4\right ]$

Explanation:

$f (x) = \sqrt{4-x}$ has as its domain the set of values of for which its radicand is nonnegative; that is,

$4 - x \geq 0$

$4 - x + x \geq 0 + x$

$4 \geq x$ or $(- \infty, 4]$

Similarly, $g = \sqrt{x+3}$ has as its domain the set of values of for which its radicand is nonnegative; that is,

$x+3 \geq 0$

$x+3 -3 \geq 0-3$

$x \geq -3$ or $[-3,\infty )$

The domain of the sum of two functions is the intersection of the domains of the two individual functions. This intersection is

$(- \infty, 4] \cap [-3,\infty ) = \left [ -3, 4\right ]$

Report an Error

View Tutors

Eva
Certified Tutor

Technicka Univerzita Liberec, Bachelor of Education, Education.

View Tutors

Crystal
Certified Tutor

SUNY at Binghamton, Bachelor of Science, Mechanical Engineering.

View Tutors

Pushpendra
Certified Tutor

university of allahabad, Bachelor of Science, Mathematics.

All ISEE Upper Level Quantitative Resources

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

Popular Subjects

GRE Tutors in Phoenix, Chemistry Tutors in Los Angeles, English Tutors in Washington DC, Physics Tutors in Philadelphia, SAT Tutors in San Diego, English Tutors in New York City, Calculus Tutors in Atlanta, LSAT Tutors in Seattle, English Tutors in Dallas Fort Worth, Physics Tutors in Miami

Popular Courses & Classes

ACT Courses & Classes in Chicago, LSAT Courses & Classes in Los Angeles, MCAT Courses & Classes in Houston, SAT Courses & Classes in New York City, SSAT Courses & Classes in New York City, MCAT Courses & Classes in Miami, MCAT Courses & Classes in Los Angeles, ACT Courses & Classes in Washington DC, SAT Courses & Classes in Chicago, SSAT Courses & Classes in Atlanta

Popular Test Prep

LSAT Test Prep in Miami, SAT Test Prep in Houston, ACT Test Prep in Chicago, ACT Test Prep in Denver, ACT Test Prep in Washington DC, ACT Test Prep in Boston, MCAT Test Prep in Chicago, MCAT Test Prep in Houston, GRE Test Prep in Atlanta, LSAT Test Prep in Washington DC

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 : ISEE Upper Level (grades 9-12) Quantitative Reasoning

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #761 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #84 : Algebraic Concepts

Example Question #84 : Equations

Example Question #85 : Algebraic Concepts

Example Question #81 : Algebraic Concepts

Example Question #86 : Equations

Example Question #91 : How To Find The Solution To An Equation

Example Question #91 : How To Find The Solution To An Equation

Example Question #93 : How To Find The Solution To An Equation

Example Question #91 : 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: