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 #1 : Circles

Chords 1

Refer to the above figure. Which is the greater quantity?

(a) $\frac{a}{d}$

(b) $\frac{c}{b}$

Possible Answers:

(b) is the greater quantity

(a) is the greater quantity

(a) and (b) are equal

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

Correct answer:

(a) and (b) are equal

Explanation:

If two chords intersect inside a circle, both chords are cut in a way such that the products of the lengths of the two chords formed in each are the same - in other words,

ab = cd

Divide both sides of this equation by , then cancelling:

$\frac{ab }{bd}= \frac{cd}{bd}$

$\frac{a }{d}= \frac{c}{b}$

The two quantities are equal.

Report an Error

Example Question #141 : Plane Geometry

The area of Circle B is four times that of Circle A. The area of Circle C is four times that of Circle B. Which is the greater quantity?

(a) Twice the radius of Circle B

(b) The sum of the radius of Circle A and the radius of Circle C

Possible Answers:

It cannot be determined from the information given.

(a) and (b) are equal.

(a) is greater.

(b) is greater.

Correct answer:

(b) is greater.

Explanation:

Let be the radius of Circle A. Then its area is $\pi r^{2}$ .

The area of Circle B is $4\pi r^{2} =2^{2}\pi r^{2} = \pi (2r)^{2}$ , so the radius of Circle B is twice that of Circle A; by a similar argument, the radius of Circle C is twice that of Circle B, or 2 (2r ) = 4r .

(a) Twice the radius of circle B is 2 (2r) = 4r .

(b) The sum of the radii of Circles A and B is r + 4r = 5r .

This makes (b) greater.

Report an Error

Example Question #2 : Circles

The time is now 1:45 PM. Since noon, the tip of the minute hand of a large clock has moved $\frac{14\pi}{3}$ feet. How long is the minute hand of the clock?

Possible Answers:

$2 \textrm{ ft }6 \textrm{ in }$

$1 \textrm{ ft }3 \textrm{ in }$

$1 \textrm{ ft }4 \textrm{ in }$

$2 \textrm{ ft }8 \textrm{ in }$

$2 \textrm{ ft }$

Correct answer:

$1 \textrm{ ft }4 \textrm{ in }$

Explanation:

Every hour, the tip of the minute hand travels the circumference of a circle. Between noon and 1:45 PM, one and three-fourths hours pass, so the tip travels $1 \frac{3}{4}$ or $\frac{7}{4}$ times this circumference. The length of the minute hand is the radius of this circle , and the circumference of the circle is $C = 2 \pi r$ , so the distance the tip travels is $\frac{7}{4}$ this, or

$\frac{7}{4} C = \frac{7}{4} \cdot 2 \pi r = \frac{7 \pi r }{2}$

Set this equal to $\frac{14\pi}{3}$ feet:

$\frac{7 \pi r }{2} = \frac{14\pi}{3}$

$\frac{7 \pi r }{2} \times \frac{2}{7 \pi}= \frac{14\pi}{3}\times \frac{2}{7 \pi}$

$r= \frac{2}{3}\times \frac{2}{1} = \frac{4}{3} = 1 \frac{1}{3}$ feet.

This is equivalent to 1 foot 4 inches.

Report an Error

Example Question #143 : Plane Geometry

The tip of the minute hand of a giant clock has traveled $40 \pi$ feet since noon. It is now 2:30 PM. Which is the greater quantity?

(A) The length of the minute hand

(B) Three yards

Possible Answers:

(A) is greater

(A) and (B) are equal

(B) is greater

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

Correct answer:

(B) is greater

Explanation:

Betwen noon and 2:30 PM, the minute hand has made two and one-half revolutions; that is, the tip of minute hand has traveled the circumference of its circle two and one-half times. Therefore,

$C \cdot 2 \frac{1}{2} = 40 \pi$

$C = 40 \pi \div 2 \frac{1}{2} = \frac{40 \pi}{1} \div \frac{5}{2} = \frac{40 \pi}{1} \cdot \frac{2}{5}= \frac{80 \pi}{5} = 16\pi$ feet.

The radius of this circle is the length of the minute hand. We can use the circumference formula to find this:

$2 \pi r = C$

$2 \pi r = 16 \pi$

$r = 16 \pi \div 2 \pi = 8$

The minute hand is eight feet long, which is less than three yards (nine feet), so (B0 is greater.

Report an Error

Example Question #141 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Compare the two quantities:

Quantity A: The radius of a circle with area of $64\pi$

Quantity B: The radius of a circle with circumference of $50\pi$

Possible Answers:

The relationship cannot be determined from the information given.

The quantity in Column A is greater.

The two quantities are equal.

The quantity in Column B is greater.

Correct answer:

The quantity in Column B is greater.

Explanation:

Recall for this question that the formulae for the area and circumference of a circle are, respectively:

$A=\pi * r^2$

$C=2*\pi*r$

For our two quantities, we have:

Quantity A

$64\pi = \pi * r^2$

Therefore, r^2 = 64

Taking the square root of both sides, we get: r = 8

Quantity B

$50\pi = 2 * \pi * r$

Therefore, r = 25

Therefore, quantity B is greater.

Report an Error

Example Question #1 : How To Find The Length Of A Radius

Compare the two quantities:

Quantity A: The radius of a circle with area of $144\pi$

Quantity B: The radius of a circle with circumference of $24\pi$

Possible Answers:

The relationship cannot be determined from the information given.

The quantity in Column A is greater.

The quantity in Column B is greater.

The two quantities are equal.

Correct answer:

The two quantities are equal.

Explanation:

Recall for this question that the formulae for the area and circumference of a circle are, respectively:

$A=\pi * r^2$

$C=2*\pi*r$

For our two quantities, we have:

Quantity A

$144\pi = \pi * r^2$

Therefore, r^2 = 144

Taking the square root of both sides, we get: r = 12

Quantity B

$24\pi = 2 * \pi * r$

Therefore, r = 12

Therefore, the two quantities are equal.

Report an Error

Example Question #11 : Circles

If the diameter of a circle is equal to $5x^{2}+4x-2$ , then what is the value of the radius?

Possible Answers:

7x-1

$2.5x^{2}+2x+1$

$2.5x^{2}+2x-1$

$2(x^{2}+x)-1$

Correct answer:

$2.5x^{2}+2x-1$

Explanation:

Given that the radius is equal to half the diameter, the value of the radius would be equal to $5x^{2}+4x-2$ divided by 2. This gives us:

$\frac{5x^{2}+4x-2}{2}$

$2.5x^{2}+2x-1$

Report an Error

Example Question #3 : Radius

The area of a circle is $81x^{2}$ . Give its radius in terms of .

(Assume is positive.)

Possible Answers:

$\frac{81x^{2}}{\pi}$

$9 \pi x$

$\frac{9x}{\pi}$

$\frac{9x}{\sqrt{\pi}}$

$\frac{81x^{2}}{2\pi}$

Correct answer:

$\frac{9x}{\sqrt{\pi}}$

Explanation:

The relation between the area of a circle and its radius is given by the formula

$A = \pi r^{2}$

Since

$A= 81x^{2}$ :

$81x^{2} = \pi r^{2}$

We solve for :

$\pi r^{2} = 81x^{2}$

$\frac{\pi r^{2} }{\pi}= \frac{81x^{2}}{\pi}$

$r^{2} = \frac{81x^{2}}{\pi}$

$\sqrt{r^{2} }= \sqrt{\frac{81x^{2}}{\pi}}$

Since is positive, as is :

$r =\frac{ \sqrt{81} \cdot \sqrt{x^{2}}}{\sqrt{\pi}} = \frac{9x}{\sqrt{\pi}}$

Report an Error

Example Question #1 : How To Find The Length Of A Radius

The areas of five circles form an arithmetic sequence. The smallest circle has radius 4; the second smallest circle has radius 8. Give the radius of the largest circle.

Possible Answers:

$4 \sqrt{13}$

$8\sqrt{13}$

Correct answer:

$4 \sqrt{13}$

Explanation:

The area of a circle with radius is $A = \pi r^{2}$ . Therefore, the areas of the circles with radii 4 and 8, respectively, are

$A_{1} = \pi \cdot 4^{2} = 16 \pi$

and

$A_{2} = \pi \cdot 8^{2} = 64\pi$

The areas form an arithmetic sequence, the common difference of which is

$64 \pi - 16 \pi = 48 \pi$ .

The circles will have areas:

$16 \pi, 64 \pi, 112 \pi, 160 \pi , 208 \pi$

Since the area of the largest circle is $208 \pi$ , we can find the radius as follows:

The radius can be calculated now:

$\pi r^{2} = 208 \pi$

$r^{2} = 208$

$r = \sqrt{208} = \sqrt{16} \cdot \sqrt{13} = 4 \sqrt{13}$

Report an Error

Example Question #12 : Circles

Circle B has a radius $\frac{2}{3}$ as long as that of Circle A.

Which is the greater quantity?

(a) The area of Circle A

(b) Twice the area of Circle B

Possible Answers:

(b) is greater.

(a) and (b) are equal.

It is impossible to tell from the information given.

(a) is greater.

Correct answer:

(a) is greater.

Explanation:

If we call the radius of Circle A , then the radius of Circle B is $\frac{2}{3} r$ .

The areas of the circles are:

(a) $\pi r^{2}$

(b) $\pi \left( \frac{2}{3} r \right ) ^{2} = \frac{4}{9} \pi r^{2}$

Twice the area of Circle B is

$2 \cdot \pi \left( \frac{2}{3} r \right ) ^{2} =2 \cdot \frac{4}{9} \pi r^{2} = \frac{8}{9} \pi r^{2} < \pi r^{2}$ ,

making (a) the greater number.

Report an Error

View Tutors

Sundeep
Certified Tutor

Indian Institute of Technology, Engineering in Computer Science, Electrical Engineering. New York University, Masters in Busi...

View Tutors

Gregory
Certified Tutor

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

View Tutors

Eva
Certified Tutor

Technicka Univerzita Liberec, Bachelor of Education, Education.

All ISEE Upper Level Quantitative Resources

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

Popular Subjects

Math Tutors in Washington DC, Algebra Tutors in San Diego, Biology Tutors in Miami, Calculus Tutors in Atlanta, Algebra Tutors in Houston, LSAT Tutors in Boston, Spanish Tutors in Phoenix, English Tutors in New York City, Algebra Tutors in Philadelphia, Math Tutors in Denver

Popular Courses & Classes

ISEE Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Houston, ACT Courses & Classes in Seattle, ISEE Courses & Classes in Seattle, Spanish Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Washington DC, GMAT Courses & Classes in Boston, Spanish Courses & Classes in Boston, GRE Courses & Classes in Phoenix, Spanish Courses & Classes in Atlanta

Popular Test Prep

MCAT Test Prep in Los Angeles, SAT Test Prep in Seattle, GRE Test Prep in Denver, ACT Test Prep in Washington DC, GRE Test Prep in Houston, LSAT Test Prep in Dallas Fort Worth, LSAT Test Prep in San Diego, ACT Test Prep in Seattle, ISEE Test Prep in San Diego, SSAT Test Prep in Houston

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 #1 : Circles

Example Question #141 : Plane Geometry

Example Question #2 : Circles

Example Question #143 : Plane Geometry

Example Question #141 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #1 : How To Find The Length Of A Radius

Example Question #11 : Circles

Example Question #3 : Radius

Example Question #1 : How To Find The Length Of A Radius

Example Question #12 : Circles

All ISEE Upper Level Quantitative Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: