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

What is the slope of a line that passes through points (4,12) and (8, 20) ?

Possible Answers:

0.5

2.5

Correct answer:

Explanation:

The equation for solving for the slope of a line is $m=\frac{y2-y1}{x2-x1}$ .

Thus, if (x1,y1)=(4,12) and (x2,y2)=(8,20) , then:

$m=\frac{20-12}{8-4}=\frac{8}{4}=2$

Report an Error

Example Question #92 : Plane Geometry

Tangents 1

Figure NOT drawn to scale

In the above figure, $\overline{TN}$ and $\overline{TO}$ are tangent segments. The ratio of the length of $\overarc{NPO}$ to that of $\overarc{N O}$ is 5 to 3. Which is the greater quantity?

(a) $m \angle NTO$

(b) $30 ^{\circ }$

Possible Answers:

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

(a) and (b) are equal

(a) is the greater quantity

(b) is the greater quantity

Correct answer:

(a) is the greater quantity

Explanation:

For the sake of simplicity, let us assume that the lengths of $\overarc{NPO}$ and $\overarc{N O}$ are 5 and 3; this reasoning depends only on their ratio and not their actual length. The circumference of the circle is the sum of the lengths, which is 8, so $\overarc{NPO}$ and $\overarc{N O}$ comprise $\frac{5}{8}$ and $\frac{3}{8}$ of the circle, respectively. Therefore,

$m \overarc{NPO} = \frac{5}{8} \cdot 360 ^{\circ } = 225 ^{\circ }$ ; and

$m \overarc{N O} = \frac{3}{8} \cdot 360 ^{\circ } = 135 ^{\circ }$ .

If two tangents are drawn to a circle, the measure of the angle they form is half the difference of the measures of the arcs they intercept, so

$m \angle NTO = \frac{1}{2}(m \overarc{NPO} - m \overarc{N O} ) = \frac{1}{2}(225 ^{\circ }- 135^{\circ } ) = \frac{1}{2}(90^{\circ } ) = 45^{\circ }$

This is greater than $30 ^{\circ }$ .

Report an Error

Example Question #92 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Which is the greater quantity?

(a) The length of the line segment connecting (0,0) and (a,b)

(b) The length of the line segment connecting (a,0) and (0,b)

Possible Answers:

(a) and (b) are equal.

(a) is greater.

It is impossible to tell from the information given.

(b) is greater.

Correct answer:

(a) and (b) are equal.

Explanation:

(a) The length of the line segment connecting (0,0) and (a,b) is

$\sqrt{(a -0)^{2}+(b -0)^{2} } = \sqrt{a^{2}+b^{2} }$ .

(b) The length of the line segment connecting (a,0) and (0,b) is

$\sqrt{(a -0)^{2}+(0-b)^{2} } = \sqrt{a^{2}+\left ( - b \right ) ^{2} }= \sqrt{a^{2}+b^{2} }$ .

The segments have equal length.

Report an Error

Example Question #93 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Which is the greater quantity?

(a) The area of a regular hexagon with sidelength 1

(b) The area of an equilateral triangle with sidelength 2

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:

A regular hexagon with sidelength s = 1 can be seen as a composite of six equilateral triangles, each with sidelength s = 1 . Since area is in direct proportion to the square of the sidelength, the area of the equilateral triangle with sidelength s = 2 is equal to that of four of those triangles. This makes the hexagon greater in area, and it makes (a) the greater quantity.

Report an Error

Example Question #94 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Which is the greater quantity?

(a) The perimeter of a regular pentagon with sidelength 1 foot

(b) The perimeter of a regular hexagon with sidelength 10 inches

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:

The sides of a regular polygon are congruent, so in each case, multiply the sidelength by the number of sides to get the perimeter.

(a) Since one foot equals twelve inches, $5 \times 12 = 60$ inches.

(b) Multiply: $6 \times 10 = 60$ inches

The two polygons have the same perimeter.

Report an Error

Example Question #95 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

A hexagon has six angles with measures $(x-5)^{\circ}, x^{\circ}, (x+5)^{\circ}, (y-10)^{\circ}, y^{\circ}, (y + 10)^{\circ}.$

Which quantity is greater?

(a) x + y

(b) 240

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:

The angles of a hexagon measure a total of 180 (6-2) = 720 . From the information, we know that:

(x - 5) + x + (x+5) + (y-10) + y + (y+10) = 720

x+ x + x + y+ y + y - 5+5 -10 +10= 720

3x + 3y = 720

3 (x + y) = 720

$3 (x + y) \div 3 = 720 \div 3$

x + y = 240

The quantities are equal.

Report an Error

Example Question #96 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

A hexagon has six angles with measures $(x-10)^{\circ}, x^{\circ}, (x+5)^{\circ}, (y-10)^{\circ}, y^{\circ}, (y + 20)^{\circ}.$

Which quantity is greater?

(a) x + y

(b) 240

Possible Answers:

It is impossible to tell from the information given.

(a) is greater.

(a) and (b) are equal.

(b) is greater.

Correct answer:

(b) is greater.

Explanation:

The angles of a hexagon measure a total of 180 (6-2) = 720 . From the information, we know that:

(x-10)+x+(x+5)+ (y-10)+ y+ (y + 20)= 720

x + x + x + y + y + y -10+5 -10 + 20= 720

3x + 3y +5= 720

3x + 3y +5-5= 720-5

3x + 3y = 715

$3\left ( x + y \right )= 715$

$3\left ( x + y \right ) \div 3= 715\div 3$

$x + y = 238 \frac{1}{3} < 240$

This makes (b) greater.

Report an Error

Example Question #97 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

The angles of Hexagon A measure

$A ^{\circ }, B ^{\circ }, 150 ^{\circ }, 150 ^{\circ }, 150 ^{\circ }, 150 ^{\circ }$

The angles of Octagon B measure

$C ^{\circ }, D^{\circ }, 150^{\circ },150^{\circ },150^{\circ },150^{\circ },150^{\circ },150^{\circ }$

Which is the greater quantity?

(A) A + B

(B) C + D

Possible Answers:

(B) is greater

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

(A) is greater

(A) and (B) are equal

Correct answer:

(B) is greater

Explanation:

The sum of the measures of a hexagon is $180 ^{\circ } \times (6-2)= 720 ^{\circ }$ . Therefore,

A + B + 150 + 150 + 150 + 150 = 720

A + B +600= 720

A + B = 120

The sum of the measures of an octagon is $180 ^{\circ } \times (8-2)= 1,080 ^{\circ }$ . Therefore,

C + D + 150 + 150 + 150 + 150+ 150 + 150 = 1,080

C + D + 900 = 1,080

C + D = 180

C + D > A + B , so (B) is greater.

Report an Error

Example Question #98 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

The angles of Pentagon A measure $110^{\circ }, 110^{\circ }, 110^{\circ }, y^{\circ }, y^{\circ }$

The angles of Hexagon B measure $130^{\circ }, 130^{\circ }, 130^{\circ }, 130^{\circ },z^{\circ }, z^{\circ }$

Which is the greater quantity?

(A)

(B)

Possible Answers:

(B) is greater

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

(A) and (B) are equal

(A) is greater

Correct answer:

(A) is greater

Explanation:

The sum of the measures of the angles of a pentagon is $180^{\circ } \times (5-2) =540^{\circ }$ . Therefore,

y + y + 110 + 110 + 110 = 540

2y +330 = 540

2y = 210

y = 105

The sum of the measures of a hexagon is $180^{\circ } \times (6-2) =720 ^{\circ }$ . Therefore,

z + z + 130 + 130 + 130 + 130 = 720

2z + 520 = 720

2z= 200

z = 100

y> z , so (A) is greater.

Report an Error

Example Question #7 : Hexagons

Right_triangle

A regular hexagon has the same perimeter as the above right triangle. What is the length of one side of the hexagon?

Possible Answers:

$12 \frac{2}{5}\textrm{ in}$

$22 \frac{2}{5} \textrm{ in}$

The length cannot be determined from the information given.

$18 \frac{2}{3} \textrm{ in}$

$10 \frac{1}{3}\textrm{ in}$

Correct answer:

$18 \frac{2}{3} \textrm{ in}$

Explanation:

By the Pythagorean Theorem, the hypotenuse of the right triangle is

$\sqrt{14^{2}+48^{2}} = \sqrt{196+2,304} = \sqrt{2,500} = 50$ inches, making its perimeter

14 + 48 + 50 =112 inches.

The regular hexagon, which has six sides of equal length, has the same perimeter, so each side measures

$112 \div 6 = 18 \frac{2}{3}$ inches.

Report an Error

View Tutors

Kaitlyn
Certified Tutor

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

View Tutors

Gabby
Certified Tutor

University of Oregon, Bachelor in Arts, Journalism. University of Oregon, Current Grad Student, Communication, General.

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

GMAT Tutors in Dallas Fort Worth, ISEE Tutors in San Diego, SAT Tutors in San Diego, SSAT Tutors in Boston, SSAT Tutors in Atlanta, MCAT Tutors in Washington DC, Statistics Tutors in San Diego, Spanish Tutors in Miami, LSAT Tutors in Denver, Physics Tutors in New York City

Popular Courses & Classes

ACT Courses & Classes in Seattle, GMAT Courses & Classes in Chicago, GMAT Courses & Classes in Houston, GRE Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in New York City, GMAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Boston, LSAT Courses & Classes in Philadelphia, SAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

ISEE Test Prep in Philadelphia, MCAT Test Prep in Miami, SSAT Test Prep in San Diego, ACT Test Prep in Houston, GRE Test Prep in Dallas Fort Worth, GMAT Test Prep in San Francisco-Bay Area, GRE Test Prep in Atlanta, ACT Test Prep in Washington DC, ISEE Test Prep in Houston, LSAT Test Prep in Dallas Fort Worth

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

Example Question #92 : Plane Geometry

Example Question #92 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #93 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #94 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #95 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #96 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #97 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #98 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #7 : Hexagons

All ISEE Upper Level Quantitative Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: