We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Quantitative : Numbers and Operations

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

← Previous 1 2 … 5 6 7 8 9 10 11 12 13 Next →

Example Question #12 : Exponents

$\frac{ \left ( 30 -2 \cdot 15\right )^{0}}{\left ( 30 -15\right )^{0}}$

Possible Answers:

The expression is undefined.

Correct answer:

The expression is undefined.

Explanation:

$\frac{ \left ( 30 -2 \cdot 15\right )^{0}}{\left ( 30 -15\right )^{0}} = \frac{ \left ( 30 -30\right )^{0}}{15^{0}}=\frac{ 0^{0}}{15^{0}}$

The numerator is undefined, since 0 raised to the power of 0 is an undefined quantity. Therefore, the entire expression is undefined.

Report an Error

Example Question #2 : How To Divide Exponents

Column A Column B

$\left(\frac{1}{16}\right)^\frac{1}{2}$ $\left(\frac{1}{16}\right)^{-\frac{1}{2}}$

Possible Answers:

There is not enough information to determine the relationship between the quantities.

The quantity in Column A is greater.

The quantity in Column B is greater.

The quantities are equal.

Correct answer:

The quantity in Column B is greater.

Explanation:

Let's simplify both quantities first before we compare them. $\left(\frac{1}{16}\right)^\frac{1}{2}$ becomes $\sqrt{\frac{1}{16}}$ because the fractional exponent indicates a square root. We can simplify that by knowing that we can take the square roots of both the numerator and denominator, as shown by: $\frac{\sqrt{1}}{\sqrt{16}}$ . We can simplify further by taking the square roots (they're perfect squares) and get $\frac{1}{4}$ . Then, let's simplify Column B. To get rid of the negative exponent, we put the numerical expression on the denominator. There's still the fractional exponent at play, so we'll have a square root as well. It looks like this now: $\frac{1}{\sqrt{\frac{1}{16}}}$ . We already simplified $\sqrt{\frac{1}{16}}$ , so we can just plug in our answer, $\frac{1}{4}$ , into the denominator. Since we don't want a fraction in the denominator, we can multiply by the reciprocal of $\frac{1}{4}$ , which is 4 to get 1(4) , which is just 4. Therefore, Column B is greater.

Report an Error

Example Question #3 : How To Divide Exponents

Give the reciprocal of $1.6 \times 10 ^{-7}$ in scientific notation.

Possible Answers:

$6.25 \times 10^{6 }$

$6.25 \times 10^{-7 }$

$6.25 \times 10^{8 }$

$6.25 \times 10^{7 }$

$6.25 \times 10^{-6 }$

Correct answer:

$6.25 \times 10^{6 }$

Explanation:

The reciprocal of $1.6 \times 10 ^{-7}$ is the quotient of 1 and the number;

$\frac{1}{ 1.6 \times 10 ^{-7} }$

$= \frac{1 \times 10^{0}}{ 1.6 \times 10 ^{-7} }$

$= \frac{1 }{ 1.6 } \times \frac{ 10^{0}}{ 10 ^{-7} }$

$=0.625 \times 10^{0- (-7) }$

$=0.625 \times 10^{7 }$

This is not in scientific notation, so adjust.

$6.25 \times 10^{-1 } \times 10^{7 }$

$= 6.25 \times 10^{-1+7 }$

$= 6.25 \times 10^{6 }$

Report an Error

Example Question #1 : How To Divide Exponents

Give the reciprocal of $3.2 \times 10 ^{9}$ in scientific notation.

Possible Answers:

$-3.2 \times 10 ^{-10}$

$3.125 \times 10 ^{-10}$

$3.125 \times 10 ^{-9}$

$-3.2 \times 10 ^{-9}$

$-3.125 \times 10 ^{9}$

Correct answer:

$3.125 \times 10 ^{-10}$

Explanation:

The reciprocal of $3.2 \times 10 ^{9}$ is the quotient of 1 and the number, or

$\frac{1}{ 3.2 \times 10 ^{9} }$

$= \frac{1 \times 10^{0}}{ 3.2 \times 10 ^{9}}$

$= \frac{1 }{ 3.2 } \times \frac{ 10^{0}}{ 10 ^{9} }$

$=0.3125 \times 10 ^{-9}$

This is not in scientific notation, so adjust:

$3.125 \times 10 ^{-1}\times 10 ^{-9}$

$=3.125 \times 10 ^{-1+ (-9)}$

$=3.125 \times 10 ^{-10}$

Report an Error

Example Question #1 : How To Divide Exponents

x> 1

Column A Column B

$\frac{x^3}{x^2}$ $\sqrt{x}$

Possible Answers:

The quantity in Column B is greater.

The quantities in both columns are equal.

The relationship between the columns cannot be determined.

The quantity in Column A is greater.

Correct answer:

The quantity in Column A is greater.

Explanation:

You can simplify Column A first. When you're dividing with exponents and bases are the same, subtract the exponents. Therefore, it simplifies to x. We know that x is positive since it is greater than 1. X is greater than $\sqrt{x}$ . Try plugging in a number to test. 25 is greater than $\sqrt{25}$ , which is 5. Even 1.1 is greater than $\sqrt{1.1}$ . Therefore, Column A is greater.

Report an Error

Example Question #1 : How To Add Exponents

Two quantities are given - one in Column A and the other in Column B. Compare the quantities in the two columns.

Assume, in both columns, that $x\neq0$ .

Column A Column B

2x^2+6x^2 11x^2-x^2

Possible Answers:

The relationship cannot be determined from the info given.

The quantities in both columns are equal.

The quantity in Column B is greater.

The quantity in Column A is greater.

Correct answer:

The quantity in Column B is greater.

Explanation:

When you are adding and subtracting terms with exponents, you combine like terms. Since both columns have expressions with the same exponent throughout, you are good to just look at the coefficients. Remember, a coefficient is the number in front of a variable. Therefore, Column A is 8x^2 since 2+6=8 . Column B is 10x^2 since 11-1=10 . We can see that Column B is greater.

Report an Error

Example Question #21 : Exponential Operations

Add all of the perfect squares between 50 and 100 inclusive.

Possible Answers:

245

294

194

145

The correct answer is not among the other choices.

Correct answer:

245

Explanation:

The perfect squares between 50 and 100 inclusive are

$8^{2} = 64$

$9^{2} = 81$

$10 ^{2} = 100$

Their sum is 64 + 81 + 100 = 245

Report an Error

Example Question #481 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Which is the greater quantity?

(A) The sum of the first ten perfect square integers

(B) The sum of the first five perfect cube integers

Possible Answers:

(A) and (B) are equal

(A) is greater

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

(B) is greater

Correct answer:

(A) is greater

Explanation:

The sum of the first ten perfect square integers:

$\begin{matrix} \;\; \; 1\\ \;\; \; 4\\ \;\; \; 9\\ \;16\\ \;25\\ \;36\\ \;49\\ \;64\\ \;81\\ \underline{100}\\ 385 \end{matrix}$

The sum of the first five perfect cube integers:

$\begin{matrix} \;\; \; 1\\ \;\; \; 8\\ \;27\\ \;64\\ \underline{125}\\ 225 \end{matrix}$

(A) is greater.

Report an Error

← Previous 1 2 … 5 6 7 8 9 10 11 12 13 Next →

View Tutors

Aaron
Certified Tutor

Portland State University, Bachelors, Economics. Portland State University, Masters, Environmental and Resource Management.

View Tutors

Chase
Certified Tutor

Western Governors University, Bachelor of Science, Mathematics.

View Tutors

Andrew
Certified Tutor

Swarthmore College, Bachelor in Arts, Philosophy.

All ISEE Upper Level Quantitative Resources

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

Popular Subjects

Statistics Tutors in Philadelphia, LSAT Tutors in Los Angeles, GMAT Tutors in New York City, ACT Tutors in San Francisco-Bay Area, English Tutors in Los Angeles, ACT Tutors in New York City, Chemistry Tutors in Philadelphia, Algebra Tutors in Seattle, English Tutors in San Diego, Algebra Tutors in Washington DC

Popular Courses & Classes

SSAT Courses & Classes in San Diego, LSAT Courses & Classes in Los Angeles, LSAT Courses & Classes in Phoenix, LSAT Courses & Classes in Atlanta, GRE Courses & Classes in Atlanta, GRE Courses & Classes in Washington DC, Spanish Courses & Classes in Houston, ACT Courses & Classes in New York City, ACT Courses & Classes in Los Angeles, SAT Courses & Classes in Houston

Popular Test Prep

MCAT Test Prep in Dallas Fort Worth, LSAT Test Prep in New York City, SAT Test Prep in San Diego, GMAT Test Prep in New York City, ACT Test Prep in New York City, ACT Test Prep in Los Angeles, ISEE Test Prep in Chicago, GRE Test Prep in San Francisco-Bay Area, LSAT Test Prep in Los Angeles, MCAT 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 : Numbers and Operations

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #12 : Exponents

Example Question #2 : How To Divide Exponents

Example Question #3 : How To Divide Exponents

Example Question #1 : How To Divide Exponents

Example Question #1 : How To Divide Exponents

Example Question #1 : How To Add Exponents

Example Question #21 : Exponential Operations

Example Question #481 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

All ISEE Upper Level Quantitative Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: