Call Now to Set Up Tutoring:

(888) 888-0446

PSAT Math : Evaluating and Simplifying Expressions

Study concepts, example questions & explanations for PSAT Math

Create An Account

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #15 : Evaluating Expressions

x * y = –a, a – x = 2a. What is y?

Possible Answers:

-2

-a

Insufficient Information.

Correct answer:

Explanation:

Use the second equation to find x in terms of a. Plug it back in the second equation, that will give you 1 = y.

Report an Error

Example Question #21 : Evaluating Expressions

The projected sales of a movie are given by the function s(p) = 3000/(2p + a) where s is the number of movies sold, in thousands; p is the price per movie, in dollars; and a is a constant. If according to projections, 75,000 cartidges will be sold at $15 each, how many movies are sold at $20 each?

Possible Answers:

200,000

50,000

60,000

20,000

150,000

Correct answer:

60,000

Explanation:

You set up the equation to solve for a.

75 = 3000/(2(15) + a)

a = 10

You then set up the formula again for each movie costing $20, s(20) = 3000/(2(20) + 10), and solve for x, the number sold, giving you 60.

Report an Error

Example Question #22 : Evaluating Expressions

Half of one hundred divided by five and multiplied by one-tenth is __________.

Possible Answers:

1/2

Correct answer:

Explanation:

Let's take this step by step. "Half of one hundred" is 100/2 = 50. Then "half of one hundred divided by five" is 50/5 = 10. "Multiplied by one-tenth" really is the same as dividing by ten, so the last step gives us 10/10 = 1.

Report an Error

Example Question #23 : Evaluating Expressions

Let x&y be defined as (x – y)^xy . What is the value of –1&2?

Possible Answers:

–1/3

1/9

–3

–1/9

Correct answer:

1/9

Explanation:

We are told that x&y = (x – y)^xy.

–1&2 = (–1 – 2)^(–1)(2) = (–3)^–2

To simplify this, we can make use of the property of exponents which states that a^–^b = 1/(a^b).

(–3)^–2 = 1/(–3)² = 1/9

The answer is 1/9.

Report an Error

Example Question #21 : Evaluating And Simplifying Expressions

If 18 – w is 8 less than 32, what is the value of $\dpi{100} \small -\frac{1}{3}w$ ?

Possible Answers:

–2

–3

–6

Correct answer:

Explanation:

We need to rewrite this problem in mathematic terms.

8 less than 32 can be written as 32 – 8

so we will get the equation

18 – w = 32 – 8.

Now, we need to solve for w.

–w = 32 – 8 – 18

–w = 6

w = –6

Find the value of the given expression, $\dpi{100} \small -\frac{1}{3}w$ , by plugging in –6 for w.

$\dpi{100} \small -\left (\frac{1}{3} \right )\left ( -6 \right )=2$

Report an Error

Example Question #23 : Evaluating Expressions

If x and y are integers such that x > y > 0 and x²+ y²= 100

Which of the following can be the value of x + y?

I. 10

II. 12

III. 14

IV. 16

V. 18

Possible Answers:

Correct answer:

Explanation:

Note that x must be greater than y and that y must be greater than 0. This means that x and y are different, positive integers. In addition, the sum, x²+ y²must equal to 100. If we list squares beginning from the square of the first integer greater than 0 (1²) up to the square of the greatest integer less than 100 (9²) we will get:

1, 4, 9, 16, 25, 36, 49, 64, 81

We must observe that the only two numbers that will add up to 100 are 36 and 64.

Remember that x > y > 0 and that x²+ y²=100.

This means that x must be $\dpi{100} \small \sqrt{64}$ and y must be $\dpi{100} \small \sqrt{36}$

When we solve for x and y we get:

x = 8

and y = 6.

Therefore, x + y can only be 14.

Report an Error

Example Question #24 : Evaluating Expressions

If $m > n$ , which of the following has to be true?

Possible Answers:

$m^{2} > n^{2}$

$\frac{m}{2} > \frac{n}{2}$

$mn > 0$

$\left | m \right | > \left | n \right |$

$mn > -mn$

Correct answer:

$\frac{m}{2} > \frac{n}{2}$

Explanation:

Plug in numbers for each alternative. If both sides of the inequality $\frac{m}{2} > \frac{n}{2}$ are multiplied by 2, the result is the original inequality, $m > n$ . The other options fail (if confused, try plugging in $m$ as a positive, $n$ as a negative).

Report an Error

Example Question #22 : Evaluating Expressions

Billy began lifting weights in February. After 6 months, he can lift 312 lbs, a 20% increase in the amount he could lift in February. How much weight could Billy lift in February?

Possible Answers:

$250\ lbs.$

$280\ lbs.$

$260\ lbs.$

$290\ lbs.$

$270\ lbs.$

Correct answer:

$260\ lbs.$

Explanation:

$1.2w = 312$

$w = 260 lbs$

Report an Error

Example Question #733 : Algebra

A metal rod is 36 inches long and divided into 3 sections. The middle section is twice as long as the first section. The third section is 4 inches shorter than the first section. How long are the sections?

Possible Answers:

None of the above answers

The first piece is 6 inches, the second piece is 10 inches and the third piece is 20 inches

First piece is 20 inches, the second piece is 10 inches and the third piece is 6 inches

The first piece is 15 inches, the second piece is 15 inches and the third piece is 6 inches

First piece is 10 inches, the middle piece is 20 inches, and third piece is 6 inches long.

Correct answer:

First piece is 10 inches, the middle piece is 20 inches, and third piece is 6 inches long.

Explanation:

Assume the first section equals $x$ inches, then the second(or the middle section) must be equal to $2x$ and the third piece must be equal to $x-4$ .

$x+2x+(x-4)=36$ and now you solve for $x$ which equals 10. Hence the middle piece must be equal to 20 inches and the third piece is only 6 inches long.

Report an Error

Example Question #734 : Algebra

A B

1 2

2 4

3 10

5 34

Using the table above, please select the answer below that expresses the relationship between A and B.

Possible Answers:

$B=A^3-2A^2+2A+1$

$B=A^2+A-2$

$B=2A$

$B=8A-6$

$B=2A^2-4A+4$

Correct answer:

$B=2A^2-4A+4$

Explanation:

By testing the answers, it can be seen that the only equation to satisfy all cases in the table above is

$B=2A^2-4A+4$

Report an Error

View PSAT Mathematics Tutors

Joy
Certified Tutor

Boston University, Bachelor in Arts, Conservation Biology.

View PSAT Mathematics Tutors

Yongmao
Certified Tutor

Nankai University, Bachelor of Science, Chemistry. Washington University in St Louis, Doctor of Philosophy, Organic Chemistry.

View PSAT Mathematics Tutors

Bagher
Certified Tutor

San Jose State University, Master's/Graduate, Physics.

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Computer Science Tutors in Chicago, English Tutors in Atlanta, Chemistry Tutors in San Francisco-Bay Area, Spanish Tutors in Phoenix, GRE Tutors in Boston, Computer Science Tutors in Denver, Spanish Tutors in Philadelphia, SSAT Tutors in Phoenix, ACT Tutors in San Diego, Math Tutors in Washington DC

Popular Courses & Classes

GMAT Courses & Classes in Chicago, Spanish Courses & Classes in Seattle, GMAT Courses & Classes in Denver, GMAT Courses & Classes in San Diego, GRE Courses & Classes in San Diego, MCAT Courses & Classes in Washington DC, MCAT Courses & Classes in Chicago, SSAT Courses & Classes in Phoenix, Spanish Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Atlanta

Popular Test Prep

SSAT Test Prep in Philadelphia, MCAT Test Prep in Chicago, SAT Test Prep in Atlanta, SAT Test Prep in Chicago, SSAT Test Prep in Phoenix, GMAT Test Prep in Phoenix, ISEE Test Prep in Seattle, GRE Test Prep in Denver, MCAT Test Prep in New York City, SSAT 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

PSAT Math : Evaluating and Simplifying Expressions

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #15 : Evaluating Expressions

Example Question #21 : Evaluating Expressions

Example Question #22 : Evaluating Expressions

Example Question #23 : Evaluating Expressions

Example Question #21 : Evaluating And Simplifying Expressions

Example Question #23 : Evaluating Expressions

Example Question #24 : Evaluating Expressions

Example Question #22 : Evaluating Expressions

Example Question #733 : Algebra

Example Question #734 : Algebra

All PSAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: