Call Now to Set Up Tutoring:

(888) 888-0446

PSAT Math : Algebra

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 #1808 : Sat Mathematics

With a $25\ mph$ head wind a plane can fly a certain distance in five hours. The return flight takes an hour less. How fast was the plane flying?

Possible Answers:

$225\ mph$

$275\ mph$

$300\ mph$

$125\ mph$

$175\ mph$

Correct answer:

$225\ mph$

Explanation:

In general, $distance=rate\times time$ .

The distance is the same going and coming; however, the head wind affects the rate. The equation thus becomes $(r-25)\times 5=(r+25)\times 4$ .

Solving for $r$ gives $r=225\ mph$ .

Report an Error

Example Question #32 : Algebra

How much water should be added to $2\ L$ of 90% cleaning solution to yield 50% cleaning solution?

Possible Answers:

$1.6\ L$

$0.8\ L$

$1.2\ L$

$1.5\ L$

$2.4\ L$

Correct answer:

$1.6\ L$

Explanation:

Pure water is 0% and pure solution 100%. Let $x$ = water to be added.

$V_{1}P_{1} + V_{2}P_{2} = V_{f}P_{f}$ in general where $V$ is the volume and $P$ is the percent.

So the equation to solve becomes $x(0)+2(0.90)= (x+2)(0.50)$

and $x=1.6\ L$

Report an Error

Example Question #31 : Algebra

Solve $x+2y=14$ and $2x+y=13$

Possible Answers:

$(5,4)$

$(3,2)$

$(4,5)$

$(1,3)$

$(-4,-5)$

Correct answer:

$(4,5)$

Explanation:

This problem is a good example of the substitution method of solving a system of equations. We start by rewritting the first equation in terms of $x$ to get $x=14-2y$ and then substutite the $x$ into the second equation to get

$2(14-2y)+y=13$ .

Solving this equation gives $y=5$ and substituting this value into one of the original equations gives $x=4$ , thus the correct answer is $(4,5)$ .

Report an Error

Example Question #71 : How To Find The Solution To An Equation

Joy bought some art supplies. She bought colored pencils for $1.25 per box and sketch pads for $2.25 each. Joy bought one more sketch pad than colored pencil boxes and spent $9.25. How many sketch pads did she buy?

Possible Answers:

$2$

$5$

$1$

$4$

$3$

Correct answer:

$3$

Explanation:

Let $x$ = # of color pencil boxes and $x+1$ = # of sketch pads purchased.

So the equation to solve becomes $1.25x+2.25(x+1)=9.25$ .

Solving this equations leads to 2 colored pencil boxes and 3 sketch pads.

Report an Error

Example Question #31 : Algebra

$\left | 2x - 3 \right |-x= 5$

Possible Answers:

$x=-8$

$x=8\ or\ x=-\frac{2}{3}$

$x=-8\ or \ x=-\frac{3}{2}$

$x=-\frac{2}{3}$

$x=8$

Correct answer:

$x=8\ or\ x=-\frac{2}{3}$

Explanation:

This question deals with absolute value equations which will normally gives you two solutions.

You need to solve two sets of equations for absolute value problems:

$2x-3 = x+5$

and

$2x-3=-\left ( x+5 \right )$

Report an Error

Example Question #32 : How To Find The Solution To An Equation

Steve sells cars. His monthly salary is $1,000. He gets a $500 commission for each car he sells. If Steve wants to make $7,500 this month, how many cars would he have to sell?

Possible Answers:

Correct answer:

Explanation:

Let = money earned and = number of cars sold

So y = 500x + 1000

7500 = 500x + 1000 and solving shows that he needs to sell 13 cars to make $7,500.

Report an Error

Example Question #33 : Algebra

A chemistry student needs to dilute some acid. How much pure water should be added to 2 gallons of 80% acid solution to yield 20% acid solution?

Possible Answers:

$6\ gallons$

$2\ gallons$

$4\ gallons$

$5\ gallons$

$8\ gallons$

Correct answer:

$6\ gallons$

Explanation:

Let pure water = 0 % and pure acid = 100%

The general equation to use is:

$V_{1}P_{1} + V_{2}P_{2} = V_{f}P_{f}$ where is the volume and is the percent solution.

So the equation to solve becomes x(0) + 2(.80) = (x + 2)(.20) and x = 6 gallons of pure water needs to be added to get a 20% acid solution.

Report an Error

Example Question #71 : How To Find The Solution To An Equation

The Widget Company makes widgets. The monthly fixed costs are $750. It costs $45 to make each widget. The widgets sell for $75 a piece.

What is the monthly break-even point?

Possible Answers:

Correct answer:

Explanation:

The break-even point is where the costs equal revenue.

Let = # of widgets sold.

Costs: C(w) = 45w + 750

Revenue: R(w) = 75w

So the equation to solve becomes 45w + 750 = 75w

So the break-even point occurs when they sell 25 widgets.

Report an Error

Example Question #142 : Gre Quantitative Reasoning

The Widget Company makes widgets. The monthly fixed costs are $750. It costs $45 to make each widget. The widgets sells for $75 a piece.

The Widget Company wants to make a profit of $3,000. How many widgets must be sold?

Possible Answers:

125

140

150

100

Correct answer:

125

Explanation:

Profits = Revenues - Costs

Revenue: R(w) = 75w

Costs: C(w) = 45w + 750

Profit: P(w) = 75w - (45w + 750) = 30w -750

So the equation to solve becomes 3,000 = 30w - 750

So a $3,000 profit occurs when they sell 125 widgets

Report an Error

Example Question #131 : Equations / Inequalities

Sally sells custom picture frames. Her monthly fixed costs are $350. It costs $10 to make each frame. Sally sells her picture frames for $35 each.

How many picture frames must Sally sell in order to break even?

Possible Answers:

Correct answer:

Explanation:

The break-even point is where the costs equal the revenues.

Let = # of frames sold

Costs: C(x) = 10x +350

Revenues: R(x) = 35x

Thus, 10x + 350 = 35x

So 14 picture frames must be sold each month to break-even.

Report an Error

View PSAT Mathematics Tutors

Robert
Certified Tutor

Rensselaer Polytechnic Institute, Bachelors, Electrical Engineering. Brooklyn Polytechnic, Masters, Computer Science.

View PSAT Mathematics Tutors

Joseph
Certified Tutor

CUNY College of Staten Island, Bachelor in Arts, Applied Psychology. New York University, Master of Arts, Applied Psychology.

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

MCAT Tutors in Atlanta, SAT Tutors in Chicago, Algebra Tutors in Philadelphia, ACT Tutors in Atlanta, Reading Tutors in Denver, Biology Tutors in Washington DC, Algebra Tutors in Phoenix, Biology Tutors in San Francisco-Bay Area, Chemistry Tutors in San Diego, French Tutors in Miami

Popular Courses & Classes

ACT Courses & Classes in Miami, GRE Courses & Classes in Chicago, ISEE Courses & Classes in Washington DC, ACT Courses & Classes in Chicago, MCAT Courses & Classes in Denver, SSAT Courses & Classes in Denver, LSAT Courses & Classes in Atlanta, ACT Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Phoenix, ACT Courses & Classes in Washington DC

Popular Test Prep

SSAT Test Prep in New York City, LSAT Test Prep in New York City, ACT Test Prep in Miami, ACT Test Prep in Dallas Fort Worth, SSAT Test Prep in Denver, GRE Test Prep in Phoenix, SSAT Test Prep in Los Angeles, LSAT Test Prep in Philadelphia, SSAT Test Prep in Dallas Fort Worth, ACT 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

PSAT Math : Algebra

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1808 : Sat Mathematics

Example Question #32 : Algebra

Example Question #31 : Algebra

Example Question #71 : How To Find The Solution To An Equation

Example Question #31 : Algebra

Example Question #32 : How To Find The Solution To An Equation

Example Question #33 : Algebra

Example Question #71 : How To Find The Solution To An Equation

Example Question #142 : Gre Quantitative Reasoning

Example Question #131 : Equations / Inequalities

All PSAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: