Home > Articles

Math Section

This chapter is from the book

This chapter is from the book

Answer Explanations

Multiple Choice (Questions 1–8)

  1. The correct answer is C. To solve this problem, simply count the numbers that appear both in set P and in set Q. Sets P and Q share the following numbers: 16, 17, 18, 19, and 20. Therefore, five numbers in set P are also in Set Q.

  2. The correct answer is C. You are given that John traveled 30 miles in 6 hours and that Seth traveled three times as far in half the time. This means that Seth traveled 30(3), or 90 miles in 6(), or 3 hours. Therefore, Seth traveled , or 30 miles per hour.

  3. The correct answer is D. You are given that r = -2. Therefore, the best approach to solving this problem is to replace r with -2 in each of the answer choices as follows:

    • Answer choice A: 4pr2 = 4p(-2)2, which equals (4)(4)p, or 16p.

    • Answer choice B: 2pr3 = 2p(-2)3, which equals (2)(-8)p, or -16p.

    • Answer choice C: -2pr4 = -2p(-2)4, which equals (-2)(16)p, or -32p.

    • Answer choice D: -4pr5 = -4p(-2)5, which equals (-4)(-32)p, or 128p.

    • Answer choice E: -6pr6 = -6p(-2)6, which equals (-6)(64)p, or -384p.

    The question asks for the least value. You are given that p < 0, which means that p is a negative number. If you substitute any negative number into the results obtained above, only answer choices A and D will yield a negative value. Therefore, you can eliminate answer choices B, C, and E, because they will all be larger than either answer choice A or D. When p < 0, 128p will always be less than 16p, so answer choice D is correct.

  4. The correct answer is C. The equation of the line is given in the slope-intercept form (y = mx + b), where b is the y-intercept. The y-intercept is the point at which the line intersects the y-axis. Since the graph shown has the equation y = ax + b, and the new graph has the equation y = ax + b, both graphs should have the same y-intercept. The graph shown has a y-intercept of 1. Eliminate answer choices A, B and D, since they do not have a y-intercept of 1. The slope of the graph shown is a, and the slope of the new graph (based on its equation) is a. Because both slopes are positive, you can eliminate answer choice E, which has a negative slope. This leaves you with answer choice C.

  5. The correct answer is B. To solve this problem, you must recognize that the triangle is a "special triangle." A right triangle in which the length of the longer leg is times the length of the shorter leg is a 30°–60°–90° right triangle. Another property of this type of right triangle is that the hypotenuse is 2 times the length of the shorter leg. So, this right triangle has lengths x, x, and 2x. The perimeter is the sum of the lengths of the sides. You are given that the perimeter equals 12 + 4. Plug this value into the formula for the perimeter of a triangle, as follows:

    • 12 + 4 = x + x + 2x

    • 12 + 4 = 3x + x

    For the right side of the equation to equal the left side of the equation, x must be equal to 4.

  6. The correct answer is C. The median of a list of values is the middle value when the list is in chronological order and there are an odd number of values. In this case, if we include Mike and his 75 coins, there will be 19 coin collectors. List the number of coins for each collector in chronological order as follows:

  7. As you can see, the middle number is 85, so that is the median.

  8. The correct answer is C. To solve, first translate the words into their mathematical equivalents:

    • 4 more than twice n translates to 4 + 2n. You are given that this quantity is a negative number, which translates to 4 + 2n < 0.

    • 6 more than n translates to 6 + n. You are given that this quantity is a positive number, which translates to 6 + n > 0.

    Solve each inequality as follows:

    • 4 + 2n < 0

    • n < -2

    • 6 + n > 0

    • n > -6

    So, n could be any number less than -2 and greater than -6. Only -4, answer choice C, is greater than -6 and less than -2.

  9. The correct answer is D. Since the figure is a rectangle, the adjacent sides are perpendicular. Perpendicular lines have slopes that are negative reciprocals of each other, meaning that the product of their slopes is -1. Since there are four lines and four perpendicular angles, the product of the slopes is (-1)(-1)(-1)(-1), or 1.

Student-Produced Response (Questions 9–18)

  1. Answer: . To solve this problem, convert hours into minutes. 2 hours is equivalent to 150 minutes. You are given that the movie included 30 minutes of commercials; therefore, the movie included 120 minutes that were not commercials. The fraction of the movie that was not commercials is , or .

  2. Answer: 2.66, 2.67, or .

  3. To solve this problem, set up an equation based on the information given:

    • 0.75x = 2

    Solve for x.

    • x = 2 ÷ 0.75

    • x = 2.66666 (This is a repeating decimal.)

    For the purposes of the PSAT, the answer can be simplified to either 2.66 or 2.67. If you first converted .75 to , you would arrive at as your answer, which is also correct.

  4. Answer: . You are given that 8s = 96. Therefore, s = , or 12. You are given that sp = 4, and you now know that s = 12. Therefore, 12p = 4 and p = , or .

  5. Answer: 2 or 3. The formula for the area of a rectangle is A = (l)(w). Therefore, the area of ACFD will be (AC)(AD). Because you must solve for the value of AB, let AB = x. Since ABED is a square, it follows that AB = AD = x. Therefore, since BC = 8, the area of ACFD will be (8 + x)x, or x2 + 8x. Since, according to the question, the area must be between 14 and 35, set up the inequality 14 < x2 + 8x < 35. Now, pick some easy numbers to work with to replace x in the inequality. Because x is a positive value and 14 and 35 are not particularly large numbers, start with x = 1. If x = 1, then the area is x2 + 8x, or (1)2 + 8(1), or 9. This value is not between 14 and 35, so x cannot be 1. If x = 2, then the area is x2 + 8x, or (2)2 + 8(2), or 20. This value is between 14 and 35, so x = 2 is a possible solution. If x = 3, then the area is x2 + 8x, or (3)2 + 8(3), or 33. This value is between 14 and 35, so x = 3 is another possible solution. If x = 4, then the area is x2 + 8x, or (4)2 + 8(4) or 48. This value is not between 14 and 35, so x cannot be 4, or any number greater than 4. Therefore, x, or AB, can be either 2 or 3.

  6. Answer: 100. To solve this problem, let the total number of napkins in the box equal x. According to information in the problem, there are 25 red napkins in the box. One quarter of the total number of napkins is blue, so there are ()x blue napkins in the box. There are twice as many white napkins as blue napkins, so there are 2()x, or ()x white napkins in the box. To calculate the total number of napkins in the box, set up an equation and solve for x.

    • x = 25 + x + x

    • x = 25 + x

    • x = 25

    • x = 100

  7. Answer: 20. You are given that there are 4 points on line l, and 5 points on the line parallel to line l. Therefore, from each of the 4 points on line l, T, U, V, and W, you can draw one line to each of the 5 points on the second line. This means that there can be(4)(5), or 20 different lines containing exactly 2 of the 9 points.

  8. Answer: 4. To solve this problem, rewrite 42x + 42x + 42x + 42x as 4(42x). Now you have 4(42x) = 49. When you multiply numbers with the same base, you add the exponents. The number 4 is equivalent to 41. Therefore, 4(42x) = 42x + 1. Now, because 42x + 1 = 49, set the exponents equal to each other, and solve for x.

    • 2x + 1 = 9

    • 2x = 8

    • x = 4

  9. Answer: 496. If the average of the 9 numbers is 56, then the total value of the 9 numbers is (9)(56), or 504. The question asks for the greatest possible integer on one card, so set the values of the other cards at the lowest possible integer, which is 1. If there are 8 cards with a value of 1, then the value of the ninth card must be 504 – 8(1), or 496.

  10. Answer: 3. Let j be the length of one of Jeff's steps, and let s be the length of one of Scott's steps. If they each take 12 steps away from each other, the distance between them is 12j + 12s. Since it takes Jeff 16 steps to reach Scott, then 12j + 12s = 16j. Subtract 12j from both sides to get 12s = 4j. Divide both sides by 4 to get 3s = j. The length of one of Jeff's steps (j) is 3 times the length of one of Scott's steps (s).

  11. Answer: 130. To solve this problem, you should recognize that rs is a factor of 3r2s + 2rs2. Rewrite 3r2s + 2rs2 as rs(3r + 2s). You are given that rs = 13 and 3r + 2s = 10. Substitute those values into rs(3r + 2s) to get 13(10), which equals 130.

Pearson IT Certification Promotional Mailings & Special Offers

I would like to receive exclusive offers and hear about products from Pearson IT Certification and its family of brands. I can unsubscribe at any time.

Overview


Pearson Education, Inc., 221 River Street, Hoboken, New Jersey 07030, (Pearson) presents this site to provide information about Pearson IT Certification products and services that can be purchased through this site.

This privacy notice provides an overview of our commitment to privacy and describes how we collect, protect, use and share personal information collected through this site. Please note that other Pearson websites and online products and services have their own separate privacy policies.

Collection and Use of Information


To conduct business and deliver products and services, Pearson collects and uses personal information in several ways in connection with this site, including:

Questions and Inquiries

For inquiries and questions, we collect the inquiry or question, together with name, contact details (email address, phone number and mailing address) and any other additional information voluntarily submitted to us through a Contact Us form or an email. We use this information to address the inquiry and respond to the question.

Online Store

For orders and purchases placed through our online store on this site, we collect order details, name, institution name and address (if applicable), email address, phone number, shipping and billing addresses, credit/debit card information, shipping options and any instructions. We use this information to complete transactions, fulfill orders, communicate with individuals placing orders or visiting the online store, and for related purposes.

Surveys

Pearson may offer opportunities to provide feedback or participate in surveys, including surveys evaluating Pearson products, services or sites. Participation is voluntary. Pearson collects information requested in the survey questions and uses the information to evaluate, support, maintain and improve products, services or sites; develop new products and services; conduct educational research; and for other purposes specified in the survey.

Contests and Drawings

Occasionally, we may sponsor a contest or drawing. Participation is optional. Pearson collects name, contact information and other information specified on the entry form for the contest or drawing to conduct the contest or drawing. Pearson may collect additional personal information from the winners of a contest or drawing in order to award the prize and for tax reporting purposes, as required by law.

Newsletters

If you have elected to receive email newsletters or promotional mailings and special offers but want to unsubscribe, simply email information@informit.com.

Service Announcements

On rare occasions it is necessary to send out a strictly service related announcement. For instance, if our service is temporarily suspended for maintenance we might send users an email. Generally, users may not opt-out of these communications, though they can deactivate their account information. However, these communications are not promotional in nature.

Customer Service

We communicate with users on a regular basis to provide requested services and in regard to issues relating to their account we reply via email or phone in accordance with the users' wishes when a user submits their information through our Contact Us form.

Other Collection and Use of Information


Application and System Logs

Pearson automatically collects log data to help ensure the delivery, availability and security of this site. Log data may include technical information about how a user or visitor connected to this site, such as browser type, type of computer/device, operating system, internet service provider and IP address. We use this information for support purposes and to monitor the health of the site, identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents and appropriately scale computing resources.

Web Analytics

Pearson may use third party web trend analytical services, including Google Analytics, to collect visitor information, such as IP addresses, browser types, referring pages, pages visited and time spent on a particular site. While these analytical services collect and report information on an anonymous basis, they may use cookies to gather web trend information. The information gathered may enable Pearson (but not the third party web trend services) to link information with application and system log data. Pearson uses this information for system administration and to identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents, appropriately scale computing resources and otherwise support and deliver this site and its services.

Cookies and Related Technologies

This site uses cookies and similar technologies to personalize content, measure traffic patterns, control security, track use and access of information on this site, and provide interest-based messages and advertising. Users can manage and block the use of cookies through their browser. Disabling or blocking certain cookies may limit the functionality of this site.

Do Not Track

This site currently does not respond to Do Not Track signals.

Security


Pearson uses appropriate physical, administrative and technical security measures to protect personal information from unauthorized access, use and disclosure.

Children


This site is not directed to children under the age of 13.

Marketing


Pearson may send or direct marketing communications to users, provided that

  • Pearson will not use personal information collected or processed as a K-12 school service provider for the purpose of directed or targeted advertising.
  • Such marketing is consistent with applicable law and Pearson's legal obligations.
  • Pearson will not knowingly direct or send marketing communications to an individual who has expressed a preference not to receive marketing.
  • Where required by applicable law, express or implied consent to marketing exists and has not been withdrawn.

Pearson may provide personal information to a third party service provider on a restricted basis to provide marketing solely on behalf of Pearson or an affiliate or customer for whom Pearson is a service provider. Marketing preferences may be changed at any time.

Correcting/Updating Personal Information


If a user's personally identifiable information changes (such as your postal address or email address), we provide a way to correct or update that user's personal data provided to us. This can be done on the Account page. If a user no longer desires our service and desires to delete his or her account, please contact us at customer-service@informit.com and we will process the deletion of a user's account.

Choice/Opt-out


Users can always make an informed choice as to whether they should proceed with certain services offered by Adobe Press. If you choose to remove yourself from our mailing list(s) simply visit the following page and uncheck any communication you no longer want to receive: www.pearsonitcertification.com/u.aspx.

Sale of Personal Information


Pearson does not rent or sell personal information in exchange for any payment of money.

While Pearson does not sell personal information, as defined in Nevada law, Nevada residents may email a request for no sale of their personal information to NevadaDesignatedRequest@pearson.com.

Supplemental Privacy Statement for California Residents


California residents should read our Supplemental privacy statement for California residents in conjunction with this Privacy Notice. The Supplemental privacy statement for California residents explains Pearson's commitment to comply with California law and applies to personal information of California residents collected in connection with this site and the Services.

Sharing and Disclosure


Pearson may disclose personal information, as follows:

  • As required by law.
  • With the consent of the individual (or their parent, if the individual is a minor)
  • In response to a subpoena, court order or legal process, to the extent permitted or required by law
  • To protect the security and safety of individuals, data, assets and systems, consistent with applicable law
  • In connection the sale, joint venture or other transfer of some or all of its company or assets, subject to the provisions of this Privacy Notice
  • To investigate or address actual or suspected fraud or other illegal activities
  • To exercise its legal rights, including enforcement of the Terms of Use for this site or another contract
  • To affiliated Pearson companies and other companies and organizations who perform work for Pearson and are obligated to protect the privacy of personal information consistent with this Privacy Notice
  • To a school, organization, company or government agency, where Pearson collects or processes the personal information in a school setting or on behalf of such organization, company or government agency.

Links


This web site contains links to other sites. Please be aware that we are not responsible for the privacy practices of such other sites. We encourage our users to be aware when they leave our site and to read the privacy statements of each and every web site that collects Personal Information. This privacy statement applies solely to information collected by this web site.

Requests and Contact


Please contact us about this Privacy Notice or if you have any requests or questions relating to the privacy of your personal information.

Changes to this Privacy Notice


We may revise this Privacy Notice through an updated posting. We will identify the effective date of the revision in the posting. Often, updates are made to provide greater clarity or to comply with changes in regulatory requirements. If the updates involve material changes to the collection, protection, use or disclosure of Personal Information, Pearson will provide notice of the change through a conspicuous notice on this site or other appropriate way. Continued use of the site after the effective date of a posted revision evidences acceptance. Please contact us if you have questions or concerns about the Privacy Notice or any objection to any revisions.

Last Update: November 17, 2020