Ds St Business Math

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DSSTIntroduction to Business Math

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Copyright © 2010Peterson's

, which was not involved in theproduction of and does not endorse this product.

Time—120 Minutes

100 Questions

Each incomplete statement is followed by four suggestedcompletions. Select the one that is best in each case.

1. Five years ago, the share price of a company was $10. Today’s share price of $127 corresponds to apercent increase of

(A) 117%

(B) 127%

(C) 1,170%

(D) 1,270%

2. Two days ago, the price of a stock was $100. Yesterday, the price decreased by 10%, while today the

price increased by 10%. What is the current price?

(A) $90

(B) $99

(C) $100

(D) $110

3. The expression

3 2

11 3÷ is equivalent to which of the following?

(A)

2

11

(B)6

22

(C)9

22

(D)6

11


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4. What values of x satisfy the compound inequality 4 < 6 – 5 x < 12?

(A)6 2

5 5 x<


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9. An apparel shop sells skirts for $45 and blouses for $35. The shop’s entire stock at the beginning of themonth is worth $51,750. At the end of the month, only two thirds of the blouses and one half of the skirtshave been sold for a total of $30,600. How many blouses are left in the store?

(A) 260

(B) 270

(C) 520

(D) 810

10. A real estate agent receives $52,000 profit from the sale of some land and invests part at 5% interest andthe rest at 4% interest. If the agent earns a total of $2,290 interest per year, how much did the agent investat 4%?

(A) $20,000

(B) $21,000(C) $31,000

(D) $32,000

11. Walter gave his sister 40% of his color pencils. If he had 45 color pencils, how many did Walter give hissister?

(A) 5

(B) 18

(C) 27

(D) 40

12. The value x of a new piece of equipment depreciates by 20% of the original price each year over a 5-yearperiod. Three years from now, what will be the value of a piece of equipment that is new today?

(A) 0.2 x

(B) 0.4 x

(C) 0.6 x

(D) 0.8 x


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13. Which of the following is the most widely accepted disadvantage of using the mean as a measure ofcentral tendency?

(A) The mean is difficult to compute as compared to other measures of central tendency.

(B) The mean does not take all data points into consideration.(C) The mean is not reliable; it changes considerably for repeated samples.

(D) The mean is influenced by extreme values (skewed distributions).

14. Given five numbers, which of the statements below is always true?

(A) The arithmetic mean cannot be smaller than the largest one of the numbers.

(B) The arithmetic mean cannot be smaller than the smallest two of the numbers.

(C) The arithmetic mean cannot be smaller than the median.

(D) The arithmetic mean cannot be smaller than three of the numbers.

15. A construction company pays its hourly employees $18.50, $16.50, $20.50, $17.50, and $22.50 per hour.What are the mean and the median hourly rates paid to the employees?

(A) Mean = $18.90 and median = $20.50

(B) Mean = $18.50 and median = $18.90

(C) Mean = $19.10 and median = $18.50

(D) Mean = $16.50 and median = $22.50

16. Find the mode and the median in the following daily production of pizzas in a pizza parlor for the firsttwo weeks of February:

155, 150, 153, 165, 145, 160, 153, 160, 149, 153, 160, 148, 147, 160

(A) Mode = 153 and median = 160

(B) Mode = 154 and median = 153

(C) Mode = 160 and median = 153

(D) Mode = 160 and median = 154


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17. Calculate the sample standard deviation for the following data set. Round the final answer to the nearesttenth.

85.6, 94.3, 58.5, 45.5, 79.1, 68.7

(A) 16.4

(B) 16.5

(C) 18.0

(D) 18.1

18. The total number of college credits for a sample of college students is given below:

College Credits Frequency

0–24 4

25–49 3

50–74 6

75–99 3

100–124 5

125–149 9

(A) 44.4

(B) 44.5

(C) 46.0

(D) 46.8

19. A pizza recipe calls for 29

cup of tomato sauce. A recipe for spaghetti sauce requires 56

1 cups of tomato

sauce. How much tomato sauce is needed for both recipes?

(A)11

27

(B)7

115

(C)11

118

(D)1

218


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20. A company creates the following table to estimate the expected value of its new product.

–$2,000,000 0 $10,000 $100,000 $1,000,000 $10,000,000

15% 15% 15% 25% 15% 15%

What is the approximate expected value of the new product in millions of dollars?

(A) $0.10

(B) $1.38

(C) $1.52

(D) $9.11

21. Find the solution to the system of equations.

2 7

2 1

x y

x y

+ =

− =

(A) (1, 5)

(B) (2, 3)

(C) (3, 1)

(D) no solution


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22. Which of the following are NOT valid histograms of a probability distribution?

I.

II.

III.

IV.

(A) I and II

(B) I and IV

(C) II and III

(D) III and IV


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23. The following is the frequency distribution table of the number of sales made by 20 salespeople on agiven day:

Number of Sales Frequency

0 3

1 2

2 5

3 3

4 4

5 1

6 2

This distribution table shows that

(A) fifty percent of the salespeople had less than 3 sales.

(B) forty-five percent of the salespeople had between 2 and 4 sales.

(C) thirty-five percent of the salespeople had only 2 sales.

(D) twenty percent of the salespeople had more than 4 sales.

24. The average weight of a particular mixed fruit bag is 1.81 kg, with a standard deviation of 0.05 kg. If theweights of all the bags are normally distributed, what is the percentage of bags that weigh less than 1.76kg?

(A) 2.5%

(B) 13.5%

(C) 16.0%

(D) 34.0%


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25. What is the average yearly profit for the business below? The business operated for only 8 months in theyear in 2001 and the data is reported for only the first 7 months in 2005. Round the result to the closestnumber listed. (Use the number of months to calculate the weighted average yearly revenue to correct forthe partial years 1 and 5).

Year 2001

(May-Dec) 2002 2003 2004 2005

(Jan-Jul)

Profit $120,000 $200,000 $220,000 $245,000 $150,000

(A) $187,000

(B) $199,000

(C) $200,000

(D) $220,000

26. A student received a 92% score on the first test, a 95% on the second test, and 91% on the final. Thestudent received 100% on the homework. According to the syllabus, each test counts twice as much asthe homework and half as much as the final exam. What is the average score for the course, weighted asprescribed by the syllabus?

(A) 93.1%

(B) 93.6%

(C) 94.1%

(D) 94.5%

27. What is the weighted mean (to the nearest tenth) for the data in the following table?

Value Frequency

5 6

4 5

3 8

(A) 3.0

(B) 3.9

(C) 4.0

(D) 6.3


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28. From the following, calculate the weighted average unit cost, rounded to the nearest cent:

Number of goods

purchased for resale Cost per unit

April 1 inventory 40 $4

May 1 50 $3

October 1 30 $5

December 1 70 $2

(A) $2

(B) $3

(C) $3.16

(D) $3.50

29. From the following, calculate the weighted average unit cost, rounding to the nearest cent:

Number of goodspurchased for resale

Cost per unit

April 1 inventory 30 $8

May 1 25 $9

October 1 20 $10

December 1 20 $13

(A) $8.65

(B) $9.53

(C) $9.74

(D) $10.87

30. Find the roots of the equation y = x2 – 3 x – 28.

(A) {–7, –4}

(B) {–7, 4}

(C) {–4, 7}

(D) {4, 7}


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31. A student’s test grade of 70 represents the 78th percentile of the grades. What percent of students scoredhigher than 70?

(A) 22%

(B) 23%(C) 77%

(D) 78%

32. Which of the following is the graph of y = 2 x – 3?

(A)

(B)

(C)

(D)


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33. What amount of money needs to be deposited in a bank now at 3.29% effective yield to allow cashpayment for a $20,000 car 5 years from now?

(A) $17,012

(B) $17,175(C) $19,342

(D) $20,000

34. When

1i

n= in the formula A = P(1 + i)n, which of these is true as n approaches infinity?

(A) A approaches πP.

(B) A approaches eP.

(C) A approaches 2 .P

(D) A approaches 0.

35. Which of these banks should a business use to receive the maximum interest on its deposits?

(A) A bank that pays 3.15% interest, compounded annually

(B) A bank that pays 3.10% interest, compounded semi-annually

(C) A bank that pays 3.05% interest, compounded quarterly

(D) A bank that pays 3% interest, compounded monthly

36. A person borrows money for car repairs and agrees to pay a total of $140.60 interest at an annual rate of5% for a period of 9 months. How much has the person borrowed using the simple interest method?

(Round to the nearest dollar.)

(A) $312

(B) $937

(C) $2,109

(D) $3,749

37. After purchasing a wristwatch for $420 on a 15%, 180-day note, a customer pays the note on day 120.How much did the customer save by prepaying the note? Assume a 360-day year and that there are noprepayment penalties.

(A) $10.36(B) $10.50

(C) $21

(D) $31.50


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38. A car was bought at the end of the year 2002 for $22,000 and is worth $9,000 at the end of the year 2009.Assuming the depreciation is linear, what is the approximate annual depreciation rate?

(A) $1,440

(B) $1,750(C) $1,860

(D) $2,070

39. A company uses straight-line depreciation to write off the cost of a $100,000 piece of equipment over thenext 20 years. If the annual depreciation expense is $4,000, what is the salvage value of the equipment?

(A) $4,000

(B) $5,000

(C) $10,000

(D) $20,000

40. A business purchased a mainframe computer for $200,000 that at the end of its useful life of 5 years has aresidual value of $50,000. If the declining-balance method with depreciation rate 30% is used, what arethe book values of the computer at the beginning of each of the 5 years?

(A) $200,000; $140,000; $98,000; $68,600; and $48,020

(B) $200,000; $140,000; $98,000; $68,600; and $50,000

(C) $200,000; $160,000; $120,000; $80,000; and $40,000

(D) $200,000; $170,000; $140,000; $110,000; and $80,000

41. A property owner buys a refrigerator for a rental unit for $3,500. The book value of the refrigerator is$500 at the end of 5 years. Using the declining-balance method, given that the depreciation rate is twicethe rate of the straight-line method, what is the book value at the end of the second year?

(A) $840

(B) $1,200

(C) $1,260

(D) $1,400


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42. Company ABC buys equipment for $10,000. At the end of 5 years, the book value will be $2,000. Findthe book value at the end of the second year. Use the declining-balance method, given that thedepreciation rate is twice the rate of the straight-line method.

(A) $2,400(B) $3,600

(C) $4,000

(D) $6,000

43. If a bank charges a discount of 6% for a 6-month loan, what is the equivalent interest rate?

(A) 3.0%

(B) 6.0%

(C) 6.2%

(D) 6.5%

44. Which of the following statements is TRUE for a simple discount note?

(A) The discount is equal to the discount rate applied to the proceeds of the loan.

(B) The discount is the difference between the nominal interest rate and a lower interest ratecharged for the loan.

(C) The discount is the interest deducted in advance from the amount of the loan.

(D) The discount is the option that the borrower can pay back the loan early at a lower interestrate.

45. A baker borrows $10,000 from a bank to purchase a franchise bakery. The loan is at 7.25% payable at theend of the year. Six months into the year, the baker decides to purchase a new high-efficiency oven andgets a simple 12% discount note from the bank against the loan (the full value of the discount note shouldpay for the loan balance at the end of the year). How much cash does the baker get for the discount note?

(A) $10,000.50

(B) $10,081.50

(C) $10,600.75

(D) $10,725.25


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46. Complete the following table by calculating the discount and credit periods using the receipt of goods(ROG) method and assume a non-leap year.

Invoice

date

Date of goods

received Terms

Last day of discount

period

Final day bill is due

(end of credit period)

June 20 July 273/10, n/30

ROG

(A) June 29, July 19

(B) June 30, July 20

(C) August 5, August 25

(D) August 6, August 26

47. Complete the following table by calculating the discount and credit periods.

Invoice

date Terms

Last day of discount

period Final day bill is due

(end of credit period)

February 25 3/10, EOM

(A) March 7, March 27

(B) March 10, March 30

(C) April 10, April 20

(D) April 10, April 30

48. A loan of $9,000 is to be paid in 24 monthly installments of $440. If the loan is repaid at the end of 9months, what is the final pay off?

(A) $6,065

(B) $6,366

(C) $8,376

(D) $8,766


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49. The monthly payment on a $64,000 loan at 12% annual interest is $704.64. Approximately how much ofthe first monthly payment will go toward interest?

(A) $60

(B) $64(C) $640

(D) $644

50. The monthly payment on a $61,000 loan at 11% annual interest rate is $693.57. How much of the firstmonthly payment will go toward the principal?

(A) $93.57

(B) $134.40

(C) $559.17

(D) $600

51. An advertisement offers a car for $11,900 with 60 monthly payments of $199 and a down payment of$199. What is the amount financed and what is the deferred payment price?

(A) Amount financed: $11,900; deferred payment price: $11,940

(B) Amount financed: $11,900; deferred payment price: $12,139

(C) Amount financed: $11,701; deferred payment price: $11,940

(D) Amount financed: $11,701; deferred payment price: $12,139

52. A customer who bought a lawn mower for $650 using a 5-month payment plan of $150 per month

decided to pay off the balance at the end of the third month. What was the payment?

(A) $350

(B) $410

(C) $450

(D) $490

53. A sports shop buys fishing poles for $50 each. The shop adds a 45% markup to each fishing pole. What isthe selling price? (Round to the nearest penny.)

(A) $72.50

(B) $77.50(C) $90.91

(D) $111.11


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54. A corporation with $250,000 annual taxable income has a federal corporate tax rate of 39% and a statecorporate tax rate of 4.63%. If state taxes are deductible on the corporation’s federal income taxes, thenthe total annual tax rate for the corporation is

(A) 34.27%(B) 41.82%

(C) 43.63%

(D) 45.44%

55. A company plans to locate a new manufacturing plant in a state with a 4% corporate tax rate. Thecompany will receive a 50% tax credit for each of the first 3 years after the plant begins operation. Howmuch will the total tax credit be if the company’s taxable income in the first year is $300,000 and doubleseach year after that?

(A) $6,000

(B) $12,000(C) $36,000

(D) $42,000

56. A company sells one of its cars with a current book value of $10,000 to a private party for $12,000. Whathappens to the company’s taxable income as a result of the sale?

(A) It decreases by $12,000.

(B) It decreases by $2,000.

(C) It increases by $2,000.

(D) It increases by $12,000.

57. The cost function of a whitewater rafting business is given by the formula C ( x) = $25,000 + $70 x, where x represents the number of customers. What is the average cost per customer if the business has 2,000customers?

(A) $70

(B) $75

(C) $83

(D) $88


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58. An office-supply store pays its stockers according to the following weekly differential pay schedule:

Items Stocked Amount per Item

1–500 $0.30

501–1000 $0.50

Over 1000 $0.60

(A) $520

(B) $560

(C) $600

(D) $720

59. A pizza restaurant pays its delivery drivers according to the following weekly differential pay schedule:

Orders Delivered Amount per Order

1–60 $3.00

61–100 $3.50

Over 100 $4.50

(A) $420

(B) $490

(C) $500

(D) $630

60. A small business is selling widgets for $125 each. The per-widget production costs are $97.50, and thebusiness can sell 130 widgets per month. What level of fixed costs per month would correspond to thebusiness breaking even (revenues equal the expenses)?

(A) $3,575

(B) $3,610

(C) $3,625

(D) $3,652


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61. A small airline has fixed expenses of $10,000 per month and can sell tickets for $250 per seat. Thevariable costs are $200 per passenger. If the airline starts with 100 tickets sold per month in January andhopes to increase sales by 30 additional tickets each month, what is the first month of the year when itwill break even?

(A) February

(B) March

(C) April

(D) May

62. A mobile phone manufacturer has fixed costs of $100,000 per month. The per-phone production cost istypically 50% of the manufacturer’s suggested retail price, while phones normally sell for $60 after adiscount of 25% off the manufacturer’s suggested retail price. How many phones does the manufacturerneed to sell per month to break even?

(A) 1,000(B) 2,000

(C) 5,000

(D) 10,000

63. A company that produces pens sells each for $1.99. Its variable cost per unit is $0.74. What is thecontributing margin (CM) and the breakeven point (BE) for the company assuming it has a fixed cost of$75,000?

(A) CM = $0.74; BE = 101,352

(B) CM = $1.25; BE = 37,689

(C) CM = $1.25; BE = 60,000

(D) CM = $1.99; BE = 37,689


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64. A restaurant sells pizzas for $9.99 each with the variable cost for making one pizza being $3.50.Assuming an annual fixed cost of $815,000, use the given graph to determine what the breakeven point(BE) is.

(A) BE = 232,858

(B) BE = 150,000

(C) BE = 125,578

(D) BE = 81,582

65. The following is a part of the annual report of a small business company:

(Dollars in millions)

Net revenue (sales) $ 265

Net earnings 147

Total assets 2,015

Total liabilities 1,768

Total stockholders’ equity 427

(A) 34.43%

(B) 44.53%(C) 57.85%

(D) 62.06%


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66. From the following facts, find the current ratio. Round the final answer to the nearest hundredth

Current assets $14,000

Accountsreceivables

$5,000

Current liabilities $20,000

Inventory $4,000

Net sales $40,000

Total assets $38,000

Net income $10,100

(A) 0.61

(B) 0.70

(C) 0.90

(D) 0.95

67. Give the trend analysis for the following company’s net income assuming that the base year is 2005.Round to the nearest whole percent.

Year 2005 2006 2007

Net income $54,000 $42,000 $64,000

(A)Year 2005 2006 2007

Net income 100% 78% 119%

(B)Year 2005 2006 2007

Net income 100% 129% 84%

(C)

Year 2005 2006 2007

Net income 84% 66% 100%

(D)Year 2005 2006 2007

Net income 100% 78% 152%


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68. Using 2009 as the base year, express sales, gross profit, and net income to give a trend analysis for 2010.(Round to the nearest percent.)

Given (Base Year 2009)

2010 2009

Sales 225,000 215,000

Gross Profit 90,000 110,000

Net Income 80,000 65,000

(A)

Trend Analysis

2010 2009

Sales 105% 100%

Gross Profit 82% 100%

Net Income 123% 100%

(B)

Trend Analysis

2010 2009

Sales 96% 100%


Net Income 81% 100%

(C)

Trend Analysis2010 2009

Sales 100% 106%


Net Income 100% 123%

(D)

Trend Analysis

2010 2009

Sales 100% 96%

Gross Profit 100% 122%Net Income 100% 81%


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69. From the information given, what is the profit margin of net sales for May’s Flower Shop?

May’s Flower Shop

Total Current Assets: $10,000

Accounts Receivable: $12,000

Total Current Liabilities: $ 4,000

Inventory: $ 8,000

Net Sales: $15,000

Total Assets: $20,000

Total Liabilities: $ 6,000

Net Income: $ 6,000

(A) 20%

(B) 30%

(C) 40%

(D) 50%


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70. Which of the following histograms shows the coffee-drinking habits of the people in one office if 5people drink either 1 or no cups of coffee, 4 people drink 2 cups, 6 people drink 4 cups, and 3 peopledrink 5 cups?

(A)

(B)

(C)

(D)

71. Stock in Value Unlimited Ltd. sells for $150 per share, which puts it at a P/E ratio of 25. The P/E ratio isthe ratio of the stock price per share to the dividend paid per share. What is the expected dividend for astockholder who owns 1,000 shares?

(A) $3,750

(B) $6,000

(C) $25,000(D) $150,000


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72. Troglodyte Networks Inc. has 1.5 million shares outstanding and is trading at $20 per share. The P/Eratio is the ratio of the stock price per share to the dividend paid per share and is 10 for Troglodyte. Whattotal amount of earnings is the company expected to pay?

(A) $3,000,000(B) $15,000,000

(C) $30,000,000

(D) $150,000,000

73. A company with 2.5 billion shares outstanding announced earnings per share of $2. The company stockis valued at $40 billion. What is the P/E ratio for the company (the P/E ratio being the ratio of the stockprice per share to the dividend paid per share)?

(A) 1.25

(B) 8

(C) 16

(D) 20

74. From the following Dow stock quotation calculate the price-earnings ratio (P/E ratio) (to the nearestwhole number) and the yield (YLD) on the stock (to the nearest tenth percent). Assume Dow earnsannually $5.48 per share.

52 WEEKS

HI LO

STOCK(SYM)

DIV YLD%

PE VOL100’S

CLOSE NETCHG

45.87 15.98 XYZ 2.19 20580 93.64 +.83

(A) P/E = 17; YLD = 2.3%

(B) P/E = 17; YLD = 5.9%

(C) P/E = 43; YLD = 2.3%

(D) P/E = 43; YLD = 5.9%

75. Find the minimum value of z = 23 x + 21 y + 22 subject to: x 0, y 0 and x + y 1.

(A) 22

(B) 43

(C) 45

(D) 63


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76. A company designs and sells two types of rings, M and N, and can produce up to 24 rings each day usingup to 60 total hours of labor. If it takes 3 hours to make one M ring, versus 2 hours to make one N ring,what is the maximum profit possible, if the profit on a M ring is $30 and on a N ring is $40?

(A) $880(B) $960

(C) $1040

(D) $1120

77. A manufacturer of bicycles builds one-, three-, and ten-speed models of both aluminum and steel. Thecompany has available 91,800 units of steel and 42,000 units of aluminum. The one-, three-, and ten-speed models respectively need 20, 30, and 40 units of steel and 12, 21, and 16 units of aluminum. Thecompany makes a profit of $8 per one-speed bike, $12 per three-speed bike, and $24 per ten-speed bike.What is the maximum possible profit?

(A) $54,360(B) $55,080

(C) $56,420

(D) $57,195

78. Minimize z = 3 x + 2 y, subject to the constraints x + y 100 and 3 x + 4 y 350, with x 0 and y 0.

(A) 0

(B) 180

(C) 400

(D) 440


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79. The following table is a section of a 12-month amortization schedule for a loan of $1,000.

Payment

Number Payment

Amount Interest for

Period Portion to

Principal Principal at

end of Period

4 $88.85 7.61 $81.24 $679.84

5 $88.85 6.80 $82.05 $597.79

6 $88.85 5.98 $82.87 $514.92

According to the table, what is the total amount paid to the loan’s principal during months 4, 5, and 6?

(A) $20.39

(B) $164.92

(C) $246.16

(D) $266.55

80. Five years from now, a company will have to replace a machine that will cost $2 million. Approximatelyhow much money should the company start putting aside in a bank account at 6% per year to ensure themoney for replacement will be available?

(A) $1,410,000

(B) $1,495,000

(C) $1,570,000

(D) $1,887,000

81. The amount of money A that must be added each year to a bank account paying i% annual interest tocreate a desired future value F after n years can be calculated by the formula:

( )1 1

Fi A

ni

=

+ −

According to the formula, approximately how much money should be added to the account each year at4.5% annual interest to create a value of $1,000,000 twenty-four years from now?

(A) $24,000

(B) $28,800

(C) $41,700(D) $45,000


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82. A person deposits $2,000 split between two bank accounts, both advertising a rate of 5%. On account A,interest is compounded semi-annually, while on account B, interest is compounded daily (assume a 365-day year). How much more money will there be in account B than in account A at the end of the year?

(A) $0.64(B) $0.96

(C) $1.03

(D) $1.14

83. What annual percentage rate compounded annually is needed to grow $250,000 into $270,000 in 6 years?

(A) 1.25%

(B) 1.29%

(C) 1.33%

(D) 1.35%

84. A worker deposits a promotion bonus of $ x in an interest bearing account at rate r 1 compounded monthly.Six years later, the rate decreases to r 2, still compounded monthly. Another four years later, the workerconsults a financial planner and learns that because of the change to the lower rate the account is nowworth only 80% of what it could have been had the higher rate remained in effect for the entire period.What is the incremental difference between rates r 1 and r 2?

(A) 1.83%

(B) 2.74%

(C) 3.63%

(D) 5.57%

85. A designer signs an agreement to pay a bank $25,000 in 5 months. The bank charges a 13% discount rate.Calculate the actual interest rate paid by the designer. Round the final answer to the nearest tenth percent.

(A) 13.0%

(B) 13.7%

(C) 13.8%

(D) 14.0%


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DSST Business Math

29



86. Find the effective annual rate corresponding to a nominal annual rate of 12% compounded monthly.Round the final answer to the nearest hundredth percent.

(A) 12.00%

(B) 12.67%(C) 12.68%

(D) 12.69%

87. Find the effective annual rate corresponding to a nominal annual rate of 8% compounded quarterly.

(A) 8.00%

(B) 8.21%

(C) 8.22%

(D) 8.24%

88. Four banks, A, B, C, and D, charge interest, respectively, at the rate of 8.06% compounded monthly,8.12% compounded quarterly, 8.25% compounded semiannually, and 8.35% compounded annually.Which of these four banks charges the highest finance charge on the money borrowed?

(A) Bank A

(B) Bank B

(C) Bank C

(D) Bank D


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30



89. An airline charges the following fees based on the weight of a passenger’s checked luggage:

I. No fee for luggage weighing up to 40 poundsII. Flat fee of $50 for luggage weighing between 40 and 80 pounds

III. Additional fee of $1.25 per pound for luggage weighing more than 80 pounds

Which of the following graphs represents this situation?

(A)

(B)

(C)

(D)


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31



90. Suppose the tax, T , paid by a person with taxable income of x dollars is given by the following function:

0.05 if 0 20,000( )

0.1 1,000 if 20,000

x xT x

x x

≤ ≤=

− >

What is the tax that a person with a taxable income of $30,000 will have to pay?

(A) $1,000

(B) $1,500

(C) $2,000

(D) $2,500

91. The profit P, in thousands of dollars, of a company is given as a function of the number x of units it sells:

P( x) = –0.4 x2 + 12 x – 15

What is the profit if the company sells 10 units?

(A) $65,000

(B) $101,000

(C) $109,000

(D) $145,000

92. Emile bought two jackets for $35.75 each, three pairs of jeans for $25, and a hat for $10.60. What is thetotal price of the items she purchased?

(A) $71.35

(B) $107.10

(C) $132.10

(D) $157.10

93. Jason is being paid $120 a month for a bike that he sold with an interest rate of 5% compounded monthlyfor 4 years. What is the present value?

(A) $5,318.87

(B) $5,760

(C) $5,990.40(D) $6,048


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32



94. Al plans to loan his friend $10,000 to open a restaurant. Al will collect the loan in 7 years with an interestrate of 7% compounded annually. How much will Al receive at the end of the loan term?

(A) $10,415.55

(B) $10,770(C) $16,057.81

(D) $22,521.92

95. Jan received $15,000 in graduation gifts. She placed it in an account paying 7% interest compoundedsemi-annually. Two years later, she inherited $7,000 and placed it in the same account. How much willshe have at the end of 5 years?

(A) $23,540

(B) $29,613.58

(C) $30,856.14

(D) $96,000

96. Stan bought a 4-year certificate of deposit for $10,000 with a rate of 6% compounded semi-annually.How much will he make in interest after 4 years?

(A) $600

(B) $2,624.77

(C) $2,667.70

(D) $12,667.70

97. Kevin is saving for his senior trip. He plans to place $300 in an account every quarter for 2 years with 8%interest compounded quarterly. What will be the final total?

(A) $858

(B) $2,574.89

(C) $3,200

(D) $3,433.19

98. What is the effective annual rate of interest for a loan with a nominal interest rate of 9%? The loan iscompounded monthly. Round the final answer to the nearest thousandth percent.

(A) 9.000%(B) 9.308%

(C) 9.381%

(D) 9.416%


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99. What is the effective annual rate of interest for a savings account with a nominal interest rate of 1.5%?The loan is compounded daily. Round the final answer to the nearest thousandth percent.

(A) 1.500%

(B) 1.509%(C) 1.511%

(D) 3.000%

100. Carl has $1,000 to invest. If he would like to have $1,500 at the end of three years, what should be theinterest rate of the investment account? Round the final answer to the nearest hundredth percent.

(A) 13.89%

(B) 16.67%

(C) 50.00%

(D) 66.67%


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ANSWER KEY - Page 34

1. The correct answer is C. Find the difference between the current price and the original price and dividethe result by the original price:

$127 $10 $117

$11711.7, or 1,170%

$10

− =

=

2. The correct answer is B. Find the product of the original stock price, 1 minus 10%, and 1 plus 10%:

$100 × 0.90 × 1.10 = $99

3. The correct answer is C. Multiply the first fraction by the reciprocal of the second fraction:

3 3 9

11 2 22=×

4. The correct answer is A. Subtract 6 from each part, divide each part by –5, and reverse each inequalitysign:

4 6 5 12

2 5 6

2 5 6

5 5 5

6 2

5 5

x

x

x

x

< − <

− < − <

− −< <

− − −

−< <

5. The correct answer is B. Subtract the equations and then simplify:

$312 11

$240 3$72 8

$9

T NV F

V F

V F V

V

= +

= +

= +

=

=

Substitute V = $9 into the first equation and solve for F :


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ANSWER KEY

DSST Business Math


$312 11 $9

$213

$312 $99

F

F

F

= × +

=

= +

Plug N = 25, V = $9, and F = $312 into T = NV + F and solve:

T = 25 × 9 + $213 = $438

6. The correct answer is B. Divide both sides by 4; then add 8 to both sides:

( )4 8 20

8 5

13

Q

Q

Q

− =

− =

=

7. The correct answer is C. Divide both sides by 4; then add 6 to both sides:

4( 6) 28

6 7

13

d

d

d

− =

− =

=

8. The correct answer is C. Subtract 3 from both sides; then multiply both sides by 4:

3 154

124

48

B

B

B

+ =

=

=

9. The correct answer is B. The beginning inventory equation is:

$45s + $35b = $51,750

The inventory sold equation is:

$45 $70

$30,6002 3s b+ =

Then employ the elimination method. Multiply the inventory sold equation by 2 so that coefficient of s is the

same in each equation:


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ANSWER KEY

DSST Business Math


$45 $70$30,600

2 3

$140$45 $61,200

3

s b

s b

+ =

+ =

You can then eliminate the s-term and solve for b, the beginning number of blouses:

359,450

3

810

b

b

=

=

Substitute b = 810 into the first equation and solve for s, the beginning number of skirts:

45 35(810) 51, 750

520

s

s

+ =

=

Then multiply the beginning number of blouses by one-third:

1810 270

3=

10. The correct answer is C. The questions produces two equations:

x + y = $52,000

and

0.05 x + 0.04 y = $2,290,

where x is the amount invested at 5% and y is the amount invested at 4%.

This is the elimination method. Multiply the second equation by 20 so that coefficient of x is the same in each

equation:

x + 0.8 y = $45,800

You can then eliminate the x-term and solve for y.

0.2 $6, 200

$31,000

y

y

=

=

11. The correct answer is B. Find the product of 40% and 45:


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ANSWER KEY

DSST Business Math


0.4 × 45 = 18

12. The correct answer is B. From 1, subtract the product of 3 and 20% to find the coefficient of x:

1 – (3 × 0.2) = 0.4

The value after three years is 0.4 x.

13. The correct answer is D. The biggest disadvantage to using the mean as a measure of central tendency isthat it is affected by outliers (extreme values).

14. The correct answer is B. The arithmetic mean cannot be smaller than the smallest two of the numbers.

15. The correct answer is C. Divide the sum of the elements by 5 to find the mean:

$18.50 16.50 20.50 17.50 22.50$19.10

5

+ + + +=

To find the median, put the elements in ascending order then find the middle element:

$16.50, $17.50, $18.50, $20.50, $22.50

16. The correct answer is C. Write the elements in ascending order:

145, 147, 148, 149, 150, 153, 153, 153, 155, 160, 160, 160, 160, 165

The element that occurs most often, 160, is the mode.

The average of the two middle values is the median:

153 153153

2

+=

17. The correct answer is C. Find the mean:

85.6 94.3 58.5 45.5 79.1 68.7

71.956

+ + + + +=

Square the difference between the mean and each element:


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ANSWER KEY

DSST Business Math


2

2

2

2

2

2

(85.6 71.95) 186.3225

(94.3 71.95) 499.5225

(58.5 71.95) 180.9025(45.5 71.95) 699.6025

(79.1 71.95) 51.1225

(68.7 71.95) 10.5625

− =

− =

− =

− =

− =

− =

Take the square root of the average of the previous values:

186.3225 499.5225 180.9025 699.6025 51.1225 10.562518.0

6 1

+ + + + +

−

=

18. The correct answer is C. Find the mean of the midpoints of the classes:

85.6 94.3 58.5 45.5 79.1 68.771.95

6

+ + + + +=

Square the difference between the mean and each element:

2

2

2

2

2

2

(85.6 71.95) 186.3225

(94.3 71.95) 499.5225

(58.5 71.95) 180.9025(45.5 71.95) 699.6025

(79.1 71.95) 51.1225

(68.7 71.95) 10.5625

− =

− =

− =

− =

− =

− =

Take the square root of the average of the previous values:

186.3225 499.5225 180.9025 699.6025 51.1225 10.562518.0

6 1

+ + + + +

−

=


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ANSWER KEY

DSST Business Math


19. The correct answer is D. Rewrite each fraction using the least common denominator, which is 18:

2 4

9 18

5 11 331

6 6 18

and

=

= =

Add the fractions together and then simplify:

4 33 3718 18 18

12

18

+ =

=

20. The correct answer is B. Find the sum of the products of each percent and value pair (in millions):

(0.15 × –2) + (0.15 × 0) + (0.15 × 0.01) + (0.25 × 0.1) + (0.15 × 1) + (0.15 × 10) = 1.38

21. The correct answer is C. Multiply the second equation by –2 and get:

–2 x + 4 y = –2

Add this equation to the first equation, then solve for y:

5 5

1

y

y

=

=

Substitute y = 1 into the first equation, then solve for x:

2 (1) 7

2 6

3

x

x

x

+ =

=

=

The solution is (3, 1).


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22. The correct answer is D. The values for a probability distribution total 1. The values in graph III total0.8 and the values in graph IV total 1.2.

23. The correct answer is A. There were 10 people with less than 3 sales. That amounts to 50% of thesalespeople surveyed.

24. The correct answer is C. The value 1.76 is one standard deviation below the mean. In a normaldistribution, one to four standard deviations below the mean accounts for about 15.8% of the set, which isabout 16%.

25. The correct answer is B. Multiply each profit by the number of months reported. Then add the valuesand divide by the total months in the table:

(8 120, 000) (12 200, 000) (12 220, 000) (12 245, 000) (7 150, 000)$195,882.35

8 12 12 12 7

× + × + × + × + ×=

+ + + +

26. The correct answer is A. If homework counts for h, then a test counts for 2h and the final counts as 4h.Set the sum of the values of each assignment equal to 100 and solve for h:

2 2 4 100

100

9

h h h h

h

+ + + =

=

Test one:100

0.92 2 20.49

× × =

Test two:100

0.95 2 21.19

× × =

Homework:100

100 1 11.19

× × =

Final exam:100

0.91 4 40.49

× × =

Add these values to find the student's course score:

20.4 21.1 11.1 40.4 93.1+ + + =


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ANSWER KEY

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27. The correct answer is B. Find the sum of the products of the ordered pairs, then divide by the sum of thefrequencies:

(5 6) (4 5) (3 8)3.9

6 5 8

× + × + ×=

+ +

28. The correct answer is C. Find the sum of the products of the number pairs, and then divide by the sumof the frequencies:

(4 40) (3 50) (5 30) (2 70)$3.16

40 50 30 70

× + × + × + ×=

+ + +

29. The correct answer is C. Find the sum of the products of the number pairs, and then divide by the sumof the frequencies:

(8 30) (9 25) (10 20) (13 20)$9.7430 25 20 20

× + × + × + ×

=+ + +

30. The correct answer is C. Factor the right-hand side:

y = ( x + 4)( x – 7)

Set each factor equal to zero, and then solve for x:

4 0

4

7 0

7

x

x

x

x

+ =

= −

− =

=

The roots of the equation are –4 and 7.

31. The correct answer is A. Scoring in the 78th percentile means the grade of 78 is better than or equal to78% of the test population. Subtract 78% from 1 to find the percent of students who scored higher than 70:

1 – 0.78 = 0.22, or 22%

32. The correct answer is A. The points that make the equation true are (0, 3), (2, 1), and (4, 5). Choice A isthe graph of the line containing these points.

33. The correct answer is A. Use the compound interest formula 1 ,nt

r A P

n

= +

where A is the final

amount, P is the principal, r is the rate, n is the yearly compoundings, and t is the time in years:


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ANSWER KEY

DSST Business Math


( )

1 5

5

0.0329$20,000 1

1

$20,000

1.0329

$17,011.34

P

P

P

×

= +

=

=

34. The correct answer is B. Constant e is given by the limit1

lim 1 .n

n n→∞

+

Therefore, as n approaches

infinity in A = P(1 + i)n, (1 + i)n approaches e and A approaches eP.

35. The correct answer is A. Substitute each value into the rate portion of the compound interest formula

1

nt r

A P

n

= +

and simplify to find the largest value.

Choice A:

10.0315

1 1.03151

t t

+ =

Choice B:

20.031

1 1.031242

t t

+ =

Choice C:

40.0305

1 1.030854

t t

+ =

Choice D:

120.03

1 1.0304212

t t

+ =

Choice A is the largest value, so it would maximize the interest.

36. The correct answer is D. Substitute the given values into the simple interest formula I = PRT and solvefor P:

9$140.60 0.05

12

$3,749.33

P

P

= × ×

=


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ANSWER KEY

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37. The correct answer is B. Substitute the two sets of values into the simple interest formula I = PRT , andthen subtract to find the savings from prepaying. So:

Interest for 180 days:

180$420 0.15 $31.50

360 I = × × =

Interest for 120 days:

120$420 0.15 $21

360 I = × × =

The difference:

$31.50 – $21 = $10.50

38. The correct answer is C. Subtract the original cost from the ending value, and then divide by the years inuse:

22,000 9,000$1,857.14

2009 2002

−=

−

39. The correct answer is D. Find the difference between the original cost and the product of the usableyears and annual depreciation expense:

$100,000 – (20 × $4,000) = $20,000

40. The correct answer is A. Multiply the value at the beginning of a year by 1 minus 30% to find the nextyear's beginning-of-year value.

At the start of Year 1, the value was $200,000.Beginning value for Year 2: $200,000 × 0.7 = $140,000Beginning value for Year 3: $140,000 × 0.7 = $98,000Beginning value for Year 4: $98,000 × 0.7 = $68,600Beginning value for Year 5: $68,600 × 0.7 = $48,020

41. The correct answer is C. Subtract the cost and salvage value, and then divide by usable years to find the

straight-line depreciation:

$3,500 $500$600

5

−=

Divide the straight-line depreciation by the difference in cost and salvage value to find the straight-line

depreciation rate:


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ANSWER KEY

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$60020%

$3,500 $500=

−

Double the straight-line depreciation rate to get the declining-balance rate of 40%.

Multiply the cost by 1 minus the declining-balance rate to find the book value at the end of the first year:

$3,5000 × (1 – 0.4) = $2,100

Multiply the first year-end value by 1 minus the declining-balance rate to find the book value at the end of the

second year:

$2,100 × (1 – 0.4) = $1,260

42. The correct answer is B. Subtract the cost and salvage value, then divide by usable years to find thestraight-line depreciation:

$3,500 $500$600

5

−=

Divide the straight-line depreciation by the difference in cost and salvage value to find the straight-line

depreciation rate:

$60020%

$3,500 $500=

−

Double the straight-line depreciation rate to get the declining-balance rate of 40%.

Multiply the cost by 1 minus the declining-balance rate to find the book value at the end of the first year:

$10,000 × (1 – 0.4) = $6,000

Multiply the first year-end value by 1 minus the declining-balance rate to find the book value at the end of the

second year:

$6,000 × (1 – 0.4) = $3,600


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ANSWER KEY

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43. The correct answer is C. Use the simple interest formula I = PRT to find the interest:

60.06

120.03

I P

P

= × ×

=

Subtract the interest from the principal to find the proceeds of the loan:

P – 0.03P = 0.97P

Divide the interest by the product of the proceeds and time to find the interest rate:

0.03 0.03

6 0.485

0.97 12

6.2%

P P

P

P

=

×

=

44. The correct answer is C. A simple discount note has the bank discount deducted in advance.

45. The correct answer is B. Substitute the original loan values into the following formulas:

Maturity Value × Rate × Time = Interest

$10, 000 0.0725 1 $725× × =

Original Proceeds × Rate × Time = Interest

$10,725 0.12 0.5 $643.50× × =

Then:

($10,000 + $725) – $843.50 = $10,081.50

46. The correct answer is D. The last day of the discount period is determined by the second number in theterms column, or 10 days. Ten days from July 27, the date the goods were received, is August 6. The finalday the bill is due is the third number in the terms column, or 30 days after receipt of goods (ROG). Thirtydays from receipt of goods (July 27) is August 26.

47. The correct answer is B. The buyer can take the cash discount if he or she pays the invoice by the first10 days of the next month, which is by March 10. The final due date of the bill is within 20 days of the end ofthe discount period, which is March 30.

48. The correct answer is A. Multiply the unpaid months by the monthly installment to find the balance ofthe outstanding loan:

16 × $440 = $7,040


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ANSWER KEY

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Find the monthly principal payment:

$9,000 $37524

=

Find the product of the months past the ninth payment and the difference between monthly installment

payment and the monthly principal payment to find the expected interest for the remaining payments:

15 × ($440 – $375) = $975

Subtract the balance of the outstanding loan and the expected interest for the remaining payments:

$7,040 – $975 = $6,065

49. The correct answer is C. Substitute the given values into the interest formula: I = PRT :

1$64,000 0.12 $639.97

12× × =

50. The correct answer is B. Substitute the given values into the interest formula, I = PRT :

1$61,000 0.11 $599.17

12× × =

Then substitute the result value into the formula P – I = A:

$693.57 – $559.17 = $134.40

51. The correct answer is D. Substitute the given values into the following formulas:

Cash price – Down payment = Amount Financed

$11,900 – $199 = $11,701

Total of payment + Down payment = Deferred payment price

$11,940 + $199 = $12,139


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52. The correct answer is B. Multiply the remaining months by the monthly installment to find the balanceof the outstanding loan:

3 × $150 = $450

Divide the price of the mower by 5 to find the monthly principal payment:

$650$130

5=

Find the product of the remaining months and the difference between monthly installment payment and the

monthly principal payment to find the expected interest for the remaining payments:

2 × ($150 – $130) = $20

Subtract the expected interest for the remaining payments from the balance of the outstanding loan:

$450 – $40 = $410

53. The correct answer is A. To find the selling price use the following formula:

( )

( )

Selling Price Cost Markup Percentage Cost

$50 × 45% + $50

$72.50

= × +

=

=

54. The correct answer is B. Calculate the state income tax:

$250,000 × 0.0463 = $11,575

Subtract the amount of the state tax from the taxable income and multiply that amount by the federal tax rate

to find the federal tax:

$250,000 – $11,575 = $238,425

$238,425 × 0.39 = $92,985.75

Divide the total of the taxes by the original annual taxable income to find the tax rate:

$11,575 $92,985.750.418243, or 41.82%

$250,000

+=


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55. The correct answer is D. Calculate the total tax credit for Year 1:

$300,000 × 0.02 = $6,000

Double the year 1 value to find year 2, double the year 2 value to find year 3, then add the totals:

$6,000 + $12,000 + $24,000 = $42,000

56. The correct answer is C. The company's taxable income increases by $2,000 because it sold the car formore than its book value.

57. The correct answer is C. Substitute the given values into the formula:

( ) $25,000 $70

$25,000 ($70 2,000)$165,000

C x x= +

= + ×

=

then find the average cost per customer:

# of customers 2, 000

( ) $165,000

$83

C x=

=

58. The correct answer is A. Substitute the given values into the following formula:

( ) ( ) ( )

Gross Pay = Amount per Item Items Stocked

$0.30 500 $0.50 500 $0.60 200

$150 $250 $120

$520

×

= × + × + ×

= + +

=

59. The correct answer is C. Substitute the given values into the formula:

( ) ( ) ( )

Gross Pay = Amount per Order × Orders Delivered

$3.00 60 $3.50 40 $4.50 40

$180 $140 $180

$500

= × + × + ×

= + +

=


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ANSWER KEY

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60. The correct answer is A. Substitute the given values into the formula:

( ) ( )

Fixed Cost = Selling Price(Quanity) - Variable Cost (Quanity)

$125 130 $97.50 130$16,250 $12,675

$3,575

= × − ×

= −

=

61. The correct answer is D. Substitute the given values into the breakeven point formula:

Fixed CostBreakeven Point =

Selling Price - Variable Cost

$10,000002

$250 $200=

−

Starting with 100 ticket sales in January and adding 30 sales per month (100 in January, 130 in February, 160in March, etc.), May will be the first month the airline will have at least 200 passengers.

62. The correct answer is C. Solve for the manufacturer's suggested retail price:

$60$80

0.75=

Then calculate production cost:

$80 × 50% = $40

Substitute the values into the breakeven point formula:



$100,0005,000

$60 $40=

−

63. The correct answer is C. Substitute the given values into the contributing margin (CM) formula:

CM = Selling Price - Variable Cost

$1.99 $0.74

$1.25

= −

=

Substitute the given values into the breakeven point formula:


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ANSWER KEY

DSST Business Math




$75,000

60,000

$1.99 $0.74

=

=−

64. The correct answer is C. Substitute the given values into the breakeven point formula:

Breakeven Point =

$815,000

125,577.78

Fixed Cost

Selling Prince - Variable Cost

$9.99 $3.50=

=

−

65. The correct answer is A. Substitute the given values into the return on equity formula:

Net EarningsReturn on Equity =

Stockholders' Equity

147

.3443, or 34.43%

427

0

=

=

66. The correct answer is B. Substitute the values into the current ratio formula:

Current AssetsCurrent Ratio =Current Liabilities

$14,000

0.70, or 70%

$20,000

=

=

67. The correct answer is A. Divide the net income for 2006 and 2007 by the net income for base year 2005:

$42,0000.777, or 78%

$54,000

$64,0001.185, or 119%

$54,000

2006:

2007:

=

=


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ANSWER KEY

DSST Business Math


68. The correct answer is A. Divide the sales, gross profit, and net income for 2010 by the respective valuesduring base year 2009:

$225,000 1.0465, or 105%$215,000

Sales: =

$90,0000.818, or 82%

$110,000Gross Profit: =

$80,0001.231, or 123%

$65,000Net Income: =

69. The correct answer is C. Use this formula to find the profit margin of net sales:

Net incomeProfit margin =

Net sales

$6,000

$15,000

.40, or 40%=

=

70. The correct answer is A. Graph A shows 5 people drink either 1 cup or less of coffee, 9 people drink 2cups or less of coffee, 9 people drink 3 cups or less of coffee, 15 people drink 4 cups or less of coffee, and 18people drink 5 cups or less of coffee.

71. The correct answer is B. Substitute the given values into the PE ratio formula and solve for dividendspaid per share and then solve where DPS is $6 and total shares is 1000:

Market PriceP/E =

Earnings per Share

$150$25

$6

x

x

=

=

$6 × 1,000 shares = $6,000


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ANSWER KEY

DSST Business Math


72. The correct answer is A. First, substitute the given values into the P/E formula and solve:

Market PriceP / E =

Earnings per Share$20

$10

$2

x

x

=

=

Knowing that earnings per share (EPS) is $2, substitute the value into the EPS formula, where EPS is $2 and

TSO is 1.5 million:

Annual Earnings = EPS × TSO

$2 1,500,000

$3,000,000

= ×

=

73. The correct answer is B. Substitute the values into the P/E ratio formula and solve where CP is $16 andA/E is $2:

Closing Price Per ShareP/E =

Annual Earnings Per Share

$16

$2

8

=

=

74. The correct answer is A. Substitute the values into the P/E ratio formula where CP is $93.64 and AE is$5.48:

Closing Price Per ShareP/E =

Annual Earnings Per Share

$93.64

$5.48

17.09, or 17=

=

Substitute the values into the stock yield formula where AD is 2.19 and AE is 93.64:

Annual Dividend Per ShareYield =

Today's Closing Price Per Share

$2.19

$93.64

2.3%0.023, or

=

=


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ANSWER KEY

DSST Business Math


75. The correct answer is B.

1 2

1 2

1 2

2 3

1 1 101 0

23 21 22

1 1 23

01 21

01 22

230 01 1 1

0 0 0 211 1

0 0 0 221 1

0 0 21 1 1

0 0 0 211 1

0 0 0 1 1

x s s z y

x s s z y

R R

R R

−

− → −

+ → 43

The minimization is z = 43.

76. The correct answer is B. Maximize z = 30 x1 + 40 x2, subject to 3 x1 + 2 x2 60 and x1 + x2 24, with x1 0and x2 0:

1 2 1 2

1 2 1 2

1 2

2 3

3 0 0 602 1

0 01 1 1 24

-30 -40 0 0 01

2 0 01 1 -2 12

0 01 1 1 24

40 10 0 0 40 9601

x x s s z

x x s s z R R

R R

− →

+ →

The maximum profit is $960 when 24 N rings are produced.


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ANSWER KEY

DSST Business Math


77. The correct answer is B. Maximize z = 8 x1 + 12 x2 + 24 x3, subject to 20 x1 + 30 x2 + 40 x3 91,800 and12 x1 + 21 x2 + 16 x3 42,000, with x1 0, x2 0, and x3 0.

( )

( )

31 2 1 2

31 2 1 2

1 2

1 3

91,80020 30 40 0 01

42,00016 0 012 21 1

0-8 0 0-12 -24 1

91,80020 30 40 0 01

26, 40020 45 0 5 0-2

275, 40020 30 0 3 0 5

- 5

3 5

x x x s s z

x x x s s z

R R

R R

→

→

+

+

It follows that x1 = 0, x2 = 0, and x3 = 2,295 where x3 is the number of ten-speed bikes needed to maximizeprofits. Multiply x3 = 2,295 by the respective profit per unit:

$2,295 × $24 = $55,080


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ANSWER KEY

DSST Business Math


78. The correct answer is C.

1 2 1 2

1 2 1 2

1 2

2 3

1 2 1 2

1 2

2 3

1001 1

3 3504

3 02

3 31

1 4 2

100 350 0

3 0 0 31 10 01 4 1 2

100 350 0 0 01

4 3 0 3 0 61 4

0 01 4 1 2

175 2 25 0 0 175 3502

0 04 4 4

0 01 4 1

25 0 100

x x s s z

x x s s z

R R

R R

x x s s z

R R

R R

− −

− → −

+ → −

− → − −

+ →

4

2

0 200 2

400

The minimization is z = 400.

79. The correct answer is C. Add the amounts in the portion to principal column:

$81.24 + $82.05 + $82.87 = $246.16


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ANSWER KEY

DSST Business Math


80. The correct answer is B. Substitute the given values into the present value formula where FV is$2,000,000, i is 6%, and n is 5:

( )( )

-5

-

1

$2,000,000 1 0.06

$1,495,516.35

$1,495,000

n

PV iFV = +

= +

=

=

81. The correct answer is A. Substitute the given values into the formula where F is $1,000,000, i is 4.5%,and n is 24:

( )

( )

( )24

1 1

$1,000,000 0.045

1 0.045 1

$23,987.03

$24,000

Fi A

ni

=

+

+ −

=

=

−

=

82. The correct answer is A. Substitute the given values into the future value for lump sum formula, whereFV is future value and PV is present value. Solve the two equations and find the difference between theresults.

For account A, where i is 5%, PV is $1,000, and n is 365:

( )

( ) ( )365

1

,000 1 0.05 ,000 1 0.025

$1,051.27

$1 $1

nFV PV i= +

+ += −

=

For account B, where i is 5%, PV is $1,000, and n is 2:

( )

( ) ( )2

1

,000 1 0.05 ,000 1 0.025

$1,050.63

1 1

nFV PV i= +

+ += −

=

Subtract to find the difference between the accounts:

$1,051.27 – $1,050.63 = $0.64


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ANSWER KEY

DSST Business Math


83. The correct answer is C. Substitute the given values into the annual percentage rate formula I

r Pt

= ,

where I is $20,000, P is $250,000, and t is 6:

$20,0000.013333, 13.33%

$250,000 6or

×

=

84. The correct answer is D. Use the compound interest formula to solve = + 1

nt r

A P n

where P is

principal, r is the rate, n is the number of yearly compounding, and t is the number of years. Set 0.8 equal tothe ratio of the actual balance and the possible balance with a consistent rate:

( ) ( )

( ) ( )

72 481 2

1201

482

481

248

1

48 48 1 2

48 481 2

48 481 2

1 2

1 1

12 120.8

112

112

0.8

112

1 120.8

112

0.8 0.8 112 12

12 0.8 0.8 12

0.8 12 0.8 1

0.995 0.0556564

r r x

r x

r

r

r

r

r r

r r

r r

r r

⋅ + ⋅ +

=

⋅ +

+

=

+

+

=

+

+ − =

+ − =

+ − =

− =

Since 0.995 r 1 is about r 1, the difference between r 1 and r 2 is about 0.0556564 ≈ 5.57%.


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ANSWER KEY

DSST Business Math


85. The correct answer is B. Substitute the given values into the bank discount formula to calculate interestbeing paid:

Bank Discount Maturity Value × Discount Rate × Time

5 $25,000 0.13

12

$1,354.17

=

= × ×

=

Substitute the values into , I

EF PT

= where I is $1,354.17, P is 23,645.83, and T is 5 :12

$1,354.17

$23,645.83 0.41667

13.7%

I EF

PT =

×=

=

86. The correct answer is C. Substitute the given values into the formula 1 1,

ni

n+ −

where i is 12% and n

is 12:

12.01

1 1 12.68%12

+ =

−

87. The correct answer is D. Substitute the given values into the formula 1 1,

ni

n+ −

where i is 8% and n is

4:

+ − =

4.08

1 1 8.24%4

88. The correct answer is C. Substitute the given values into the formula for each bank 1 1

ni

n

+ −

and

compare.

Bank A:

120.0806

1 1 8.365%12

+ − =

Bank B:

40.0812

1 1 8.371%4

+ − =


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ANSWER KEY

DSST Business Math


Bank C:

20.0825

1 1 8.420%2

+ − =

Bank D:

1

0.08351 1 8.35%1

+ − =

89. The correct answer is D. Graph D shows no fee for luggage weighing up to 40 pounds, a flat fee of $50for luggage weighing between 40 and 80 pounds, then an additional fee of $1.25 per pound for luggageweighing more than 80 pounds.

90. The correct answer is C. Substitute the given values into formula and solve where x is $30,000:

( )

( ) 0.1 $1,000

0.1 $30,000 1,000

$2,000

$

T x x= −

= ×

=

−

91. The correct answer is A. Substitute the given values into formula and solve where x is 10:

( ) ( )

2

2

( ) 0.4 12 15

10 12 10 15

P x x x= − + −

= − + −

=

0.4

$65,000

92. The correct answer is D.

($35.75 × 2) + ($25 × 3) + ($10.60 × 1) = $157.10

93. The correct answer is A. Substitute the given values into the present value of non-annual compoundingformula where i is 5%, PMT is $120, m is 12, and Y is 4

( )48

1 1.0033$120

0.0033

$5,318.87

1 1mY

i

mPV PMT

i

m

−

−−

=

− +

=

=

94. The correct answer is C. Substitute the given values into the future value for lump sum formula where iis 7%, PV is $10,000, and n is 7:


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ANSWER KEY

DSST Business Math


( )

( )7

1

10, 000 1 0.07

$16,057.81

$

nFV PV i= +

+

=

=

95. The correct answer is B. Substitute the given values into the future value for lump sum formula where i1 is 7%, PV 1 is $15,000, n1 is 5, i2 is 7%, PV 2 is $7,000, and n2 is 3:

( ) ( )

( ) ( )

1 2

1 1 2 2

5

1 1

3$15,000 1 0.07 7,000 1 0.07

$29,613.58

$

n nFV PV i PV i= + +

= + +

+

+

=

96. The correct answer is C. Substitute the given values into the future value for lump sum formula and

subtract the present value where i is 0.062

, PV is $10,000, and n is 8:

( )

( )8

1

$10, 000 1 0.03 $10, 000

$2,667.70

nFV PV i PV = +

= + −

=

−

97. The correct answer is B. Substitute the given values into the future value for lump sum formula and

solve where i is0.08

4, PMT is $300, and n is 8:

( )

( )

1 1

81 0.02 -1

$3000.02

$2,574.89

ni

FV PMT i

+ −=

+=

≈


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ANSWER KEY

DSST Business Math

98. The correct answer is C. Substitute the given values into the effective annual rate formula , where i is9% and n is 12:

12

1 1

0.091 1 9.381%

12

n

in

+ −

+ − =

99. The correct answer is C. Substitute the given values into the effective annual rate formula, where i is1.5% and n is 365:

365

1 1

0.0151 1 1.511%

365

ni

n+ −

+ =

−

100. The correct answer is B. Substitute the given values into the annual percentage rate formula, where I is$500, P is $1000, and t is 3:

( )

$50016.67%

$1,000 3

I r

Pt =

=

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