DSST Introduction to Business Math

DSST Introduction to Business Math Time 120 Minutes 100 Questions Each incomplete statement is followed by four suggested completions. 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 a percent 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 is equivalent to which of the following? 11 3 (A) (B) (C) (D) 2 11 6 22 9 22 6 11 1

4. What values of x satisfy the compound inequality 4 < 6 5x < 12? (A) (B) (C) (D) 6 2 < x < 5 5 2 6 < x < 5 5 2 6 < x < 5 5 6 2 < x < 5 5 5. The total cost T for a manufacturing process is given by the formula T = NV + F, where N is the number of items manufactured, V is the variable cost per item, and F is fixed cost. If it costs $240 to manufacture 3 items and $312 to manufacture 11 items, how much would it cost to manufacture 25 items? (A) $421 (B) $438 (C) $447 (D) $452 6. Solve the equation 4(Q 8) = 20. (A) 7 (B) 13 (C) 24 (D) 32 7. Solve the equation 4(d 6) = 28. (A) 1 (B) 8 (C) 13 (D) 52 8. B Solve the equation + 3 = 15. 4 (A) 3 (B) 21 (C) 48 (D) 57 2

9. An apparel shop sells skirts for $45 and blouses for $35. The shop s entire stock at the beginning of the month is worth $51,750. At the end of the month, only two thirds of the blouses and one half of the skirts have 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 and the rest at 4% interest. If the agent earns a total of $2,290 interest per year, how much did the agent invest at 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 his sister? (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-year period. Three years from now, what will be the value of a piece of equipment that is new today? (A) 0.2x (B) 0.4x (C) 0.6x (D) 0.8x 3

13. Which of the following is the most widely accepted disadvantage of using the mean as a measure of central tendency? (A) (B) (C) (D) The mean is difficult to compute as compared to other measures of central tendency. The mean does not take all data points into consideration. The mean is not reliable; it changes considerably for repeated samples. The mean is influenced by extreme values (skewed distributions). 14. Given five numbers, which of the statements below is always true? (A) (B) (C) (D) The arithmetic mean cannot be smaller than the largest one of the numbers. The arithmetic mean cannot be smaller than the smallest two of the numbers. The arithmetic mean cannot be smaller than the median. 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 first two 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 4

17. Calculate the sample standard deviation for the following data set. Round the final answer to the nearest tenth. (A) 16.4 (B) 16.5 (C) 18.0 (D) 18.1 85.6, 94.3, 58.5, 45.5, 79.1, 68.7 18. The total number of college credits for a sample of college students is given below: (A) 44.4 (B) 44.5 (C) 46.0 (D) 46.8 College Credits Frequency 0 24 4 25 49 3 50 74 6 75 99 3 100 124 5 125 149 9 19. A pizza recipe calls for 2 9 cup of tomato sauce. A recipe for spaghetti sauce requires 5 1 cups of tomato 6 sauce. How much tomato sauce is needed for both recipes? (A) (B) (C) (D) 11 27 7 1 15 11 1 18 1 2 18 5

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. (A) (1, 5) (B) (2, 3) (C) (3, 1) (D) no solution 2x + y = 7 x 2y = 1 6

22. Which of the following are NOT valid histograms of a probability distribution? I. II. III. IV. (A) (B) (C) (D) I and II I and IV II and III III and IV 7

23. The following is the frequency distribution table of the number of sales made by 20 salespeople on a given day: This distribution table shows that Number of Sales Frequency 0 3 1 2 2 5 3 3 4 4 5 1 6 2 (A) (B) (C) (D) fifty percent of the salespeople had less than 3 sales. forty-five percent of the salespeople had between 2 and 4 sales. thirty-five percent of the salespeople had only 2 sales. 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 the weights of all the bags are normally distributed, what is the percentage of bags that weigh less than 1.76 kg? (A) 2.5% (B) 13.5% (C) 16.0% (D) 34.0% 8

25. What is the average yearly profit for the business below? The business operated for only 8 months in the year in 2001 and the data is reported for only the first 7 months in 2005. Round the result to the closest number listed. (Use the number of months to calculate the weighted average yearly revenue to correct for the 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. The student received 100% on the homework. According to the syllabus, each test counts twice as much as the homework and half as much as the final exam. What is the average score for the course, weighted as prescribed 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? (A) 3.0 (B) 3.9 (C) 4.0 (D) 6.3 Value Frequency 5 6 4 5 3 8 9

28. From the following, calculate the weighted average unit cost, rounded to the nearest cent: (A) $2 (B) $3 (C) $3.16 (D) $3.50 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 29. From the following, calculate the weighted average unit cost, rounding to the nearest cent: (A) $8.65 (B) $9.53 (C) $9.74 (D) $10.87 Number of goods purchased for resale Cost per unit April 1 inventory 30 $8 May 1 25 $9 October 1 20 $10 December 1 20 $13 30. Find the roots of the equation y = x 2 3x 28. (A) { 7, 4} (B) { 7, 4} (C) { 4, 7} (D) {4, 7} 10

31. A student s test grade of 70 represents the 78th percentile of the grades. What percent of students scored higher than 70? (A) 22% (B) 23% (C) 77% (D) 78% 32. Which of the following is the graph of y = 2x 3? (A) (B) (C) (D) 11

33. What amount of money needs to be deposited in a bank now at 3.29% effective yield to allow cash payment for a $20,000 car 5 years from now? (A) $17,012 (B) $17,175 (C) $19,342 (D) $20,000 34. 1 When i = in the formula A = P(1 + i) n, which of these is true as n approaches infinity? n (A) (B) A approaches πp. 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) (B) (C) (D) A bank that pays 3.15% interest, compounded annually A bank that pays 3.10% interest, compounded semi-annually A bank that pays 3.05% interest, compounded quarterly 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 of 5% 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 no prepayment penalties. (A) $10.36 (B) $10.50 (C) $21 (D) $31.50 12

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 the next 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 a residual value of $50,000. If the declining-balance method with depreciation rate 30% is used, what are the 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 twice the 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 13

42. Company ABC buys equipment for $10,000. At the end of 5 years, the book value will be $2,000. Find the book value at the end of the second year. Use the declining-balance method, given that the depreciation 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) (B) (C) (D) The discount is equal to the discount rate applied to the proceeds of the loan. The discount is the difference between the nominal interest rate and a lower interest rate charged for the loan. The discount is the interest deducted in advance from the amount of the loan. The discount is the option that the borrower can pay back the loan early at a lower interest rate. 45. A baker borrows $10,000 from a bank to purchase a franchise bakery. The loan is at 7.25% payable at the end of the year. Six months into the year, the baker decides to purchase a new high-efficiency oven and gets a simple 12% discount note from the bank against the loan (the full value of the discount note should pay 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 14

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 27 3/10, 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 9 months, what is the final pay off? (A) $6,065 (B) $6,366 (C) $8,376 (D) $8,766 15

49. The monthly payment on a $64,000 loan at 12% annual interest is $704.64. Approximately how much of the 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 first monthly 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 is the selling price? (Round to the nearest penny.) (A) $72.50 (B) $77.50 (C) $90.91 (D) $111.11 16

54. A corporation with $250,000 annual taxable income has a federal corporate tax rate of 39% and a state corporate tax rate of 4.63%. If state taxes are deductible on the corporation s federal income taxes, then the 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. The company will receive a 50% tax credit for each of the first 3 years after the plant begins operation. How much will the total tax credit be if the company s taxable income in the first year is $300,000 and doubles each 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. What happens 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 + $70x, where x represents the number of customers. What is the average cost per customer if the business has 2,000 customers? (A) $70 (B) $75 (C) $83 (D) $88 17

58. An office-supply store pays its stockers according to the following weekly differential pay schedule: (A) $520 (B) $560 (C) $600 (D) $720 Items Stocked Amount per Item 1 500 $0.30 501 1000 $0.50 Over 1000 $0.60 59. A pizza restaurant pays its delivery drivers according to the following weekly differential pay schedule: (A) $420 (B) $490 (C) $500 (D) $630 Orders Delivered Amount per Order 1 60 $3.00 61 100 $3.50 Over 100 $4.50 60. A small business is selling widgets for $125 each. The per-widget production costs are $97.50, and the business can sell 130 widgets per month. What level of fixed costs per month would correspond to the business breaking even (revenues equal the expenses)? (A) $3,575 (B) $3,610 (C) $3,625 (D) $3,652 18

61. A small airline has fixed expenses of $10,000 per month and can sell tickets for $250 per seat. The variable costs are $200 per passenger. If the airline starts with 100 tickets sold per month in January and hopes to increase sales by 30 additional tickets each month, what is the first month of the year when it will break even? (A) (B) (C) (D) February March April May 62. A mobile phone manufacturer has fixed costs of $100,000 per month. The per-phone production cost is typically 50% of the manufacturer s suggested retail price, while phones normally sell for $60 after a discount of 25% off the manufacturer s suggested retail price. How many phones does the manufacturer need 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 the contributing 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 19

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: Net revenue (sales) $ 265 Net earnings 147 Total assets 2,015 Total liabilities 1,768 Total stockholders equity 427 (Dollars in millions) (A) 34.43% (B) 44.53% (C) 57.85% (D) 62.06% 20

66. From the following facts, find the current ratio. Round the final answer to the nearest hundredth Current assets $14,000 Accounts receivables $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) (B) (C) (D) Year 2005 2006 2007 Net income 100% 78% 119% Year 2005 2006 2007 Net income 100% 129% 84% Year 2005 2006 2007 Net income 84% 66% 100% Year 2005 2006 2007 Net income 100% 78% 152% 21

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) (B) (C) (D) Trend Analysis 2010 2009 Sales 105% 100% Gross Profit 82% 100% Net Income 123% 100% Trend Analysis 2010 2009 Sales 96% 100% Gross Profit 122% 100% Net Income 81% 100% Trend Analysis 2010 2009 Sales 100% 106% Gross Profit 100% 82% Net Income 100% 123% Trend Analysis 2010 2009 Sales 100% 96% Gross Profit 100% 122% Net Income 100% 81% 22

69. From the information given, what is the profit margin of net sales for May s Flower Shop? (A) 20% (B) 30% (C) 40% (D) 50% 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 23

70. Which of the following histograms shows the coffee-drinking habits of the people in one office if 5 people drink either 1 or no cups of coffee, 4 people drink 2 cups, 6 people drink 4 cups, and 3 people drink 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 is the ratio of the stock price per share to the dividend paid per share. What is the expected dividend for a stockholder who owns 1,000 shares? (A) $3,750 (B) $6,000 (C) $25,000 (D) $150,000 24

72. Troglodyte Networks Inc. has 1.5 million shares outstanding and is trading at $20 per share. The P/E ratio is the ratio of the stock price per share to the dividend paid per share and is 10 for Troglodyte. What total 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 stock is valued at $40 billion. What is the P/E ratio for the company (the P/E ratio being the ratio of the stock price 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 nearest whole number) and the yield (YLD) on the stock (to the nearest tenth percent). Assume Dow earns annually $5.48 per share. HI 52 WEEKS LO STOCK (SYM) DIV YLD % PE VOL 100 S CLOSE NET CHG 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 = 23x + 21y + 22 subject to: x 0, y 0 and x + y 1. (A) 22 (B) 43 (C) 45 (D) 63 25

76. A company designs and sells two types of rings, M and N, and can produce up to 24 rings each day using up 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. The company has available 91,800 units of steel and 42,000 units of aluminum. The one-, three-, and tenspeed models respectively need 20, 30, and 40 units of steel and 12, 21, and 16 units of aluminum. The company 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 = 3x + 2y, subject to the constraints x + y 100 and 3x + 4y 350, with x 0 and y 0. (A) 0 (B) 180 (C) 400 (D) 440 26

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. Approximately how much money should the company start putting aside in a bank account at 6% per year to ensure the money 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 to create a desired future value F after n years can be calculated by the formula: A = Fi n 1+ 1 ( i) According to the formula, approximately how much money should be added to the account each year at 4.5% 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 27

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 worker consults a financial planner and learns that because of the change to the lower rate the account is now worth 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% 28

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) (B) (C) (D) Bank A Bank B Bank C Bank D 29

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 pounds II. 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) 30

90. Suppose the tax, T, paid by a person with taxable income of x dollars is given by the following function: 0.05 x if 0 x 20, 000 T ( x) = 0.1x 1, 000 if x > 20, 000 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: What is the profit if the company sells 10 units? (A) $65,000 (B) $101,000 (C) $109,000 (D) $145,000 P(x) = 0.4x 2 + 12x 15 92. Emile bought two jackets for $35.75 each, three pairs of jeans for $25, and a hat for $10.60. What is the total 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 monthly for 4 years. What is the present value? (A) $5,318.87 (B) $5,760 (C) $5,990.40 (D) $6,048 31

94. Al plans to loan his friend $10,000 to open a restaurant. Al will collect the loan in 7 years with an interest rate 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 compounded semi-annually. Two years later, she inherited $7,000 and placed it in the same account. How much will she 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 is compounded monthly. Round the final answer to the nearest thousandth percent. (A) 9.000% (B) 9.308% (C) 9.381% (D) 9.416% 32

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 the interest 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% 33

ANSWER KEY DSST Business Math 1. The correct answer is C. Find the difference between the current price and the original price and divide the result by the original price: $127 $10 = $117 $117 = 11.7, 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 inequality sign: 4 < 6 5x < 12 2 < 5x < 6 2 5x 6 < < 5 5 5 6 2 < x < 5 5 5. The correct answer is B. Subtract the equations and then simplify: T = NV + F $312 = 11V + F $240 = 3V + F $72 = 8V $9 = V Substitute V = $9 into the first equation and solve for F: ANSWER KEY - Page 34

ANSWER KEY DSST Business Math $312 = 11 $9 + F $312 = $99 + F $213 = 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: ( Q ) 4 8 = 20 Q 8 = 5 Q = 13 7. The correct answer is C. Divide both sides by 4; then add 6 to both sides: 4( d 6) = 28 d 6 = 7 d = 13 8. The correct answer is C. Subtract 3 from both sides; then multiply both sides by 4: B + 3 = 15 4 B = 12 4 B = 48 9. The correct answer is B. The beginning inventory equation is: $45s + $35b = $51,750 The inventory sold equation is: $45 $70 s + b = $30, 600 2 3 Then employ the elimination method. Multiply the inventory sold equation by 2 so that coefficient of s is the same in each equation: ANSWER KEY - Page 35

ANSWER KEY DSST Business Math $45 $70 s + b = $30, 600 2 3 $140 $45 s + b = $61, 200 3 You can then eliminate the s-term and solve for b, the beginning number of blouses: 35 b = 9,450 3 b = 810 Substitute b = 810 into the first equation and solve for s, the beginning number of skirts: 45s + 35(810) = 51, 750 s = 520 Then multiply the beginning number of blouses by one-third: 1 810 270 3 = 10. The correct answer is C. The questions produces two equations: x + y = $52,000 and 0.05x + 0.04y = $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 + 0.8y = $45,800 You can then eliminate the x-term and solve for y. 0.2 y = $6, 200 y = $31, 000 11. The correct answer is B. Find the product of 40% and 45: ANSWER KEY - Page 36

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: The value after three years is 0.4x. 1 (3 0.2) = 0.4 13. The correct answer is D. The biggest disadvantage to using the mean as a measure of central tendency is that 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: 17. The correct answer is C. Find the mean: 153 + 153 = 153 2 85.6 + 94.3 + 58.5 + 45.5 + 79.1+ 68.7 = 71.95 6 Square the difference between the mean and each element: ANSWER KEY - Page 37

ANSWER KEY DSST Business Math (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 2 2 2 2 2 2 Take the square root of the average of the previous values: 186.3225 + 499.5225 + 180.9025 + 699.6025 + 51.1225 + 10.5625 = 18.0 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+ 68.7 = 71.95 6 Square the difference between the mean and each element: (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 2 2 2 2 2 2 Take the square root of the average of the previous values: 186.3225 + 499.5225 + 180.9025 + 699.6025 + 51.1225 + 10.5625 = 18.0 6 1 ANSWER KEY - Page 38

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 and 5 11 33 1 = = 6 6 18 Add the fractions together and then simplify: 4 33 37 + = 18 18 18 1 = 2 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: 2x + 4y = 2 Add this equation to the first equation, then solve for y: 5y = 5 y = 1 Substitute y = 1 into the first equation, then solve for x: 2 x + (1) = 7 2x = 6 x = 3 The solution is (3, 1). ANSWER KEY - Page 39

ANSWER KEY DSST Business Math 22. The correct answer is D. The values for a probability distribution total 1. The values in graph III total 0.8 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 the salespeople surveyed. 24. The correct answer is C. The value 1.76 is one standard deviation below the mean. In a normal distribution, one to four standard deviations below the mean accounts for about 15.8% of the set, which is about 16%. 25. The correct answer is B. Multiply each profit by the number of months reported. Then add the values and 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: h + 2h + 2h + 4h = 100 h = 100 9 Test one: Test two: 100 0.92 2 = 20.4 9 100 0.95 2 = 21.1 9 100 Homework: 100 1 = 11.1 9 Final exam: 100 0.91 4 = 40.4 9 Add these values to find the student's course score: 20.4 + 21.1 + 11.1 + 40.4 = 93.1 ANSWER KEY - Page 40

ANSWER KEY DSST Business Math 27. The correct answer is B. Find the sum of the products of the ordered pairs, then divide by the sum of the frequencies: (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 sum of 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 sum of the frequencies: (8 30) + (9 25) + (10 20) + (13 20) = $9.74 30 + 25 + 20 + 20 30. The correct answer is C. Factor the right-hand side: Set each factor equal to zero, and then solve for x: y = (x + 4)(x 7) x + 4 = 0 x = 4 The roots of the equation are 4 and 7. x 7 = 0 x = 7 31. The correct answer is A. Scoring in the 78th percentile means the grade of 78 is better than or equal to 78% 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 is the graph of the line containing these points. r 33. The correct answer is A. Use the compound interest formula A = P 1 +, where A is the final n amount, P is the principal, r is the rate, n is the yearly compoundings, and t is the time in years: nt ANSWER KEY - Page 41

ANSWER KEY DSST Business Math 0.0329 $20, 000 = P 1+ 1 $20, 000 = P ( 1.0329) 5 $17, 011.34 = P n 1 34. The correct answer is B. Constant e is given by the limit lim 1 +. Therefore, as n approaches n n 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 r A = P 1+ n nt and simplify to find the largest value. 1 5 Choice A: Choice B: Choice C: Choice D: 1t 0.0315 1+ = 1.0315 1 2t 0.031 1+ = 1.03124 2 4t 0.0305 1+ = 1.03085 4 12t 0.03 1+ = 1.03042 12 t t 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 solve for P: 9 $140.60 = P 0.05 12 P = $3, 749.33 ANSWER KEY - Page 42

ANSWER KEY DSST Business Math 37. The correct answer is B. Substitute the two sets of values into the simple interest formula I = PRT, and then subtract to find the savings from prepaying. So: Interest for 180 days: 180 I = $420 0.15 = $31.50 360 Interest for 120 days: 120 I = $420 0.15 = $21 360 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 in use: 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 usable years 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 next year'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 = $140,000 Beginning value for Year 3: $140,000 0.7 = $98,000 Beginning value for Year 4: $98,000 0.7 = $68,600 Beginning 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: ANSWER KEY - Page 43

ANSWER KEY DSST Business Math $600 $3,500 $500 = 20% 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 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: $600 $3,500 $500 = 20% 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 ANSWER KEY - Page 44

ANSWER KEY DSST Business Math 43. The correct answer is C. Use the simple interest formula I = PRT to find the interest: 6 I = P 0.06 12 = 0.03P 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: 0.03P 0.03P = 6 0.97P 0.485P 12 = 6.2% 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 the terms column, or 10 days. Ten days from July 27, the date the goods were received, is August 6. The final day the bill is due is the third number in the terms column, or 30 days after receipt of goods (ROG). Thirty days 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 first 10 days of the next month, which is by March 10. The final due date of the bill is within 20 days of the end of the discount period, which is March 30. 48. The correct answer is A. Multiply the unpaid months by the monthly installment to find the balance of the outstanding loan: 16 $440 = $7,040 ANSWER KEY - Page 45

ANSWER KEY DSST Business Math Find the monthly principal payment: $9, 000 = $375 24 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 ANSWER KEY - Page 46

ANSWER KEY DSST Business Math 52. The correct answer is B. Multiply the remaining months by the monthly installment to find the balance of 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: ( ) ( $50 45% ) + $50 Selling Price = Cost Markup Percentage + Cost = = $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 + $92,985.75 = 0.418243, or 41.82% $250, 000 ANSWER KEY - Page 47

ANSWER KEY DSST Business Math 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 for more than its book value. 57. The correct answer is C. Substitute the given values into the formula: then find the average cost per customer: ( ) = $25, 000 + $70 C x = $25, 000 + ($70 2, 000) = $165, 000 C( x) $165,000 = # of customers 2,000 = $83 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 x ANSWER KEY - Page 48

ANSWER KEY DSST Business Math 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 Cost Breakeven Point = Selling Price - Variable Cost $10, 000 200 = $250 $200 Starting with 100 ticket sales in January and adding 30 sales per month (100 in January, 130 in February, 160 in 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: Fixed Cost Breakeven Point = Selling Price - Variable Cost $100, 000 $60 $40 = 5,000 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: ANSWER KEY - Page 49

ANSWER KEY DSST Business Math Fixed Cost Breakeven Point = Selling Price - Variable Cost $75, 000 = $1.99 $0.74 = 60, 000 64. The correct answer is C. Substitute the given values into the breakeven point formula: Breakeven Point = Fixed Cost Selling Prince - Variable Cost $815, 000 = $9.99 $3.50 = 125, 577.78 65. The correct answer is A. Substitute the given values into the return on equity formula: Net Earnings Return on Equity = Stockholders' Equity 147 = 427 = 0.3443, or 34.43% 66. The correct answer is B. Substitute the values into the current ratio formula: Current Assets Current Ratio = Current Liabilities $14, 000 = $20, 000 = 0.70, or 70% 67. The correct answer is A. Divide the net income for 2006 and 2007 by the net income for base year 2005: 2006: $42, 000 = 0.777, or 78% $54, 000 2007: $64, 000 = 1.185, or 119% $54, 000 ANSWER KEY - Page 50

ANSWER KEY DSST Business Math 68. The correct answer is A. Divide the sales, gross profit, and net income for 2010 by the respective values during base year 2009: $225, 000 Sales: = 1.0465, or 105% $215, 000 $90, 000 Gross Profit: = 0.818, or 82% $110, 000 $80, 000 Net Income: = 1.231, or 123% $65, 000 69. The correct answer is C. Use this formula to find the profit margin of net sales: Net income Profit 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 2 cups or less of coffee, 9 people drink 3 cups or less of coffee, 15 people drink 4 cups or less of coffee, and 18 people 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 dividends paid per share and then solve where DPS is $6 and total shares is 1000: Market Price P/E = Earnings per Share $150 $25 = x $6 = x $6 1,000 shares = $6,000 ANSWER KEY - Page 51

ANSWER KEY DSST Business Math 72. The correct answer is A. First, substitute the given values into the P/E formula and solve: Market Price P / E = Earnings per Share $20 $10 = x x = $2 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 and A/E is $2: Closing Price Per Share P/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 Share P/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 Share Yield = Today's Closing Price Per Share $2.19 = $93.64 = 0.023, or 2.3% ANSWER KEY - Page 52

ANSWER KEY DSST Business Math 75. The correct answer is B. 1 1 1 1 0 0 23 21 22 1 1 23 1 0 21 1 0 22 x y s1 s2 z 1 1 1 0 0 23 1 0 0 1 0 21 1 0 0 0 1 22 x y s1 s2 z R1 R2 0 1 1 1 0 2 1 0 0 1 0 21 R2 + R3 0 0 0 1 1 43 The minimization is z = 43. 76. The correct answer is B. Maximize z = 30x 1 + 40x 2, subject to 3x 1 + 2x 2 60 and x 1 + x 2 24, with x 1 0 and x 2 0: x x s s z 1 2 1 2 3 2 1 0 0 60 1 1 0 1 0 24-30 -40 0 0 1 0 x x s s z 1 2 1 2 R1 2R2 1 0 1-2 0 12 1 1 0 1 0 24 40R2 + R3 10 0 0 40 960 1 The maximum profit is $960 when 24 N rings are produced. ANSWER KEY - Page 53

ANSWER KEY DSST Business Math 77. The correct answer is B. Maximize z = 8x 1 + 12x 2 + 24x 3, subject to 20x 1 + 30x 2 + 40x 3 91,800 and 12x 1 + 21x 2 + 16x 3 42,000, with x 1 0, x 2 0, and x 3 0. x1 x2 x3 s1 s2 z 20 30 40 1 0 0 12 21 16 0 1 0-8 -12-24 0 0 1 91, 800 42, 000 0 (-R1 + 5R2 ) ( 3R + 5R ) 1 3 x1 x2 x3 s1 s2 z 20 30 40 1 0 0 91, 800 20 45 0-2 5 0 26, 400 20 30 0 3 0 5 275, 400 It follows that x 1 = 0, x 2 = 0, and x 3 = 2,295 where x 3 is the number of ten-speed bikes needed to maximize profits. Multiply x 3 = 2,295 by the respective profit per unit: $2,295 $24 = $55,080 ANSWER KEY - Page 54

ANSWER KEY DSST Business Math 78. The correct answer is C. 1 1 100 3 4 350 3 2 0 1 3 3 1 4 2 100 350 0 x1 x2 s1 s2 z 1 3 1 0 0 3 1 4 0 1 0 2 100 350 0 0 1 0 x x s s z 1 4 1 4 0 1 0 2 + 2 1 2 1 2 4R1 3R2 0 3 0 6 175R2 2R3 25 0 0 175 350 x1 x2 s1 s2 z R1 R2 0 4 4 4 0 4 1 4 0 1 0 2 R + R 0 200 2 400 25 2 3 0 100 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 ANSWER KEY - Page 55

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: ( 1 i) PV = FV + -n ( ) -5 = $2,000,000 1 + 0.06 = $1, 495, 516.35 = $1,495,000 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: A = = Fi n ( 1 + i) 1 $1, 000, 000( 0.045) ( 1+ 0.045) 24 1 = $23, 987.03 = $24, 000 82. The correct answer is A. Substitute the given values into the future value for lump sum formula, where FV is future value and PV is present value. Solve the two equations and find the difference between the results. For account A, where i is 5%, PV is $1,000, and n is 365: ( 1 ) FV = PV + i 365 ( + ) ( + ) = $1,000 1 0.05 $1,000 1 0.025 = $1, 051.27 For account B, where i is 5%, PV is $1,000, and n is 2: n ( 1 ) FV = PV + i 2 ( + ) ( + ) = 1,000 1 0.05 1,000 1 0.025 = $1, 050.63 Subtract to find the difference between the accounts: n $1,051.27 $1,050.63 = $0.64 ANSWER KEY - Page 56