Practice Questions

The following test-like questions provide an opportunity to practice Problem Solving and Data Analysis questions. The calculator icon means you are permitted to use a calculator to solve a question. It does not mean that you should use it, however.

  1.  

    The blue whale is the largest creature in the world and has been found in every ocean in the world. A marine biologist surveyed the blue whale population in Monterey Bay, off the coast of California, every three years between 1995 and 2010. The figure above shows her results. If w is the number of blue whales present in Monterey Bay and t is the number of years since the study began in 1995, which of the following equations best represents the blue whale population of Monterey Bay?

    1. w = 100 + 2t

  2. Most people save money before going on vacation. Suppose Etienne saved $800 to spend during vacation, 20 percent of which he uses to pay for gas. If he budgets 25 percent of the remaining money for food, allots $300 for the hotel, and spends the rest of the money on entertainment, what percentage of the original $800 did he spend on entertainment?

    1. 14.5
    2. 17.5
    3. 22.5
    4. 28.5

  3. In a class of 25 students, 76% are currently passing with a grade of 70% or higher. If two students are selected at random from this class, what is the probability that neither student is passing with a grade of 70% or higher?

    1. 0.05
    2. 0.06
    3. 0.24
    4. 0.58

  4. In extreme climates, temperatures can vary as much as 20° Celsius in a single day. How many degrees Fahrenheit can these climates vary if the relation between Fahrenheit degrees and Celsius degrees is given by the equation  ?

    1. 20°F
    2. 36°F
    3. 62°F
    4. 68°F
  5.  
      For Against Undecided Total
    1L 32 16 10 58
    2L 24 12 28 64
    3L 17 25 13 55
    Total 73 53 51 177

    A survey is conducted regarding a proposed change in the attendance policy at a law school. The table above categorizes the results of the survey by year of the student (1L, 2L, or 3L) and whether they are for, against, or undecided about the new policy. What fraction of all 1Ls and 2Ls are against the new policy?

  6. An airline company purchased two new airplanes. One can travel at speeds of up to 600 miles per hour and the other at speeds of up to 720 miles per hour. How many more miles can the faster airplane travel in 12 seconds than the slower airplane?

    3.   2
    4. 30

  7. Marion is a city planner. The city she works for recently purchased new property on which it plans to build administrative offices. Marion has been given the task of sizing the lots for new buildings, using the following guidelines:

    • The square footage of each lot should be greater than or equal to 3,000 square feet, but less than or equal to 15,000 square feet.
    • Each lot size should be at least 30% greater in area than the size before it.
    • To simplify tax assessment calculations, the square footage of each lot must be a multiple of 1,000 square feet.

    Which list of lot sizes meets the city guidelines and includes as many lots as possible?

    1. 3,000; 5,000; 10,000; 15,000
    2. 3,000; 4,500; 6,000; 7,500; 10,000; 15,000
    3. 3,000; 4,000; 6,000; 8,000; 11,000; 15,000
    4. 3,000; 3,900; 5,100; 6,600; 8,600; 11,200; 14,600
  8.  
    image

    The figure above represents a click-through rate curve, which shows the relationship between a search result position in a list of Internet search results and the number of people who clicked on advertisements on that result’s page. Which of the following regression types would be the best model for this data?

    1. A linear function
    2. A quadratic function
    3. A polynomial function
    4. An exponential function

  9. According to a hospital’s records, the mean age of 17 new mothers who gave birth at the hospital in June was 26 years. When the final new mother who gave birth at that hospital on June 30 was added to the data, the mean age increased to 27 years. What was the age of the final new mother?

    1. 27
    2. 36
    3. 44
    4. 47

  10. The Great Pyramid of Giza, built in the 26th century BC just outside of Cairo, Egypt, had an original height of 480 feet, 8 inches, before some of the stones in which it was encased fell away. Inside the pyramid is a 53.75-foot passage, called the Dead End Shaft, which archeologists have yet to discover the purpose of. Suppose a museum is building a scale model of the pyramid for patrons to explore. Because of the museum’s ceiling height, they can only make the pyramid 71 feet, 6 inches tall. About how many feet long should the museum’s Dead End Shaft be?

    1.   8
    2. 12
    3. 30
    4. 96

  11. The percent increase from 5 to 12 is equal to the percent increase from 12 to what number?

    1. 16.8
    2. 19.0
    3. 26.6
    4. 28.8
  12.  

    Mr. Juno took his driver’s education class to the Department of Motor Vehicles to take their driver’s license test. The number of questions missed by each student in the class is recorded in the bar graph above. Which of the following statements is true?

    1. More than half of the students missed 5 or more questions.
    2. The mean number of questions missed was between 4 and 5.
    3. More students missed 3 questions than any other number of questions.
    4. Thirty-six students from Mr. Juno’s class took the driver’s license test that day.
  13.  

    The white-footed mouse, named for its darker body fur and white feet, is primarily found on the east coast of the United States, living in warm, dry forests and brushland. A scientist in Virginia studied a sample of 200 white-footed mice to see how many offspring they had per birth. The results of the study are recorded in the figure above. Based on the data, given a population of 35,000 female white-footed mice living in Virginia, how many would you expect to have a litter of seven or more pups?

    1.   3,325
    2.   4,375
    3.   7,700
    4. 15,400

  14. According to the American Association of University Women, the mean age of men who have a college degree at their first marriage is 29.9 years. The mean age of women with a college degree at their first marriage is 28.4 years. Which of the following must be true about the combined mean age m of all people with college degrees at their first marriage?

    1. m = 29.15
    2. m > 29.15
    3. m < 29.15
    4. 28.4 < m < 29.9

  15. An architect is designing a new stadium-seating movie theater. The theater company has given the architect the following guidelines for designing the rows:

    • The length of each row must be at least 20 feet long, but no longer than 90 feet.
    • Each row should be at least 20% longer than the row in front of it.
    • Each row length must be evenly divisible by the width needed for each seat, 2.5 feet.

    Which list of row lengths meets the theater company’s guidelines and includes as many row lengths as possible?

    1. 24, 30, 36, 45, 54, 66, 81
    2. 20, 32.5, 45, 57.5, 72.5, 85
    3. 20, 30, 40, 50, 60, 70, 80, 90
    4. 25, 30, 37.5, 45, 55, 67.5, 82.5

  16. A microbiologist placed a bacteria sample containing approximately 2,000 microbes in a petri dish. For the first 7 days, the number of microbes in the dish tripled every 24 hours. If n represents the number of microbes after h hours, then which of the following equations is the best model for the data during the 7-day period?

  17. The United States Senate has two voting members for each of the 50 states. The 113th Congress had a 4:1 male-to-female ratio in the Senate. Forty-five of the male senators were Republican. Only 20 percent of the female senators were Republican. How many senators in the 113th Congress were Republican?

    1. 20
    2. 49
    3. 55
    4. 65
  18.  
    From Distance to LHR
    DCA 3,718
    MIA 4,470

    Two airplanes departed from different airports at 5:30 AM, both traveling nonstop to London Heathrow Airport (LHR). The distances the planes traveled are recorded in the table. The Washington, D.C. (DCA) flight flew through moderate cloud cover and as a result only averaged 338 mph. The flight from Miami (MIA) had good weather conditions for the first two-thirds of the trip and averaged 596 mph, but then encountered some turbulence and only averaged 447 mph for the last part of the trip. Which plane arrived first and how long was it at the London airport before the other plane arrived?

    1. MIA; 2 hours, 40 minutes
    2. MIA; 3 hours, 30 minutes
    3. DCA; 1 hour, 20 minutes
    4. DCA; 3 hours, 40 minutes

  19. Each month, the Bureau of Labor Statistics conducts a survey called the Current Population Survey (CPS) to measure unemployment in the United States. Across the country, about 60,000 households are included in the survey sample. These households are grouped by geographic region. A summary of the January 2014 survey results for male respondents in one geographic region is shown in the table below.

    Age Group Employed Unemployed Not in the Labor Force Total
    16 to 19 8 5 10 23
    20 to 24 26 7 23 56
    25 to 34 142 11 28 157
    35 to 44 144 8 32 164
    45 to 54 66 6 26 98
    Over 54 65 7 36 152
    Total 451 44 155 650

    If one unemployed man from this sample is chosen at random for a follow-up survey, what is the probability that he will be between the ages of 45 and 54 ?

    1.   6.0%
    2. 13.6%
    3. 15.1%
    4. 44.9%

  20. Crude oil is sold by the barrel, which refers to both the physical container and a unit of measure, abbreviated as bbl. One barrel holds 42 gallons and, consequently, 1 bbl = 42 gallons. An oil company is filling an order for 2,500 barrels. The machine the company uses to fill the barrels pumps at a rate of 37.5 gallons per minute. If the oil company has 8 machines working simultaneously, how long will it take to fill all the barrels in the order?

    1. 5 hours and 50 minutes
    2. 12 hours and 45 minutes
    3. 28 hours and 30 minutes
    4. 46 hours and 40 minutes

  21. A company reimburses employees for a portion of their gas costs for commuting to and from work based on mileage. Based on the following data, what is the rate in dollars per gallon that the company uses to reimburse employees?

    • The company has 126 employees who commute.
    • The average employee traveled 12,250 miles to and from work over the course of the year.
    • The average gas mileage reported by all employees was 22.5 miles per gallon.
    • The company paid out a total of $96,040.00 in gas reimbursements.
    1. $0.44
    2. $0.71
    3. $1.40
    4. $1.60
  22.  
    image

    When a drug company wants to introduce a new drug, it must subject the drug to rigorous testing. The final stage of this testing is human clinical trials, in which progressively larger groups of volunteers are given the drug and carefully monitored. One aspect of this monitoring is keeping track of the frequency and severity of side effects. The figure above shows the results for the side effect of headaches for a certain drug. According to the trial guidelines, all moderate and severe headaches are considered to be adverse reactions. Which of the following best describes the data?

    1. The data is symmetric with over 50% of participants having adverse reactions.
    2. The data is skewed to the right with over 50% of participants having adverse reactions.
    3. The data is skewed to the right with over 75% of participants failing to have adverse reactions.
    4. The data is skewed to the right with approximately 50% of participants having no reaction at all.

  23. In a 2010 poll, surveyors asked registered voters in four different New York voting districts whether they would consider voting to ban fracking in the state. Hydraulic fracturing, or “fracking,” is a mining process that involves splitting rocks underground to remove natural gas. According to ecologists, environmental damage can occur as a result of fracking, including contamination of water. The results of the 2010 survey are shown in the following table.

    In Favor of Ban Against Ban No Opinion Total
    District A 23,247 17,106 3,509 43,862
    District B 13,024 12,760 2,117 27,901
    District C 43,228 49,125 5,891 98,244
    District D 30,563 29,771 3,205 63,539
    Total 110,062 108,762 14,722 233,546

    A random follow-up survey was administered to 500 of the respondents in District C. They were asked if they planned to vote in the next election. The follow-up survey results were: 218 said they planned to vote, 174 said they did not plan to vote, and 108 said they were unsure. Based on the data from both the initial survey and the follow-up survey, which of the following is most likely an accurate statement?

    1. Approximately 19,000 people in District C who support a ban on fracking can be expected to vote in the next election.
    2. Approximately 21,000 people in District C who support a ban on fracking can be expected to vote in the next election.
    3. Approximately 43,000 people in District C who support a ban on fracking can be expected to vote in the next election.
    4. Approximately 48,000 people in District C who support a ban on fracking can be expected to vote in the next election.

  24. In the United States, the maintenance and construction of airports, transit systems, and major roads is largely funded through a federal excise tax on gasoline. Based on the 2011 statistics given below, how much did the average household pay per year in federal gasoline taxes?

    • The federal gasoline tax rate was 18.4 cents per gallon.
    • The average motor vehicle was driven approximately 11,340 miles per year.
    • The national average fuel economy for noncommercial vehicles was 21.4 miles per gallon.
    • The average American household owned 1.75 vehicles.
    1.   $55.73
    2.   $68.91
    3.   $97.52
    4. $170.63
  25.  

    The United States Fish and Wildlife Service classifies animals whose populations are at low levels as either threatened or endangered. Endangered species are animals that are currently on the brink of extinction, whereas threatened species have a high probability of being on the brink in the near future. Since 1990, the Northern Spotted Owl has been listed as threatened. The figure above shows the populations of the Northern Spotted Owl in a certain region in Oregon from 1994 to 2014. Based on the line of best fit shown in the figure, which of the following values most accurately reflects the average change per year in the number of Northern Spotted Owls?

    1.  –25
    2.    –0.04
    3.      0.04
    4.    25

  26. Red tide is a form of harmful algae that releases toxins as it breaks down in the environment. A marine biologist is testing a new spray, composed of clay and water, hoping to kill the red tide that almost completely covers a beach in southern Florida. He applies the spray to a representative sample of 200 square feet of the beach. By the end of the week, 184 square feet of the beach are free of the red tide. Based on these results, and assuming the same general conditions, how many square feet of the 10,000-square-foot beach would still be covered by red tide if the spray had been used on the entire area?

    1.    800
    2.    920
    3. 8,000
    4. 9,200

  27. According to the Project on Student Debt prepared by The Institute for College Access and Success, 7 out of 10 students graduating in 2012 from a four-year college in the United States had student loan debt. The average amount borrowed per student was $29,400, which is up from $18,750 in 2004. If student debt experiences the same total percent increase over the next eight years, approximately how much will a college student graduating in 2020 owe, assuming she takes out student loans to pay for her education?

    1. $40,100
    2. $44,300
    3. $46,100
    4. $48,200
  28.  
    image

    If an exponential function is used to model the data shown in the figure, and it is written in the form f(x) = f(0)(1 + r)x, what would be the value of r ?

    1. 2
    2. 3
    3. 4
    4. 5

  29. Kudzu is a vine-like plant that grows indigenously in Asia. It was brought over to the United States in the early 20th century to help combat soil erosion. As can often happen when foreign species are introduced into a non-native habitat, kudzu growth exploded and it became invasive. In one area of Virginia, kudzu covered approximately 3,200 acres of a farmer’s cropland, so he tried a new herbicide. After two weeks of use, 2,800 acres of the farmer’s cropland were free of the kudzu. Based on these results, and assuming the same general conditions, how many of the 30,000 acres of kudzu-infested cropland in that region would still be covered if all the farmers in the entire region had used the herbicide?

    1.   3,750
    2.   4,000
    3. 26,000
    4. 26,250

  30. An architect is building a scale model of the Statue of Liberty. The real statue measures 305 feet, 6 inches from the bottom of the base to the tip of the torch. The architect plans to make her model 26 inches tall. If Lady Liberty’s nose on the actual statue is 4 feet, 6 inches long, how long in inches should the nose on the model be?

  31. An object’s weight is dependent upon the gravitational force being exerted upon the object. This is why objects in space are weightless. If 1 pound on Earth is equal to 0.377 pounds on Mars and 2.364 pounds on Jupiter, how many more pounds does an object weighing 1.5 tons on Earth weigh on Jupiter than on Mars?

    1. 1,131
    2. 4,092
    3. 5,961
    4. 7,092

  32. The figure shows the age distribution of homebuyers and the percent of the market each age range makes up in a particular geographic region.

    image

    A new real estate agent is deciding which age group she should market toward in order to get the most clients. Which of the following measures of the data would be best for her to use when making this decision?

    1. Mean
    2. Mode
    3. Range
    4. Median
  33.  

    Quarterly Profits

    Branch A Branch B Branch C Branch D
    Q1 4.1 7.4 8.0 5.4
    Q2 3.6 5.2 3.7 6.2
    Q3 5.0 4.5 4.9 4.8
    Q4 4.9 6.3 5.9 5.6
    4.4 5.85 5.625 5.5
    s 0.67 1.27 1.82 0.58

    A company affected by a downturn in the economy decides to close one of its four branches. The table shows each branch’s quarterly profits in millions of dollars for 2014, along with the mean () and the standard deviation (s) of the data. The accounting department recommends that the company’s Board of Directors close either the store with the lowest average quarterly profits or the store that performs the least consistently. According to the data in the table, which branches will the accounting department recommend for closure to the board?

    1. Branches A or C
    2. Branches A or D
    3. Branches B or C
    4. Branches B or D
  34.  

    Following the catastrophic oil spill in the Gulf of Mexico in April of 2010, more than 900 bottlenose dolphins were found dead or stranded in the oil spill area. The figure above shows the weight of a rescued dolphin during its recovery. Based on the quadratic model fit to the data shown, which of the following is the closest to the average rate of change in the dolphin’s weight between week 2 and week 8 of its recovery in pounds per week?

    1.   4
    2. 16
    3. 20
    4. 40
  35.  
    image

    A student looked at the graph above and determined based on the data that spending more money per student causes the gross domestic product (GDP) to increase. Which of the following statements is true?

    1. The student is correct; the data shows that increased spending on students causes an increase in the GDP.
    2. The student is incorrect; the data shows that having a higher GDP causes an increase in the amount of money a country spends on students.
    3. The student is incorrect; there is no correlation and, therefore, no causation between GDP and expenditures on students.
    4. The student is incorrect; the two variables are correlated, but changes in one do not necessarily cause changes in the other.
  36.  
    Bowling Scores
    Ian Mae Jin
    Game 1 160 110 120
    Game 2 135 160 180
    Game 3 185 140 105
    Game 4 135 130 160
    Game 5 185 110 135
    Mean Score 160 130 140
    Standard Deviation 22 19 27

    Ian, Mae, and Jin bowled five games during a bowling tournament. The table above shows their scores. According to the data, which of the following conclusions is correct?

    1. Ian bowled the most consistently because the mean of his scores is the highest.
    2. Mae bowled the least consistently because the standard deviation of her scores is the lowest.
    3. Mae bowled the most consistently because the standard deviation of her scores is the lowest.
    4. Jin bowled the most consistently because the standard deviation of his scores is the highest.

  37. A bakery sells three sizes of muffins—mini, regular, and jumbo. The baker plans daily muffin counts based on the size of his pans and how they fit in the oven, which results in the following ratios: mini to regular equals 5 to 2, and regular to jumbo equals 5 to 4. When the bakery caters events, it usually offers only the regular size, but it recently decided to offer a mix of mini and jumbo instead of regular. If the baker wants to keep the sizes in the same ratio as his daily counts, what ratio of mini to jumbo should he use?

    1. 1:1
    2. 4:2
    3. 5:2
    4. 25:8

  38. The Federal Reserve controls certain interest rates in the United States. Investors often try to speculate as to whether the Federal Reserve will raise or lower rates and by how much. Suppose a company conducts extensive interviews with financial analysts, and as a result, predicts that “the Fed” will increase rates by an average of 0.25 percentage points every six months for the foreseeable future. Which type of equation could be used to model the predicted interest rates over the next several years, assuming no other significant changes?

    1. A linear equation
    2. A quadratic equation
    3. A polynomial equation
    4. An exponential equation
  39.  

    Which of the following equations best represents the trend of the data shown in the figure above?

    1. y = –2.4x + 30
    2. y = –1.2x + 40
    3. y = –0.8x + 40
    4. y = –0.4x + 36

  40. An online movie subscription service charges a dollars for the first month of membership and b dollars per month after that. If a customer has paid $108.60 so far for the service, which of the following expressions represents the number of months he has subscribed to the service?

  41. The figure shows the age distribution of homebuyers and the percent of the market each age range makes up in a particular geographic region.

    image

    Based on the information in the figure, which of the following statements is true?

    1. The shape of the data is skewed to the right, so the mean age of homebuyers is greater than the median.
    2. The shape of the data is skewed to the left, so the median age of homebuyers is greater than the mean.
    3. The shape of the data is fairly symmetric, so the mean age of homebuyers is approximately equal to the median.
    4. The data has no clear shape, so it is impossible to make a reliable statement comparing the mean and the median.

  42. When a certain kitchen appliance store decides to sell a floor model, it marks the retail price of the model down 25% and puts a “Floor Model Sale” sign on it. Every 30 days after that, the price is marked down an additional 10% until it is sold. The store decides to sell a floor model refrigerator on January 15th. If the retail price of the refrigerator was $1,500 and it is sold on April 2nd of the same year, what is the final selling price, not including tax?

    1.    $820.13
    2.    $825.00
    3.    $911.25
    4. $1,012.50
  43.  
    image

    The figure above shows the trajectory of a cannonball shot into the air. Approximately how many feet farther did the cannonball travel horizontally than vertically upward? (1 yard = 3 feet)

    1.     335
    2.     425
    3. 1,035
    4. 1,390

  44. A certain real estate agent uses what he calls a step-strategy to sell houses. He puts a house on the market at a higher-than-expected selling price and if it hasn’t sold in two weeks, he drops the price by 5%. If it still hasn’t sold in another 2 weeks, he drops the price by another 5%. After that, he continues to drop the price by 3% every two weeks until it reaches a cut-off amount assigned by the homeowner, or the house sells, whichever comes first. If a house is originally listed at $200,000 and the homeowner sets a cut-off amount of $166,000, what is the final selling price given that the house sells after being on the market for 9 weeks?

    1. $162,901.25
    2. $164,737.48
    3. $166,000.00
    4. $169,832.45
  45.  

    The figure above shows the net change, as a percentage, for U.S. import and export prices from January to July 2014 as reported by the Bureau of Labor Statistics. For example, U.S. import prices declined 0.2 percent in July while export prices remained unchanged for that month. Based on this information, which of the following statements is true for the time period shown in the figure?

    1. On average, export prices increased more than import prices.
    2. Import prices showed an increase more often than export prices.
    3. Import prices showed the greatest change between two consecutive months.
    4. From January to July, import prices showed a greater overall decrease than export prices.

  46. Every weekend for 48 hours, a law firm backs up all client files by scanning and uploading them to a secure remote server. On average, the size of each client file is 2.5 gigabytes. The law firm’s computer can upload the scans at a rate of 5.25 megabytes per second. What is the maximum number of client files the law firm can back up each weekend? (1 gigabyte = 1,000 megabytes)

    1. 362
    2. 363
    3. 476
    4. 477
  47.  
    An untitled scatterplot with 13 data points in the shape of a parabola that opens downward. The vertical axis is labeled from zero to 40 in increments of 5. The horizontal axis is labeled from zero to 40 in increments of 10. The lowest data point on the left is appoximately 0 comma 6. The data points increase until they reach a maximum, which is approximately 25 comma 31. There are only a few data points to the right of the maximum, the last of which is 30 comma 30. There is a graphing calculator screenshot showing several additional data points as follows: 7.5 comma 18.75, 10 comma 22, 12.5 comma 24.75, 15 comma 27, and 17.5 comma 28.75.

    The maximum value of the data shown in the scatterplot above occurs at x = 25. If the data is modeled using a quadratic regression and the correlation coefficient is 1.0 (the fit is exact), then what is the y-value when x = 35 ?

    1. 10
    2. 15
    3. 22
    4. 27

  48. Ethanol is an alcohol commonly added to gasoline to reduce the use of fossil fuels. A commonly used ratio of ethanol to gasoline is 1:4. Another less common and more experimental additive is methanol, with a typical ratio of methanol to gasoline being 1:9. A fuel producer wants to see what happens to cost and fuel efficiency when a combination of ethanol and methanol is used. In order to keep the ratio of gasoline to total additive the same, what ratio of ethanol to methanol should the company use?

    1. 1:1
    2. 4:9
    3. 9:4
    4. 36:9

  49. Mikal has two saltwater fish tanks in his home. One has eels and lionfish in a ratio of 5 to 2. The second tank has eels and seahorses in a ratio of 2 to 3. Mikal wants to put a tank in his office with seahorses and lionfish, using the same ratio he has at home to make it easier to buy food for them in bulk. What ratio of lionfish to seahorses should he use?

    1. 2:3
    2. 5:2
    3. 7:8
    4. 4:15

  50. Mario watched a thunderstorm from his backyard. He recorded the length of time, to the nearest second, between lightning flashes in the table below.
    Time Between Lightning Flashes (in seconds)
    7 8 8 9 10
    10 11 12 12 13
    14 15 15 16 16
    17 17 18 19 30

    The outlier measurement of 30 seconds is an error. Of the mean, median, and range for the values listed, which will change the most if the 30-second measurement is removed from the data?

    1. Mean
    2. Median
    3. Range
    4. They will all change by the same amount.

  51. Medically speaking, remission is a period in which the symptoms of a disease or condition subside or, for some diseases, a period during which the condition stops spreading or worsening. In a certain drug trial in which a drug designed to treat cancer was tested, exactly 48% of patients experienced remission while taking the drug. What is the fewest number of patients who could have participated in this trial?

  52. A county employee is collecting water samples from all the houses in a subdivision where trace amounts of lead were found in the water. There are 45 houses in the subdivision. If he starts the first house at 9:00 AM and starts the sixth house at 10:00 AM, how many minutes will it take the employee to collect samples from all the houses in the subdivision, assuming it takes the same amount of time at each house?

  53. A college math professor informs her students that rather than curving final grades, she will replace each student’s lowest test score with the next to lowest test score, and then re-average the test grades. If Leeza has test scores of 86, 92, 81, 64, and 83, by how many points does her final test average change based on the professor’s policy?

  54. A bank offers a long-term savings account with a 1.0% annual interest rate. At the end of each year, the interest is rounded down to the nearest cent and added to the principal. If the initial deposit was $1,500, how much interest has the account earned at the end of 5 years?

  55. Questions 55 and 56 refer to the following information.

  56. The Great Depression began in 1929 and lasted until 1939. It was a period of extreme poverty, marked by low prices and high unemployment. The main catalytic event to the Great Depression was the Wall Street Crash (stock market crash). The Dow, which measures the health of the stock market, started Black Thursday (October 24, 1929) at approximately 306 points.

  57. The stock market had been in steady decline since its record high the month before. If the market had declined by 19.5% between its record high and opening on Black Thursday, what was the approximate value of the Dow at its record high? Round your answer to the nearest whole point.

  58. By the end of business on Black Thursday, the Dow had dropped by 2%. Over the course of Friday and the half-day Saturday session, there was no significant change. Unfortunately, the market lost 13% on Black Monday, followed by another 12% on Black Tuesday. What was the total percent decrease from opening on Black Thursday to closing on Black Tuesday? Round your answer to the nearest whole percent and ignore the percent sign when entering your answer.

    1. Questions 57 and 58 refer to the following information.

    2. Bridget is starting a tutoring business to help adults get their GEDs. She already has five clients and decides they can share a single textbook, which will be kept at her office, and that she also needs one notebook and four pencils for each of them. She records her supply budget, which includes tax, in the table shown.

      Supply Total Number Needed Cost Each
      Textbook 1 $24.99
      Notebooks 5 $3.78
      Pencils 20 $0.55

    3. The textbook makes up what percent of Bridget’s total supply budget? Round to the nearest tenth of a percent and ignore the percent sign when entering your answer.

    4. Bridget’s business does very well, and she needs more supplies. She always orders them according to the table above, for five clients at a time. At the beginning of this year, she orders the supplies for the whole year, which cost $988.02. Halfway through the year, she decides to take inventory of the supplies. She has used $713.57 worth of the supplies. How many pencils should be left, assuming the supplies were used at the rate for which she originally planned?

  60. On a map, the scale is the ratio of the distance shown on the map to the actual distance. A geography teacher has a map on her wall with a scale of 1 inch:100 miles. She uses the school’s copier to shrink the large wall map down to the size of a piece of paper to hand out to each of her students. To do this, she makes the map of its original size. Suppose on the students’ maps, the distance between two cities is 2.5 inches. How many actual miles apart are those cities?

  61.  
    image

    A company conducted a study comparing the overall job performance of its regional managers with the length of time each one spent in the company’s management-training program. The scatterplot above shows the results of the study. What is the length of the time spent in training, in months, of the manager represented by the data point that is the greatest distance from the line of best fit (not shown)?

  62. Jordan is beginning a marathon training program. During his first day of training, he wears a pedometer to get an idea of how far he can currently run. At the end of the run, the pedometer indicates that he took 24,288 steps.

    Jordan knows from experience that his average stride (step) is 2.5 feet. How many miles did he run on his first day of training? (1 mile = 5,280 feet)

  63. A student news reporter chose 500 students at random from each of two schools and asked each student how many video games he or she has. The results are shown in the table below.
    Student Video Game Survey
    Number of Video Games
    		 Jefferson School Midtown High School
    0 100 130
    1 120 120
    2 90 100
    3 130 90
    4 60 60

    What is the median number of video games for all the students surveyed?

  64.  
    image

    The histogram above shows the number of vehicles that a car rental agency currently has available to rent, categorized by fuel efficiency ratings. If a customer randomly selects one of the available cars, what is the probability that he will get a car that has a fuel efficiency rating of at least 25 miles per gallon? Enter your answer as a decimal number.

  65. The following table shows the number of houses in a development. The table categorizes the houses by type (single-family or townhouse) and by the number of bedrooms.

    Development Houses

    2 Br 3 Br 4 Br Total
    Single-Family 5 19 34 58
    Townhouse 24 42 30 96
    Total 29 61 64 154

    The homeowner’s association partners with a local daycare center. The HOA has agreed to allow the daycare center to advertise in the development using flyers. In general, families with children typically reside in single-family homes or townhouses that have 3 or more bedrooms. The daycare center has a limited budget and plans to concentrate its marketing efforts on only those homes and townhouses. 

    In addition to sending out flyers, the daycare center decides to send out invitations for a free day of daycare, but determines that it would be too expensive to do this for all of the family residences in the development. Instead, it decides to market this benefit only to the two categories in the table with the most dwellings. If a dwelling that already received a flyer is chosen at random to receive the second stage of the marketing, what is the probability that the dwelling belongs to one of these two groups? Enter your answer as a decimal.

  66. Questions 65 and 66 refer to the following information.

  67. Three cars all arrive at the same destination at 4:00 PM. The first car traveled 144 miles mostly by highway. The second car traveled 85 miles mainly on rural two-lane roads. The third car traveled 25 miles primarily on busy city streets.

  68. The first car traveled at an average speed of 64 miles per hour. The second car started its drive at 2:18 PM. How many minutes had the first car already been traveling before the second car started its drive?

  69. The third car encountered heavy traffic for the first 60% of its trip and only averaged 15 miles per hour. Then traffic stopped due to an accident, and the car did not move for 20 minutes. After the accident was cleared, the car averaged 30 miles per hour for the remainder of the trip. At what time in the afternoon did the third car start its trip? Use only digits for your answer. (For example, enter 1:25 PM as 125.)

  70. A restaurant offers a 20% discount to students and to members of the military. The restaurant is also currently participating in a charity drive. If patrons donate a gently used item of clothing, they get an additional 5% off their bill, which is applied before any other discounts, such as student or military discounts.

    Sharon is a member of the military. She dines with her friend, Damien. Damien brings an item of clothing, but Sharon forgot to bring one. If Sharon’s meal before discounts is $16.25 and Damien’s is $12.80 before discounts, how much did the discounts save them altogether?

  71.  
    Years at Company Female Male
    y < 1 38 30
    1 ≤ y ≤ 3 15 19
    y > 3 54 48

    A company conducts a survey among its employees and categorizes the results based on gender and longevity (the number of years the employee has been working for the company). The Director of Human Resources wants to conduct a small follow-up focus group meeting with a few employees to discuss the overall survey results. If the HR Director randomly chooses four employees that participated in the initial survey, what is the probability that all of them will have been with the company for longer than 3 years? Enter your answer as a fraction.

  72. Seven integers are ordered from least to greatest. If the only mode is 7, and the median is 9, what is the least possible range for the seven numbers?

    1. Questions 70 and 71 refer to the following information.

    2. Chemical Makeup of One Mole of Chloroform

      Element Number of Moles Mass per Mole (grams)
      Carbon 1 12.011
      Hydrogen 1 1.008
      Chlorine 3 35.453

      A chemical solvent is a substance that dissolves another to form a solution. For example, water is a solvent for sugar. Unfortunately, many chemical solvents are hazardous to the environment. One eco-friendly chemical solvent is chloroform, also known as trichloromethane (CHCl3). The table above shows the chemical makeup of one mole of chloroform.

    3. Carbon makes up what percent of the mass of one mole of chloroform? Round your answer to the nearest whole percent and ignore the percent sign when entering your answer.

    4. If a chemist starts with 1,000 grams of chloroform and uses 522.5 grams, how many moles of chlorine are left?

  74. Questions 72 and 73 refer to the following information.

  75. Daniel works for a pest control company and is spraying all the lawns in a neighborhood. The figure above shows the layout of the neighborhood and the times that Daniel started spraying the lawns at two of the houses. Each lawn in the neighborhood is approximately 0.2 acres in size and takes the same amount of time to spray.

  76. How many minutes will it take Daniel to spray all of the lawns in the neighborhood?

  77. Daniel uses a mobile spray rig that holds 20 gallons of liquid. It takes 1 gallon to spray 2,500 square feet of lawn. How many times, including the first time, will Daniel need to fill the spray rig, assuming he fills it to the very top each time? (1 acre = 43,560 square feet)

  78.  
    An untitled scatterplot showing 10 data points that form an upside down parabola. Height, in feet, is plotted along the vertical axis from 0 to 45 in increments of 5. Distance, in yards, is plotted along the horizontal axis from 0 to 50 in increments of 10. The data points are as follows: 0 comma 5, 5 comma 22.5, 10 comma 35, 15 comma 42.5, 20 comma 45, 25 comma 42.5, 30 comma 35, 35 comma 22.5, and 40 comma 5. The last data point is approximately (not exactly) 41 comma 0.

    The figure above represents the trajectory of a t-shirt shot from a t-shirt cannon from one end of a football field toward the other. The quadratic function can be used to model the data. Based on the model, approximately how many feet farther did the t-shirt travel horizontally than it did vertically upward, assuming that no one caught the t-shirt and that it did not roll once it hit the ground? Round your answer to the nearest whole foot.

  79. Rory left home and drove straight to the airport at an average speed of 45 miles per hour. He returned home along the same route, but traffic slowed him down and he only averaged 30 miles per hour on the return trip. If his total travel time was 2 hours and 30 minutes, how far is it, in miles, from Rory’s house to the airport?