Quantitative Literacy Test File - Fall 2020

Exam #1

For each of #1-5, identify one AND ONLY ONE of our logical fallacies that is exhibited. Give a brief explanation for your choice. 1.) When Bubba, Jr., the son of Bubba, the proprietor of Bubba's All You Can Stomach Eatery, was in college, he told a professor "I know the exam is graded based on performance, but you should give me an A. My cat has been sick, my car broke down, and I've had a cold, so it was really hard for me to study!" 2.) "I don't know of any great Lithuanian authors so there must not be any great Lithuanian literature." 3.) "Buy new and improved CRUST™ toothpaste, the toothpaste used by more people than any toothpaste in the country!" 4.) "If we allow unregulated harvesting of our forests then what are we going to do about the increase in abuse of the food stamp program." 5.) "Eighty year old people don't need to go into nursing homes. After all my mother is 85 and she power-walks two miles each day, drives her car (safely), climbs stairs, does crosswords, and reads the daily paper." (adapted from http://www.fallacyfiles.org)

6.) For each of the following, tell whether or not it is a proposition. a.) "Pick up your sister after school." b.) Arkansas is a nicer place to live than Texas. c.) Iowa is the largest state in the United States. d.) All the dogs on my desk are purple. e.) Bob Uecker is the best catcher of all-time. f.) Mickey Mouse was president of the United States in 1998.

7.) Draw a Venn Diagram to illustrate the following categorical proposition. All dogs eat acorns and some dogs ride skateboards.

8.) The following Venn diagram represents how a college class is broken down in the categories of female students (denoted "F"), students from Arkansas (denoted "A") and mathematics majors (denoted "M"). Answer the questions below the diagram.

a.) How many students are in the class? b.) How many of the students are mathematics majors from Arkansas? c.) How many female students are in the class? d.) How many psychology majors are in the class? e.) What do we know about student "x?" f.) What do we know about student "y?"

9.) Your living room is 15 feet wide and 18 feet long. What is the area of your living room in square meters? You must show the use of units and conversion factors. 10.) You are driving 100 feet per second. The speed limit is 70 miles per hour. Are you speeding? You must show the use of units and conversion factors. 11.) Methusaleh was 969 years old when he died. How many seconds old was Methusaleh when he died? 12.) Walter Young, at 6-foot-5, 322-pounds, is believed to be the heaviest major league baseball player ever. Convert his weight to kilograms. 13.) You have a basket with apples in it. There are 23 green apples, 14 red apples and 8 plaid apples. You are going to take some apples out of the basket. a.) How many apples must you take out of the basket to be absolutely certain you have removed a matching pair of apples? b.) How many apples must you take out of the basket to be absolutely certain you have removed a matching pair of plaid apples? c.) How many apples must you take out of the basket to be absolutely certain you have removed four apples of the same color? 14.) You have ten rectangular tables in a rectangular room. You must arrange the tables so that there are exactly three tables along each wall. Draw a picture to show how you could do this. 15.) Seventy-five people ate dinner at "Billy Bob's All You Can Stomach Exotic Animal Eatery" last night. Sixty-five of them ate squid. Fifty-three of them ate platypus. Forty-eight of them ate earthworm cookies. What is the fewest number of people who must have eaten all three of squid, platypus and earthworm cookies?

Exam #2

1.) Calculate (5 x 10-8) x (4.2 x 1012) without using your calculator. Be careful to show ALL of your work and express your final answer in scientific notation. 2.) Estimate the total number of slices of bread eaten each year in the United States. Be sure to clearly state all of your assumptions. 3.) Consider the following question. How do doctors' salaries compare to lawyers' salaries? Which type of study (experimental, observational, double-blind) would best answer the question? Give a reason for your answer. 4.) Do the following. a.) Write 0.00000034 in scientific notation. b.) Write 45,000,000,000 in scientific notation 5.) You start putting money in your retirement fund at age 23. You put in $500 each month. The interest of 10.15% is compounded monthly. You retire at age 65. a.) Without inserting any numbers, write out the formula that will figure out the amount of money you will have when you retire. b.) Without doing any simplification, insert all of the numbers into the formula. c.) How much money will you have at age 65? d.) What is the total of all of your payments? e.) How much interest did your money earn?

6.) Maher-Shalal-Hash-Baz started putting money in a college savings account. He wants to have $120,000 in 18 years when his son will be ready for college. The interest rate of 7.5% is compounded quarterly. a.) Without inserting any numbers, write out the formula that will figure out the amount of money Maher-Shalal-Hash-Baz will have to put in the account each quarter. b.) Without doing any simplification, insert all of the numbers into the formula. c.) How much money will he have to pay each quarter? d.) What is the total of all of his payments? 7.) A person is interested in finding out the average income of people in Arkadelphia. In order to do that, he does a survey by asking the annual income of Arkadelphia residents who are shopping at the local Waffle House. Are his results likely to be representative of Arkadelphia? Why or why not? 8.) You are buying a house. After the down payment, you need to borrow $105,000. You will take out a mortgage to cover the remaining cost of the house. The interest rate for your 30 year mortgage is 4.15%, compounded monthly. Throughout the problem we will ignore escrow payments that might be added to the payment for insurance and taxes. a.) WITHOUT SUBSTITUTING IN ANY NUMBERS, write the formula you will use to find the monthly payment on this loan. b.) WITHOUT SIMPLIFYING ANYTHING, insert the correct numbers into the formula. c.) What will be your monthly payment? d.) What will be the total of all of your monthly payments? e.) How much interest will you pay over the life of the loan? 9.) The price of a sofa was $780. Two weeks ago the price was dropped 15%. This week it was dropped 10%. What is the price now? 10.) In 2004, Bobby Abreu of the Philadelphia Phillies made a salary of $10,600,000. That was an increase of 16.4835% from his 2003 salary. What was Abreu's 2003 salary? (data from http://www.businessofbaseball.com/) 11.) Bob bought a house worth $120,000. Now, after five years he was told the house's value had gone up 26%. What is the house worth now? 12.) The listed price was $14.95. Tax of 8.25% was added on. What was the total cost? 13.) You put $2500 in a certificate of deposit account for 3 years. It receives 4.5% interest compounded quarterly. You neither take out any money nor put in any more money. a.) Without inserting any numbers, write out the formula that will figure out the amount of money you will have after 3 years. b.) Without doing any simplification, insert all of the numbers into the formula. c.) How much money will you have after 3 years?

Exam #3

1.) The following chart shows the number of runs scored by pitcher Bobo Newsom in his first six full seasons in the major leagues. Draw a bar graph to illustrate this data.

Year Runs 1934 6 1935 6 1936 11 1937 11 1938 9 1939 6 1940 9

2.) The following chart shows the breakdown of number of games won by the pitchers on the 1916 Philadelphia Athletics. The team won a total of 36 games.

a.) Who won the most games for the 1916 Athletics? b.) How many games did Elmer Myers win? c.) Add up the seven percentages. Explain why they don't add up to 100%. d.) How many games did Socks Seibold lose for the 1916 Athletics?

3.) The following chart gives the career statistics for Dode Paskert. Year Team Lg G AB R H 2B 3B HR RBI BA OBP SLG 1907 CIN NL 16 50 10 14 4 0 1 8 .280 .333 .420 1908 CIN NL 118 395 40 96 14 4 1 36 .243 .298 .306 1909 CIN NL 104 322 49 81 7 4 0 33 .252 .327 .298 1910 CIN NL 144 506 63 152 21 5 2 46 .300 .389 .374 1911 PHI NL 153 560 96 153 18 5 4 47 .273 .358 .345 1912 PHI NL 145 540 102 170 37 5 2 43 .315 .420 .413 1913 PHI NL 124 454 83 119 21 9 4 29 .262 .358 .374 1914 PHI NL 132 451 59 119 25 6 3 44 .264 .349 .366 1915 PHI NL 109 328 51 80 17 4 3 39 .244 .319 .348 1916 PHI NL 149 555 82 155 30 7 8 46 .279 .346 .402 1917 PHI NL 141 546 78 137 27 11 4 43 .251 .331 .363 1918 CHC NL 127 461 69 132 24 3 3 59 .286 .362 .371 1919 CHC NL 88 270 21 53 11 3 2 29 .196 .274 .281 1920 CHC NL 139 487 57 136 22 10 5 71 .279 .366 .396 1921 CIN NL 27 92 8 16 1 1 0 4 .174 .208 .207 totals 1716 6017 868 1613 279 77 42 577 .268 .350 .361

a.) "Doubles" is denoted by "2B." In how many years did Paskert have more than 25 doubles? b.) "Batting average" is denoted by "BA." What was Paskert's highest batting average? c.) "Runs scored" is denoted by "R" and "Runs batted in" is denoted by "RBI." In how many seasons did Paskert have more runs batted in than runs scored? d.) "Slugging Percentage" is denoted by "SLG." In how many seasons did Pakert have a slugging percentage higher than .380? e.) "Triples" is denoted by "3B." How many triples did Ty Cobb have in 1920?

4.) The following chart gives the career home runs for nine different players.

700

600

500

400 300

200

100

Ray Oyler Ray

Willie Mays

Jimmie Foxx

Bobby BonillaBobby

Mickey Mickey Mantle

Gavvy Cravath Gavvy

Willie McCovey

Mickey Mickey Morandini

Roberto Clemente Roberto

a.) Of these players, how many have over 500 career home runs? b.) Who hit more career home runs, Mickey Morandini or Ray Oyler? c.) How many career home runs did Willie Mays (the greatest all-around ball player ever) hit? d.) Who hit more career doubles, Mickey Mantle or Jimmie Foxx? e.) How many career home runs did Gavvy Cravath hit?

5.) When two events are correlated, there are three possible explanations. One is that one event caused the other. One is that some third event caused both events. What is the other possibility?

6.) The following chart tells how many games were won by the American and National League champions each year from 1940 through 1949.

110 105 100 American 95 League 90 National League 85 80 75

1940 1941 1942 1943 1944 1945 1946 1947 1948 1949

a.) In how many of these years did the National League champion win more games than the American League champion? b.) How many games did the National League champion win in 1942? c.) How many games did the Yankees win in 1944? d.) How many more games did the 1946 American League champion win than the 1945 American League champion won? e.) How many times during these years did both league champions win at least 100 games?

7.) You roll two dice. What is the probability that the sum of the numbers on the dice is greater than 9?

8.) The following are the players who had the most triples for the 1979 Cubs. Find the following WITHOUT USING YOUR CALCULATOR AT ALL AND YOU MUST GIVE SOME INDICATION OF HOW YOU FOUND THE NUMBER.

Bill Buckner 7 Ivan DeJesus 10 Jerry Martin 3 Dave Kingman 5 Scot Thompson 5 Larry Biittner 3

a.) Find the mean. b.) Find the median. c.) Find the mode. 9.) A box contains five regular tacos, seven soft tacos, eight bean burritos, and four tostadas. You reach into the box and randomly choose an item. You then reach in and take another item. What is the probability that the first item was a regular taco and the second was a tostada? 10.) Consider the nine letters G, H, I, J, K, M, L, N, and O. For our purposes, a "word" is ANY arrangement of letters (for example, GGKKJ is a "word"). a.) How many four letter "words" can be made if repetitions are allowed? b.) How many four letter "words" can be made if no repetitions are allowed?

11.) This chart lists the major league baseball pitchers (in alphabetical order) from 1972-1974 who had the most strikeouts in a single season. (source: sabermetric baseball encyclopedia) Use your calculator to answer the following questions.

Player Year Strikeouts a.) For these players, what is Bert Blyleven 1972 228 the mean number of Bert Blyleven 1973 258 Bert Blyleven 1974 249 strikeouts? Tom Bradley 1972 209 Steve Carlton 1972 310 b.) For these players, what is Steve Carlton 1973 223 Steve Carlton 1974 240 the median number of Joe Coleman 1972 222 strikeouts? Bob Gibson 1972 208 Ferguson Jenkins 1974 225 c.) For these players, what is Mickey Lolich 1972 250 Mickey Lolich 1973 214 the mode number of Andy Messersmith 1974 221 strikeouts? Gaylord Perry 1972 234 Gaylord Perry 1973 238 Gaylord Perry 1974 216 Nolan Ryan 1972 329 Nolan Ryan 1973 383 Nolan Ryan 1974 367 Tom Seaver 1972 249 Tom Seaver 1973 251

12.) Explain the difference between an exponential model and a linear model. 13.) Mineral Springs, Arkansas had a population of 546 in 1880. By 1900, it had lost half of its population. Assuming the population continued to decline exponentially at the same rate, what would the population be in 2005? (Note: the actual 2000 population was 1,264.)

14.) You are coaching a little league baseball team. You have 17 players. You are choosing a defensive arrangement involving the nine positions (pitcher, catcher, first baseman, second baseman, shortstop, third baseman, left fielder, center fielder, right fielder). a.) Is this a permutations problem, a combinations problem, or neither? b.) How many different defensive arrangements can you pick?

15.) Draw a tree diagram to illustrate the possible outcomes of flipping a coin three times. Then, use the tree diagram to determine the probability of getting 2 heads and one tail in the three flips.

16.) The following chart gives a breakdown of some people in a class. Answer the following questions based on the chart.

Male Female Totals Freshmen 8 10 18 Sophomores 6 7 13 Juniors 9 7 16 Seniors 12 13 25 Totals 35 37 72

a.) If a student is chosen at random, what is the probability that the student is male? b.) If a female student is chosen at random, what is the probability that the student is a sophomore? c.) If a student is chosen at random, what is the probability that the student is a male or a sophomore?

Exam #4

1.) A note has a frequency of 360 cycles per second. Find the frequency of the note that is 3 half- steps above our note. 2.) A note has a frequency of 360 cycles per second. Find the frequency of the note that is 4 half- steps below our note. 3.) A note has a frequency of 360 cycles per second. Find the frequency of the note that is one octave above our note. 4.) A note has a frequency of 360 cycles per second. Find the frequency of the note that is one octave below our note. 5.) A note has a frequency of 360 cycles per second. Find the frequency of the note that is three octaves above our note.

6.) Draw a section of tile hallway (include the walls), with four rows of four tiles each, that illustrates the idea of vanishing points. Identify the principal vanishing point and two other vanishing points.

7.) Consider the following shapes.

For each type of symmetry below, list the shapes that have that kind of symmetry. Some may fit more than one symmetry. a.) symmetry around a horizontal line through the middle of the shape b.) symmetry around a vertical line through the middle of the shape c.) rotational symmetry d.) none of the above symmetries

8.) A Fibonacci-like sequence has a first term of 1 and a second term of 8. Find the: a.) third term b.) fourth term c.) fifth term d.) sixth term

9.) Explain the difference between votes that are decided by majority vote and those decided by plurality vote. 10.) Give examples of two elections that require a super-majority vote. Be sure to give the percentage required in each vote. 11.) Explain how a Borda Count works. Give an example of something that is done with a Borda Count.

12.) Consider a country consisting of 5 states with populations given below. If the country's legislature is to have 120 members, find the standard divisor and fill in the table below.

Standard Divisor = State Population Standard # of representatives # of representatives Quota state "should" get you will give state A 6,305,331 B 6,305,332 C 1,815 D 19,886,060 E 10,334,549 Total 42,833,087 Population

13.) Find the area and perimeter of the following triangle. Assume all units are in centimeters.

14.) A cylindrical storage drum has a height of 4 feet and a diameter of one yard. Find the volume and surface area. GIVE AT LEAST 4 PLACES TO THE RIGHT OF THE DECIMAL POINT!! 15.) The window below is shaped like a rectangle with a semi-circle on top. What are the area and perimeter of the window? GIVE AT LEAST 4 PLACES TO THE RIGHT OF THE DECIMAL POINT!!

Part of the Final Exam

In each of the following three statements, a logical fallacy is exhibited. In each problem, identify one of our fallacies that is exhibited. Give a good explanation justifying your answer. DO NOT USE THE SAME FALLACY FOR MORE THAN ONE EXAMPLE. 1.) "Show your concern for your children's future by buying a good life insurance policy now!" 2.) "The government policies changed the housing market so now I'm going to lose my house." 3.) "Hair growth precedes the growth of teeth in babies so hair must cause teeth growth."

4.) A poll is being conducted on MSNBC's web site. Discuss any sources of bias or any other problems associated with this poll. 5.) From 1914 to 2012, the United States has seen an average annual inflation rate of 3.2332009%. If a loaf of bread cost five cents in 1914, and inflation was the only thing that affected the price of bread, what would a loaf of bread cost in 2012? Show all work. 6.) You are buying a house. After the down payment, you need to borrow $85,000. You will take out a mortgage to cover the remaining cost of the house. The interest rate for your 15 year mortgage is 3.275% compounded monthly. Throughout the problem we will ignore escrow payments that might be added to the payment for insurance and taxes. a.) WITHOUT SUBSTITUTING IN ANY NUMBERS, write the formula you will use to find the monthly payment on this loan. b.) WITHOUT SIMPLIFYING ANYTHING, insert the correct numbers into the formula. c.) What will be your monthly payment? d.) How much interest will you pay over the life of the loan? 7.) You put $3250 in a certificate of deposit account for 3 years. It receives 4.5% interest compounded quarterly. You neither take out any money nor put in any more money. a.) Without inserting any numbers, write out the formula that will figure out the amount of money you will have after 3 years. b.) Without doing any simplification, insert all of the numbers into the formula. c.) How much money will you have after 3 years? d.) How much interest did you earn?

8.) You roll two dice. What is the probability that the sum of the numbers on the dice is greater than 9?

9.) You start putting money in your retirement fund at age 23. You put in $400 each month. The interest of 10.375% is compounded quarterly. You retire at age 65. a.) Without inserting any numbers, write out the formula that will figure out the amount of money you will have when you retire. b.) Without doing any simplification, insert all of the numbers into the formula. c.) How much money will you have at age 65? d.) What is the total of all of your payments? e.) How much interest did your money earn?

10.) Draw a tree diagram to illustrate tossing three coins. Find the probability that exactly two of the coins came up heads. 11.) The following chart shows the doubles, triples and home runs for all National Leaguers with at least 10 triples in 1937. Answer the questions below. 60

30 2B 20 3B

10 HR

Al Todd Al

GusSuhr

Billy Jurges Billy

AugieGalan

LeeHandley

Jo-Jo MooreJo-Jo

GeneMoore

Billy Herman Billy

JoeMedwick

ArkyVaughan Ival Goodman DonGutteridge

a.) Of these players, which had the most doubles in 1937? How many did he have? b.) Who led the National League in home runs in 1937? c.) Who led the National League in triples in 1937? d.) How many of these players had at least 10 home runs in 1937?

12.) You are coaching a little league baseball team. You have fifteen players. You are choosing a defensive arrangement involving the nine positions (pitcher, catcher, first baseman, second baseman, shortstop, third baseman, left fielder, center fielder, right fielder). a.) Is this a permutations problem, a combinations problem, or neither? b.) How many different defensive arrangements can you pick?

13.) The following chart shows the breakdown of number of games won by the pitchers on the 1916 Philadelphia Athletics. The team won a total of 36 games.

14.) A.) You have a seven minute hour glass and a nine minute hour glass. You are cooking something that must be cooked for exactly three minutes. How would you use the two hour glasses to time your cooking? [Note: It is impossible to tell when an hour glass is exactly half empty, or has just one minute left, etc.] B.) In your drawer you have 15 identical green socks, 24 identical blue socks and 18 identical plaid socks. Without looking, you start pulling socks out of the drawer. (i) How many socks must you pull out so that it is certain you have a matching pair of socks? (ii) How many socks must you pull out so that it is certain you have a matching pair of green socks?