QUESTION 1 Suppose the American Medical Association Center for Health Policy Research included data, by state, on the number of community hospitals and the average patient stay (in days) in….

## What is the complete set of numbers for which f(x) = x + 2x – x is concave?

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1. Consider the equation 3×2 – 2x – 1 = 0. The sum of the roots of this equation is

1

2

-1/3

2/3

None of the above

2. For x > 0, which of these statements best describe the graph of y = x.25?

The slope is greater than zero and is decreasing.

The slope is greater than zero and is increasing.

The slope is less than zero and is decreasing.

The slope is less than zero and is increasing.

None of the above

3. Let p = the price in dollars charged for the dose of a drug. Suppose that the annual

demand (in millions of doses) = 1000 – 3p. The annual supply (in millions of doses) = 600

+ 2p. The annual supply will equal the annual demand if the price of a dose is ______

dollars.

4. Let q = the annual demand in pounds for a drug and p = the price per pound of the drug.

Suppose that q = 1,000,000p . Also suppose that you want to “invert the demand curve” and

express price as a function of demand. Which of the following is an expression of the inverse

demand curve?

-6

p = 0.10q

p = 10q

6

p = 10q

-1/6

-1/6

p = 0.10q /10

-1/3

None of the above

5. Suppose that a total of $10 million will be allocated to the first three finishers in the Springfield

Derby horse race in the ratio 7:2:1. The total amount received by the 2nd- and 3rd-place finishers

in the race is

$7 million

$5 million

$3 million

$1 million

None of the above

6. The fixed cost of developing a new drug is $3 billion. The unit cost of producing a single dose

of the drug is $1, and patients are charged $11 per dose. In order to make a $1 billion profit on the

drug, how many doses must be sold?

300,000,000

350,000,000

400,000,000

500,000,000

None of the above

7. When simplified, 18 + 4 × 9/2 + 5 equals _____________.

2

8. Suppose that Ln x = -3. Rounded to the nearest hundredth, what does x equal?

20.09

0.05

0.10

0.50

None of the above

9. For x = 2, the slope of the function f(x) = x – 3x is

4

10

25

15

30

None of the above

2

10. For x = 1/2 the second derivative of f(x) = 2x is

-2

3/4

100

192

25

None of the above

11. What is the complete set of numbers for which f(x) = x + 2x – x is concave?

3

x ≥ -2/3

x ≥ -3/2

x ≥ 3/2

x≥1

None of the above

2

12. The inflection point for f(x) = x – 3x + x + 5 is

3

2

x=0

x=1

x = -1

x=2

None of the above

13. The unit cost of producing a steak dinner at the Smalltown Inn is $6. If a restaurant

charges p dollars for a steak dinner, customers will demand 200 – 5p steak dinners per week. To

maximize the profit earned on steak dinners, what price should the inn charge?

$20

$21

$22

$23

$25

14. Today is January 1, 2020. On January 1 of the years 2021 through 2030, you are to receive

$50,000. If cash flows are discounted at 10% per year, the present value of these cash flows (as of

today), rounded to the nearest dollar, is

$300,000

$337,951

$310,022

$307,228

None of the above

15. On January 1 of the years 2015, 2016, and 2017, you received $15,000. If your investments earn

20% per year, how much money would you have on January 1, 2017?

$54,600

$65,520

$49,250

$63,000

None of the above

16. Last year, a barber shop generated $100,000 in profit. Assume that the shop’s profits grow at

5% per year and that cash flows are discounted at 10% per year. If profits are received at the end

of each year, what is the present value of all the shop’s future profits?

$1,500,000

$2,000,000

$2,500,000

$2,100,000

$3,000,000

17. Your bank pays 5% annual interest, compounded quarterly. Rounded to the nearest one

hundredth of a percent, the annual effective interest rate is

5.09%

5.00%

5.06%

5.12%

None of the abov

18. A 3-year bond paying 4% annual coupons pays $1000 at maturity. Today the bond sells for

$986.98. To the nearest one hundredth of one percent, the bond’s yield is

3.16%

4.87%

4.67%

4.47%

None of the above

19. A 10-year bond paying 8% annual coupons pays $1000 at maturity. If the required rate of return

on the bond is 7%, then today the bond will sell (rounded to the nearest cent) for

$1000.00

$1210.45

$987.48

$1070.24

None of the above

20. Consider a 9-month European call option with a strike price of $40 on a stock that sells for $35

today. If the annual risk-free rate (continuously compounded) is 8%, the stock pays no dividends,

and the stock’s annual volatility is 40%, then the Black-Scholes price for this option (rounded to

the nearest cent) is

$6.44

$3.77

$5.84

$8.12

None of the above

21. An

airline knows it will need to buy 100 million barrels of jet fuel 6 months from now. Of course,

if the price of jet fuel increases, the airline will be in trouble. Suppose that put and call options on

jet fuel are available for purchase.

True or False? To lower the airline’s risk associated with changes in jet fuel prices, the airline

should purchase call options on jet fuel.

True

False

22. If two dice are thrown, what is the probability that the first die shows a 4 or that the total on the

two dice is 8?

11/36

1/3

1/2

5/18

None of the above

23. If a card is drawn from a deck, what is the chance that the card is an ace, a three, or a five?

2/13

11/52

1/2

1/4

None of the above

24. A roulette wheel contains the integers 1 through 36, 0, and 00. Suppose that you spin the

wheel 6 times and that each time you bet on a single number. What is the probability (rounded to

the nearest hundredth) that you win on at least one bet?

0.09

0.11

0.13

0.15

None of the above

25. Suppose that 1% of all people have a particular disease. A test for the disease is 99% accurate.

This means that a person who tests positive for the disease has a 99% chance of actually having

the disease, while a person who tests negative for the disease has a 99% chance of not having the

disease.

If a person tests positive for the disease, what is the chance (rounded to the nearest hundredth)

that he or she actually has the disease?

0.99

0.40

0.50

0.45

None of the above

26. Suppose that you draw two cards from a deck. After drawing the first card, you do not put the

first card back in the deck. What is the probability (rounded to the nearest ten thousandth) that

both cards are diamonds?

0.0543

0.0588

0.0625

0.0643

None of the above

27. Suppose that you toss two dice. Let event A = the event that the first die shows a 4 and B = the

event that the total on the two dice is 7.

True or False? Events A and B are independent events.

True

False

28. Suppose that the number of pounds of grapes sold by the Smalltown Co-op grocery store in a

day is equally likely to be anywhere between 0 and 100 pounds (fractional values are possible). If

you use a probability density function to describe the number of pounds of grapes sold daily by

the store, the height of the function for any number of pounds between 0 and 100 is

0.01

0.02

0.005

0.10

None of the above

29. A drug company believes that the annual demand for a drug will follow a normal random

variable with a mean of 900 pounds and a standard deviation of 60 pounds. If the company

produces 1000 pounds of the drug, what is the chance (rounded to the nearest hundredth) that it

will run out of the drug? Assume that the only way to meet the demand for the drug is to use this

year’s production number.

0.062

0.054

0.048

0.033

0.073

30. Smalltown Elevator produces elevator rails. To meet specifications, an elevator rail must be

between 0.995 inches and 1.005 inches in diameter. Suppose that the diameter of an elevator rail

follows a normal random variable with mean of 1 inch and standard deviation of 0.003 inches.

Rounded to the nearest one tenth of one percent, what fraction of all elevator rails will meet

specifications?

90.4%

95.2%

93.4%

97.3%

None of the above