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Harvard Mathematics For Management Pretest

Q1. Let g(x)=x⁴-3x² What is the value of g”(x) when x=5?

22
294
470
3594

Q2. A group of students were surveyed to see if they were enrolled in a music or art course. The results are shown in the table below.

What is the probability that a randomly chosen student is taking a music course, if they are taking an art course?

3/16
1/4
1/3
3/4

Q3. There are 30 students in a class. The number of students having certain characteristics is shown in the two-way table below.

Harvard Mathematics For Management Pretest

Consider two values:

I P(blonde hair). P(blue eyes)

II P(blonde hair and blue eyes)

Which statement concerning the event “having blonde hair” and the event “having blue eyes” is correct?

The events are dependent because I and II are different
The events are dependent because I and II are the same
The events are independent because I and II are different
The events are independent because I and II are the same

Q4. Suppose that the demand for a product is modeled by q=300-2p, where p is the price of the product in dollars. What happens to the demand when the price is increased from $100 to $101?

It decreases by 1%
It decreases by 2%
It increases by 1%
It increases by 2%

Q5. Which statement concerning the inflection points of p(x) = x³ – 3x² – 9x is correct?

It has a single inflection point at x = -1
It has a single inflection point at x = 1
It has inflection points at x = -1 and x = 3
It has no inflection points

Q6. Suppose that your bank pays you an 8% annual interest rate, compounded continuously, on your investments. If you deposit $200 today, how much money will you have in exactly five years?

$280.00
$293.87
$298.36
$323.21

Q7. Bill says “I bought x jars of peanut butter for $2 each and y jars of jelly for $3 each. I bought a total of 9 jars and spent $28.” Ted turns this into a system of equations and says that Bill’s statement is bogus.
Which of the following is true?

Ted is incorrect because the system has a solution in whole numbers
Ted is correct because the system has no solution at all.
Ted is correct because the system has a solution but one of the variables is a fraction
Ted is correct because the system has a solution but one of the variables is negative

Q8. Brand X televisions cost a box store $200 apiece. If they sell one for p dollars, the annual demand is q=500-1/2p. What price should they charge to maximize profit?

$300
$400
$600
$1000

Q9. The following information about a stock is given in the table below.

Harvard Mathematics For Management Pretest

Using the attached Excel file call_with_dividends.xlsx, what is the correct price for a 3-month European call option?

$0.65
$1.11
$2.95
$3.65

Q10. An organization runs a bingo night. You pay $5 for a card and get to play two games. For each game you win, you are paid $10. The table shows the probabilities of the three possible outcomes.

Harvard Mathematics For Management Pretest

What is the expected value of the net result (“winnings”) for any participant in this bingo night?

-$3.00
-$2.05
+$1.05
+$2.00

Q11. If the following cash flows are discounted at 12%, what is the net present value (NPV) of this series of cash flows?

Harvard Mathematics For Management Pretest

$10.08
$26.15
$40.00
$160.08

Q12. Which rule for entering formulas in Excel is incorrect?

Begin every formula with =
Use ^ for raising a number to a power
Use ¸ for division
Excel uses PEMDAS to determine order of operations

Q13. The CEO of Ruthie’s Razors is considering buying a new machine that costs $5 million today. During each of the next 4 years, the CEO expects the machine to generate the following cash inflows.

What is the payback period for this machine?

Less than 1 year
Between 1 and 2 years
Between 2 and 3 years
Between 3 and 4 years

Q14. Which statement about the minimum value of C(x)=x²– 20x + 150 is correct?

The minimum value is 10
The minimum value is 50
The minimum value is 150
It has no minimum value

Q15. Assume that you are interested in buying a zero coupon bond. It has a maturity of 6 years, a price of $76, and a par value of $100. Assume that interest is compounded annually. What is the yield on this bond?

4.38%
4.68%
5.26%
31.58%

Q16. On a rainy day, 90% of the students on a campus of 10,000 students are carrying umbrellas. Two students walk into a classroom on this campus. What is the probability that at least one of them is not carrying an umbrella?

Q17. The selling prices of nine homes represented by Homepalooza Realty are shown in the table below.

Harvard Mathematics For Management Pretest

What is the median selling price of these homes?

$622,072
$335,989
$294,152
$249,317

Q18. An organization runs a bingo night. You pay $5 for a card and get to play two games. For each game you win, you are paid $10. The table shows the probabilities of the three possible outcomes.

Harvard Mathematics For Management Pretest

What is the standard deviation of the net result (“winnings”) for any participant in this bingo night, to the nearest cent?

$4.24
$6.17
$11.43
$14.61

Q19. Choose the option to correctly complete the sentence. The selling prices for ten homes represented by Brahminton Realty are given below.

Harvard Mathematics For Management Pretest

According to the rule of thumb, these data suggest that 95% of the time, a Brahminton home price will be between

$118,597 and $800,546
$136,094 and $783,048
$289,084 and $630,058
$323,621 and $828,975

Q20. An ice cream parlor has a monthly cost of 6000 + 0.5x dollars, where x is the number of ice cream cones that it sells. Each cone sells for $2.50. How many cones do they need to sell to break even?

1200
2000
2400
3000

Q21. The daily demand for mattresses at Rest of the Night Mattress Store is a normal random variable with a mean of 60 mattresses with a standard deviation of 5 mattresses. What is the probability (to the nearest tenth of a percent) that on a given day they will sell between 53 and 67 mattresses?

52.5%
76.2%
83.8%
91.9%

Q22. What is the value of 30 – 12/3 * 2?

Q23. What is the complete set of values of x where the function f(x) = 1/3x³– x² is concave?

Q24. Which inequality describes the set of all x that satisfy 26 < 6 – 4x ?

x>-8
x>-5
x<-8
x<-5

Q25. The daily demand for books at House Bookstore is a normal random variable with a mean of 200 books. On 34% of the days they are open, they sell between 200 and 215 books. On what percentage of the days they are open do they sell fewer than 185 books?

16%
22%
32%
There is not enough information to answer this question.

Q26. A group of students was surveyed to see if they were enrolled in a music or art course. The results are shown in the table below.

Harvard Mathematics For Management Pretest

What is the probability that a randomly selected student from this group is enrolled in a music or art course?

30/90
30/80
35/90
35/80

Q27. Choose the option to correctly complete the following sentence. A sequence of cash flows will have an NPV ________ zero if the IRR _______ the discount rate

less than; exceeds
equal to; is less than
greater than; is less than
greater than; exceeds

Q28. A small business owner receives a windfall of $120,000. She spends $6,000, then splits the remainder as follows. She invests money in her business, in the stock market, and puts money in an emergency fund, in a 5:2:1 ratio. How much money did she invest in the stock market?

$28,500
$30,000
$38,000
$40,000

Q29. Let p be the price, in dollars, for a car wash and let q represent the weekly demand for the service. Suppose that demand curve, or relationship between these two variables, is q=180-6p Which equation represents the “inverse demand curve” (expressing p as a function of q)?

p = 1 / 180 – 6q
p = 30 – q
p = 30 – 1/6 q
p = 180 – 1/6 q

Q30. Today is January 1, 2020. On the first day of the years 2021 to 2035, you will receive $15,000. If cash flows are discounted at 12% per year, what is the present value of these cash flows (rounded to the nearest dollar)?

$99,423
$102,163
$114,423
$225,000

Q31. There are two passengers remaining on a city bus that has 3 stops left on its route. What is the probability that one of them exits at the last stop, given that they will exit at different stops?

Q32. Suppose that today is January 1, 2020. You are scheduled to receive $4,500 on the first day of every year forever, beginning on January 1, 2021. If the annual discount rate is 8%, what is the present value of this infinite stream of cash flows?

$360
$4,167
$36,000
$56,250

Q33. The attached Excel file, data_red_banjo_daily_pints.xlsx, contains the number of pints of IPA beer sold at Red Banjo Brewing Company, per day, for the past three years. What is the mean number of pints of IPA beer sold per day (to the nearest 0.1 pint)?

189.0
165.0
162.0
156.0

Q34. The annual revenue growth rates for five years for Ruthie’s Razors are shown in the following table.

What is the Compound Annual Growth Rate (CAGR) for Ruthie’s Razors?

3.42%
3.67%
5.60%
10.34%

Q35. A certain stock had the following prices for the past five days: 17.80, 15.71, 16.74, 16.21, 15.95

To the nearest hundredth, what is the sample standard deviation of these stock prices?

0.74
0.79
0.83
1.85

Q36. The daily supply of a product is given by the function 100 + 5p, where p is the price, in dollars, of the product. The daily demand of the product is given by the function 200 – 5p. At what price will supply equal demand?

Q37. Suppose that it is equally likely that a child will be born male or female. Three babies are born in a hospital on the same day. What is the probability that exactly one of the babies is female?

Q38. What is the value of

Q39. What is the internal rate of return (IRR) of the following series of cash flows?

Harvard Mathematics For Management Pretest

Q40. Suppose that the function P(x)=-x²+100x-99 represents the daily profit from selling an item for $x. Which statement best explains if the daily profit could be as much as $2402?

It cannot be, because x² – 100x + 2501 = 0 has no solutions
It cannot be, because x² – 100x + 2501 = 0 has negative solutions
It cannot be, because x² – 100x + 2303 = 0 has positive solutions
It cannot be, because -x² + 100x – 99 = 0 has no maximum value

Q41. If f(x)=2 + 5x² then what is the value of f(-2)?

Q42. Suppose that your bank pays you 12% annual interest that is continuously compounded. What is the effective annual interest rate (rounded to the nearest hundredth of a percent)?

12.00%
12.75%
12.875%
13.00%

Q43. The heights (in inches) of the five starting players on the Erewhon College women’s basketball team are 68, 69, 70, 71, and 71. Which of the following inequalities is true for this data set?

Mean < Median < Mode
Mode < Mean < Median
Median < Mean < Mode
Mean < Mode < Median

Q44. Choose the option to correctly complete the sentence.

The closing prices for 50 stocks are given in the attached Excel file, data_stocks.xlsx. Suppose that we use Excel to create a histogram to summarize these data, using upper bin limits of 2000, 3000, 4000, 5000, 6000, 7000, and 8000.

The bin containing the most values corresponds to stock prices in the range from

$1000 to $2000
$3000.1 to $4000
$5000.1 to $6000
$7000.1 to $8000

Q45. Assume that you are interested in buying a coupon bond. It has a maturity of 7 years, a coupon rate of 6%, and a par value of $100. The required annual return for this bond is 9%. Assume that interest is compounded annually. What is the price of this bond?

$84.90
$86.54
$100.00
$116.75

Q46. Suppose that your bank pays you a 12% annual interest rate, compounded monthly, on your investments. If you deposit $200 today, how much money will you have in exactly three years?

$206.06
$272.00
$280.99
$286.15

Q47. Let y = 5x⁴ + x^-1 . What is dy/dx?

0 + 4x³ – x⁰
0 + 4x³ – x^-2
20x³ – x⁰
20x³ – x^-2

Q48. A straight line passes through the point (4,2). For each increase in the value of x by 1, the value of y decreases by 3. This line is the graph of which of the following equations?

y=-3x+14
y=3x-10
y=-3x+10
y=3x-2

Q49. The number of pints of IPA beer sold each day at Red Banjo Brewing over the past three years is in the attached Excel file, data_red_banjo_daily_pints.xlsx.

What is the median number of pints of IPA beer sold (rounded to the nearest whole number)?

Q50. Suppose that N is a positive number and log₁₀ N=q Which expression always equals the value of log₁₀ N²

2q
q²
q/2
√q

Q51. Choose the option to correctly complete the following sentence. Today is January 1, 2020. On the first day of the years 2020, 2021, 2022, and 2023, you will invest $15,000. If your expected rate of return is 9% per year, you will have a total of ___________ on January 1, 2024. (Please round your answer to the nearest dollar)

$60,000
$68,597
$74,771
$89,771

Q52. All else equal, the price of a call option increases as volatility increases. True / False

Q53. On January 1, 2018, stocks for Company A and B sold for $50 each. The stock for Company A went up by 10% in 2018. Then it went up by 10% in 2019. The stock for Company B went up by 20% in 2018. Then it went down by 10% in 2019. At the end of this time, how did the value of the two stocks compare?

Company A and B’s stock had the same value
Company A’s stock was worth $5.00 more.
Company A’s stock was worth $6.00 more.
Company A’s stock was worth $6.50 more

Q54. The table below shows the undergraduate GPA and GMAT scores for five business school students.

Harvard Mathematics For Management Pretest

What is the correlation between GPA and GMAT scores?

-0.22
0.22
0.59
0.84

Q55. What is the value of 16^3/2 * 10^-1

2.4
6.4
54
64.1

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