1.
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
2.
For x = 2,
the slope of the function f(x) = x4 – 3x2 is
·
10
·
25
·
15
·
30
·
None of the above
3. What is the complete set of numbers for which f(x)
= x3 + 2x2 – x is concave?
·
x ? ?2/3
·
x ? ?3/2
·
x ? 3/2
·
x ? 1
·
None of the above
4.
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
5.
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
6.
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
7.
For x >
0, which of these statements best describe the graph of y = x0.25?
·
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
8.
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
9.
Suppose that the average
score on the GMAT exam is 500 and that the standard deviation of all scores is
100 points. You would expect approximately 95% of all GMAT scores to be between
·
400 and 600
·
300 and 700
·
200 and 800
·
350 and 650
·
250 and 750
10.
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
·
11.
The set of all values
of x that satisfy 5(3 – x) ? 10 is expressed as
·
x ? 1
·
x ? ?1
·
x ? 1
·
x ? 2
·
None of the above
12.
Smalltown Electronics buys
MP3 players from its supplier for a price of $200 each. The store marks up the
$200 by 50% to obtain the retail price. After Christmas, the retail price is
marked down by 50%. After Christmas, the retail price will be ________ dollars.
13.
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?6. 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?
·
p = 0.10q?1/6
·
p = 10q6
·
p = 10q?1/6
·
p = 0.10q?1/3/10
·
None of the above
14.
If f(x,y) = (2x)y, then f(4,3) is equal to ____________.
·
1296
·
512
·
256
·
64
·
None of the above
15. The number of accidents at a dangerous intersection in Smalltown
during each of the last six years is as follows: 0, 1, 1, 2, 3, 5. For this
data set, which of the following is true?
·
Mean < Median < Mode
·
Mean < Mode < Median
·
Median < Mean < Mode
·
Mode < Mean < Median
·
Mode < Median < Mean
16. 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
17. Dylan Industries employs 50 workers. Blue collar workers are
paid $600 per week, and white collar workers are paid $1000 per week. Dylan’s
weekly payroll is $42,000. Dylan has _______ white collar employees.
18.When simplified, 18 + 4 × 9/22 + 5 equals _____________.
19. Suppose that 1% of all people have a particular disease. A
test for the disease is 99% accurate. This means that a person who has the
disease has a 99% chance of testing positive for the disease,
while a person who doesn’t have the disease has a 99% chance of testing negative for
the disease.
20. 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
21. The inflection point for f(x) = x3 – 3x2 + x +
5 is
·
x = 0
·
x = 1
·
x = ?1
·
x = 2
·
None of the above
22.
If f(x) = x1/6 + x?1/3, then f(64) is
equal to ________________.
23. The number of accidents at a dangerous intersection in
Smalltown during each of the last six years is as follows: 0, 1, 1, 2, 3, 5.
For this data set, the standard deviation of the number of accidents in a year
(rounded to the nearest tenth) is
·
3.2
·
1.8
·
2.0
·
4.0
·
None of the above
24. 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
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.
25. To lower the airline’s risk associated with changes in jet fuel
prices, the airline should purchase call options on jet fuel.
·
True
·
False
26. For x = 1/2 the second derivative of f(x)
= 2x?2 is
·
3/4
·
100
·
192
·
25
·
None of the above
