A. 115% of $10 is $11.50, while 120% of $9 is $10.80.
So I'll save 70 cents if I eat with my friend.
B.
(a) 33% (the exactly value is 33 and 1/3 percent)
(b) 300%
(c) 67% (the exact value is 66 and 2/3 percent)
(d) 200%
C. True. 10% × 60% = (0.10) × (0.60) = 0.06 = 6%
(and since the blond-haired women are precisely those women in the
class who have the additional characteristic of possessing blond hair).
D. False. 20% × 40% = (0.20) × (0.40) = 0.08,
so bald men comprise 8%, not 80%, of the class.
(Note that "40% × 20% = 800%" would be even sillier!)
E. False. Some of thye hotels with restaurants might
also have pools. (If all of them do, only 70% of the hotels
in town have a restaurant or a pool.) All we can conclude is
that somewhere between 70% and 90% of the hotels have a
restaurant or a pool. Since the reasoning is fallacious,
we could call the statement false. Alternatively, we could
say that the conclusion ("90% of the hotels in town have a
restaurant or a pool") cannot be conclusively judged to be
true or false on the basis of the information given.
F. True. Those who drive do not take the bus, so
(40+15)% = 55% either drive or take a bus, leaving
(100-55)% = 45% who do neither.
G.
(a) 21% increase
(b) 19% decrease
(c) 1% decrease
(d) 1% decrease
H. 4.2 × 108.
I. 3 × 10-8
J. A healthy person can keep up a steady pace of about 3 mph
for extended periods of time. Walking ten hours a day, you could
cover 30 miles per day, and walking 365 days, you could cover
just over 10,000 miles. In comparison, the as-the-crow-flies
distance from New York City to Los Angeles is about 2500 miles.
So, even allowing for the fact that the roadways open to pedestrians
are not entirely straight, and even allowing for the fact that a
person carrying food and a small amount of luggage would not be
able to cover 30 miles per day, it would be possible for a typical
healthy adult to walk across the U.S in one year.
Alternatively solution: Given that the distance to be walked is
about 3000, even if you take off one day a week and walk for only
300 days, you still have to walk only 10 hours each day, which
is quite doable for a healthy person.
K. Since the problem says "approximately 720,000",
we are not dealing with extremely exact numbers, so we
should feel free to approximate the number of days in a
year by 360, which happens to go into 720,000 evenly.
720,000 divided by 360 is 2000, so we are talking about
2000 fatal heart attacks each day. (That's somewhere
between one and two fatal heart attacks every minute.)
L.
(8 × 1012 dollars) ÷ (4.5 × 104
dollars per second) is 1.78 × 108 seconds. To measure
this in years, we divide by 60 × 60 × 24 × 365 =
3.15 × 107 to get .565 × 101,
which is between 5 and 6 years.
M.
100 million divided by 500 is 200 thousand, so we need to measure
1/200,000th the length of a football field. In inches, that's
(100 yard) × (3 feet / yard) × (12 inches / foot) / 200,000 =
.018 inches. (This is two or three times the thickness of a razor
blade.)
N.
(10 hours per week) × (15 weeks) = 150 hours. Your life is
about 24 × 360 × 75 = 648000 hours long (I used 360 days
instead of 365 to make the numbers come out rounder). 648000/150 =
4320, so we're looking at one part in 4320. If we represent
your life by one day, or 60*60*24 seconds, then we would
represent the time spent on Math 141 as about 60*60*24/4320
= 20 seconds.