Transcript File - Mathcounts at FSMS

MATHCOUNTS

2002 School Competition
Countdown Round
1. What is the value of
3
3
2  35  7 ?
Answer: 21,000
2. What is the value obtained by
dividing the number of square
inches in a square yard by the
number of square inches in a
square foot?
Answer: 9
3. What is the number of square
inches in the area of a rectangular
tablecloth that measures 4 feet by
5 feet?
Answer: 2880 (square inches)
4. What is the value of
(7  5)  (7  5) ?
2
2
Answer: 140
5. How many different positive
integers can be represented as a
difference of two distinct
members of the set
{1, 2, 3, 4, 5, 6} ?
Answer: 5 (integers)
6. How many hours will it take
Katina to drive 495 miles at 45
miles per hour?
Answer: 11 (hours)
7. Ten students stand on a
circle. No two adjacent students
have brown hair. What is the
maximum number of these
students that could have brown
hair?
Answer: 5 (students)
8. The bill for dinner was $63.
5
Joanna agreed to pay
of the
9
bill, since she had dessert. How
many dollars should Joanna pay?
Answer: 35 (dollars)
9. John’s diet requires him to
eat, at most, 30 grams of
carbohydrates at snack time. If
he selects chips with 24 grams of
carbohydrates per ounce, how
many ounces of chips may he eat
at snack time? Express your
answer as a decimal to the
nearest hundredth.
Answer: 1.25 (ounces)
10. What single percent discount
from the original price is
equivalent to a 40% discount on
an item already on sale at a 20%
discount from the original price?
Answer: 52 (percent)
11. The volume of a cone is
1
given by the formula V = 3 Bh,
where B is the area of the base
and h is the height. The area of
the base of a cone is 30 square
units, and its height is 6.5 units.
What is the number of cubic units
in its volume?
Answer: 65 (cubic units)
12. If 25% of n is 18, what is
125% of n?
Answer: 90
13. If 3x = 8y, 12y = 7z and
kz = 72x, then what is the value
of k ?
Answer: 112
14. Ashley’s old dresser has nine
drawers. Six of the drawers each
3
have a volume of 2 ft , and three
drawers each have a volume of 1
ft3. Her new dresser has the same
total volume in five equal-sized
drawers. What is the volume in
cubic feet of each drawer of her
new dresser?
Answer: 3 (cubic feet)
15. Bryan has some 3¢ stamps
and some 4¢ stamps. What is the
least number of stamps he can
combine so the value of the
stamps is 33¢?
Answer: 9 (stamps)
16. If a * b = 2a + 3b for all a
and b, then what is the value of
4 * 3?
Answer: 17
17. How many degrees are in the
complement of a 54° angle?
Answer: 36 (degrees)
18. The sum of two numbers is
352. One number is three times
the other. What is the value of
the smaller number?
Answer: 88
19. A couple plans to have three
children. The birth of a boy or
girl is equally likely. What is the
probability that all three children
will be the same sex? Express
your answer as a common
fraction.
1
Answer:
4
20. What is the positive difference,
in inches, between the greatest cabin
height and the least cabin height of
the following business jets?
Business Jet
Learjet 31A
Learjet 60
Cessna Citation V
Gulfstream V
Cabin Height
4 feet, 5 inches
5 feet, 8 inches
4 feet, 7 inches
6 feet, 2 inches
Answer: 21 (inches)
21. Charles Schultz drew 18,000
comic strips over a 50-year
period. What is the mean number
of comic strips he drew each
year?
Answer: 360 (comic strips)
22. The mean of ten numbers
th
is 7.2. When an 11 number is
added to the set, the mean
becomes 5. What is the
11th number?
Answer: -17
23. Each row of the Misty Moon
Amphitheater has 30 seats.
Rows 12 through 22 are reserved
for a special group. How many
seats are reserved for this group?
Answer: 330 (seats)
24. A circular pizza of diameter
12 inches is cut into 4 pieces of
equal area. What is the number of
square inches in the area of each
piece? Express your answer in
terms of  .
Answer: 9  (square inches)
25. On a survey, students must give
exactly one of the answers provided to
each of these three questions:
a) Were you born before 1990? (Yes/No)
b) What is your favorite color?
(Red / Green / Blue / Other)
c) Do you play a musical instrument?
(Yes / No)
How many different answer
combinations are possible?
Answer: 16 (combinations)
26. What is the remainder when
the sum of the first five primes is
divided by the sixth prime?
Answer: 2
27. What is the positive
difference between one-million
and seventy-two thousand?
Answer: 928,000
28. The value of 400,000 squared
can be written as 1.6  10n. What
is the value of n ?
Answer: 11
29. On five consecutive days, the
low temperatures in Sioux City,
SD were 2, -9, 9, 7 and -4,
measured in degrees Celsius.
How many degrees Celsius was
the mean of these low
temperatures?
Answer: 1 (degree Celsius)
30. What is the greatest possible
quotient using two distinct
numbers from the set
{ 0.2, 0.5, 0.8, 3.2 }?
Answer: 16
31. How many eighths are in
5.75?
Answer: 46 (eighths)
32. Compute: 98  102 .
Answer: 9996
33. The table below represents the
male population of students
attending Walker Middle School.
One boy is selected at random from
the male students. What is the
probability that he is in seventh
grade? Express your answer as a
common fraction.
7th Grade
Males
25
8th Grade 9th Grade
22
23
5
Answer:
14
34. Marcia has a total of
65 game pieces worth 89 points.
Each game piece is worth one or
two points. How many one-point
game pieces does she have?
Answer: 41 (one-point
game pieces)
35. The sum of three numbers
is 90. One of the numbers is 22.
What is the arithmetic mean of
the other two numbers?
Answer: 34
36. For what value of n does
8
n
3 =9 ?
Answer: 4
37. The longest side of a right
triangle is 5 meters, and the
shortest side is 3 meters. What is
the area of the triangle in square
meters?
Answer: 6 (square meters)
38. What integer x satisfies
1 x 1
 
4 7 3
?
Answer: 2
39. Compute:
1  5  9  13  17  21
6
.
Answer: 11
40. What percent of a 48-minute
basketball game is over if the
time remaining is one-third the
time played?
Answer: 75 (percent)
41. If carpet costs $18 per square
yard, how many dollars will it
cost to completely carpet a
15 foot by 18 foot rectangular
floor?
Answer: 540 (dollars)
42. Alexa has a mixture
consisting of 8 ounces of red jelly
beans and 13 ounces of green
jelly beans. What is the minimum
number of ounces of white jelly
beans she must buy so that, when
added to the old mixture, her new
mixture is an integer number of
pounds?
Answer: 11 (ounces)
43. April 1, 2002 is a Monday.
What day is April 23, 2002?
Answer: Tuesday
44. The area of a triangle is
600 ft2. If the length of the base
is 30 feet, then what is the
number of feet in the altitude?
Answer: 40 (feet)
45. For what positive integer n is
2
6
n =2 ?
Answer: 8
46. In parallelogram ABCD,
angle B measures 110°. What is
the number of degrees in the
measure of angle C?
Answer: 70 (degrees)
47. Together, Larry and Lenny
have $35. Larry has two-fifths of
Lenny’s amount. How many
more dollars than Larry does
Lenny have?
Answer: 15 (dollars)
48. An airplane travels at
360 kilometers per hour. How
many meters does it travel in one
second?
Answer: 100 (meters)
49. For what value of n does
n

0.0000048 = 4.8 10 ?
Answer: -6
50. How many degrees is the
measure of the supplement of an
angle whose complement
measures 50°?
Answer: 140 (degrees)
51. By how much does 3.5
exceed its reciprocal? Express
your answer as a common
fraction.
45
Answer:
14
52. What is
1
%
2
of 200?
Answer: 1
53. A rectangular sheet of paper
with dimensions 9 inches by
13 inches is cut into n identical
notecards, each of which is
3 inches by 2.6 inches. What is
the maximum value of n ?
Answer: 15
1 1 1
54. What is the ratio of  
2 3 4
1 1 1
to   ? Express your
2 3 4
answer as a common fraction.
7
Answer: 13
55. What is the value of 1.69 ?
Express your answer as a decimal
to the nearest tenth.
Answer: 1.3
56. How many square feet are in
a square yard?
Answer: 9 (square feet)
57. What is the number of square
units in the area of a triangle
whose sides are 9, 12 and
15 units?
Answer: 54 (square units)
b
a
58. If
12 and  20 , then
b
c
a
what is the value of ?
c
Answer: 240
59. What is the least number of
2 cm  5 cm rectangular tiles that
will completely cover a
30 cm  35 cm rectangle?
Answer: 105 (tiles)
60. Two percent of half a number
is 5. What is the number?
Answer: 500