Transcript File - Mathcounts at FSMS

MATHCOUNTS

2002 Chapter Competition
Countdown Round
1. What is the sum of the
number of faces, vertices and
edges in a triangular prism?
Answer: 20
2. One-third of a 30-student
class is absent today. One-half of
those were also absent yesterday.
What percent of the class has
been absent for two straight
days? Express your answer to the
nearest whole number.
Answer: 17 (percent)
3. Compute:
(17  10)  (17  10) .
2
2
Answer: 680
4. Two of Mr. Bernard’s classes
took the same test. His class of
20 students had an average score
of 80. His other class of
30 students had an average of 70.
What was the average score for
all 50 students?
Answer: 74
5. The radius of a circle is
increased by 100%. By what
percent is the area of the circle
increased?
Answer: 300 (percent)
6. Compute:
(5 
5 3
2
2
)
2
.
Answer: 1
7. What is the least common
multiple of 12, 18 and 30?
Answer: 180
8. In any given year, the dates
(represented as month/day) 4/4,
6/6, 8/8, 10/10 and 12/12 all fall
on the same day of the week.
June 3, 2020 is a Wednesday.
What day of the week is
December 15, 2020?
Answer: Tuesday
9. Taylor wants to buy cases to
hold her 86 compact discs. Each
case holds 9 discs. How many
cases does she need to buy?
Answer: 10 (cases)
10. A board whose length is
84 inches is cut into three pieces
in the ratio 1:2:3. What is the
number of inches in the length of
the shortest piece?
Answer: 14 (inches)
11. How many integers can be
represented as a difference of two
distinct members of the
set {1, 2, 3}?
Answer: 4 (integers)
12. At what time is the sum of
the digits which represent the
hours and minutes on a 12-hour
digital watch the greatest?
Answer: 9:59
13. What is the sum of the
coordinates of the midpoint of the
segment with endpoints (6, 12)
and (0, -6)?
Answer: 6
14. A refrigerator was originally
priced at $250. It was then put
on sale for 20% off. What is the
number of dollars in the final
price of the refrigerator if an
additional 15% is taken off of the
sale price?
Answer: 170 (dollars)
15. What is the sum of all the
prime numbers less than 10?
Answer: 17
16. Sixteen is 64% of what
number?
Answer: 25
17. Molly has seven U.S. coins
with a total value of 88 cents.
She does not have any
half-dollars. How many dimes
does Molly have?
Answer: 1 (dime)
18. What is the number of square
units in the area of a triangle
whose sides are 3, 4 and 5 units?
Answer: 6 (square units)
19. The point A(-7, 4) is reflected
across the x-axis onto point B.
Point B is reflected over the yaxis onto point C. What is the
sum of the coordinates of point
C?
Answer: 3
20. If x = 3 and y = 2, then what
2 x  3y
is the value of
6
3
2
?
Answer: 7
21. What is the value of
1
2
 4   16 
1
8
1
128
1
32
 256 
 64 
1
512
 1024 ?
Answer: 32
22. Set A has 16 elements and
set B has 37 elements. The union
of sets A and B has 43 elements.
How many elements are in the
intersection of sets A and B?
Answer: 10 (elements)
23. TV screens are described by
the lengths of their diagonals.
A 19" TV has a rectangular
screen with a diagonal length of
19 inches. The screen of a
20" TV is 12 inches tall. How
many inches wide is the screen?
Answer: 16 (inches)
24. Jonathan drove at an average
rate of 48 miles per hour. How
many miles did he travel in
40 minutes?
Answer: 32 (miles)
25. For what value
2 2
n
?

2
2
2
3
of n does
2
Express your answer as a
common fraction.
5
Answer: 
6
26. What part of 15 hours is
15 seconds? Express your
answer as a common fraction.
Answer:
1
3600
27. What is the ratio of
1 pound, 4 ounces to
3 pounds, 10 ounces? Express
your answer as a common
fraction.
10
Answer:
29
28. The cost of the daily school
lunch increased from $1.50 to
$1.95. What was the percent
increase?
Answer: 30 (percent)
29. For class president, Tom
received 50% of the votes, John
received 30% of the votes and
Alana received the remaining
88 votes. How many votes did
Tom receive?
Answer: 220 (votes)
30. Compute:
(2 + 12 + 22 + 32) +
(8 + 18 + 28 + 38).
Answer: 160
31. The average of nine
consecutive integers is 13. What
is the sum of the least and
greatest of these integers?
Answer: 26
32. If the sides of a triangle are
tripled, then the new area is what
percent of the original area?
Answer: 900 (percent)
33. Ervin made 37.5% of the
shots he took during his
basketball game. If he took
exactly 40 shots during the game,
how many shots did he make?
Answer: 15 (shots)
34. The numbers 1 through 999,
inclusive, are printed on a piece
of paper. How many digits are
printed on the paper?
Answer: 2889 (digits)
35. How many pairs of prime
numbers have a sum of 40?
Answer: 3 (pairs)
36. What is the sum of the
first 6 positive odd integers?
Answer: 36
37. What is the greatest real
number that is at least as large as
its square?
Answer: 1
38. The Catch The Spirit group is
conducting a raffle. Each ticket
costs $2, and the total expenses
are $500. What is the minimum
number of tickets that must be
sold to yield a profit of $2000?
Answer: 1250 (tickets)
39. What is the sum of the
reciprocals of all the positive
divisors of 8? Express your
answer as a mixed number.
Answer: 1 78
40. If 2  2  2 , what is
the value of x ?
20
19
x
Answer: 19
41. Solve for n:
n
2 2
(2  5 )  10,000 .
Answer: 2
42. Of the following numbers,
what is the sum of the two
smallest, to the nearest
thousandth:
0.15
0.42
0.063
0.1657 ?
Answer: 0.213
43. How many solutions does the
equation
3x  x 3 have?
Answer: 2 (solutions)
44. If n!5! = 6!, then what is
value of n ?
Answer: 3
45. If a * b = ab + ba, for all
positive integer values of a and b,
then what is the value of 4 * 3?
Answer: 145
46. Each bounce of a ball
3
goes 4 as high as the previous
bounce. The second bounce was
24 inches high. What was the
height, in inches, of the first
bounce?
Answer: 32 (inches)
47. The perimeter of an isosceles
triangle is 36 cm, and the altitude
to its base is 12 cm. What is the
number of square centimeters in
the area of the triangle?
Answer: 60 (square centimeters)
48. There are 30 equallyweighted questions
on Mr. Daven’s math final. If a
student must score 68% or
greater to pass, what is the
minimum number of questions
that must be answered correctly
to pass?
Answer: 21 (questions)
49. A pizza parlor offers six
toppings. What is the greatest
number of four-topping pizzas
that can be made such that no two
pizzas have the same topping
combination?
Answer: 15 (pizzas)
50. Jacob bought a CD for $15
and sold it for $20. He then
bought it back for $25 and sold it
again for $28. How many dollars
profit did he make?
Answer: 8 (dollars)
51. What is 150% of 0.84, to the
nearest hundredth?
Answer: 1.26
52. Given
x
y

2
3
y
and
z
x
what is the value of
?
z

3 ,
2
Answer: 1
53. What is the greatest odd
integer that is a factor of 5! ?
Answer: 15
54. What is the number of
centimeters in the diameter of a
2
circle whose area is 100  cm ?
Answer: 20 (centimeters)
55. Compute:
55  1212  15  1212 .
Answer: 48,480
56. One leg of a right triangle is
increased by 10%, and the other
leg is decreased by 10%. By
what percent does the area of the
triangle decrease?
Answer: 1 (percent)
57. Data can be entered at the
rate of 150 pieces of information
in 15 minutes. At this rate, how
many pieces of information can
1
be entered in 1 2 hours?
Answer: 900 (pieces)
58. A suitcase lock has 3 dials
with the digits 0, 1, 2,..., 9 on
each. How many different
settings are possible if all three
digits have to be different?
Answer: 720 (settings)
59. Ralph can do one-third of a
job in two-thirds of an hour. At
this rate, how many hours will it
take him to finish the entire job?
Answer: 2 (hours)
60. Compute:
6 6 6 6 6 .
Answer: 31
61. It is known that
200
 6 and n is a
n
positive integer. What is the
largest possible value for n?
Answer: 33
62. Fifty cards, numbered 1- 50,
are placed in a box. One card is
randomly selected. What is the
probability that the number on
the card is prime and is a multiple
of 7? Express your answer as a
common fraction.
1
Answer:
50
63. Tyler’s quiz scores in Math
Investigations were 5, 7, 9, 10,
13, 19 and 21. Determine the
ratio of the median of his scores
to the arithmetic mean of his
scores. Express your answer as a
common fraction.
5
Answer:
6
64. A discount card offers $5 off
for any purchase from $50 to
$99.99, and $15 off any
purchase of $100 or more. What
is the maximum percent discount
that can be obtained using this
card?
Answer: 15 (percent)
65. A rectangle has perimeter
26 inches and integer length
sides, in inches. What is the
number of square inches in the
greatest possible area?
Answer: 42 (square inches)
66. What is 1/2 of 1/3 of
1/5 of 60?
Answer: 2
67. Compute and express as a
common fraction:
3
4
4
5


1
5
1
2
.
19
Answer:
26
68. During a 24-hour period,
1440 cars pass through a toll
booth. What is the mean number
of cars that pass through per
minute?
Answer: 1 (car)
69. What is the greatest common
factor of 68 and 92?
Answer: 4
70. The angle measures of the
three angles of a triangle are in
the ratio 1:3:6. What is the
number of degrees in the measure
of the largest angle?
Answer: 108 (degrees)
71. What is the least common
multiple of 1, 2, 3, 4, 5, 6,
7 and 8?
Answer: 840
72. Express as a common
fraction:
4
59
.
7
Answer:
3
73. The number 115 can be
written as 12q + r where q and r
are integers and 0  r  12 .
What is the value of q  r ?
Answer: 2
74. How many seconds are in
1
1 4 hours?
Answer: 4500 (seconds)
75. If Mike drinks eight 8-ounce
glasses of water each day during
2002, how many gallons of water
will he consume? (A gallon is
128 ounces.) Express your
answer as a decimal to the
nearest tenth.
Answer: 182.5 (gallons)
76. Two opposite sides of a
square are each increased by
40%, while the other two sides
are each decreased by 30%. The
perimeter of the original square is
increased by what percent?
Answer: 5 (percent)
77. A book of tickets for 30 games
of a local university’s baseball
team sold for $120, and a book of
tickets for 7 games of the same
university’s football team sold for
$161. By how many dollars did the
average cost of one football game
ticket exceed that of one baseball
game ticket?
Answer: 19 (dollars)
78. A portion of a number line is
divided into 4 equal parts, as
shown. What is the value of p, to
the nearest ten-thousandth?
0.2304
p
0.4304
Answer: 0.2804
79.
Hamburgers
Cheeseburgers
Fries
Sodas
15
12
25
30
2
2
3
4
Mr. Jones
Needs:
1 Meal Deal
includes:
What is the least number of Meal Deals
that Mr. Jones must purchase to get all of
the food and beverage that he needs?
Answer: 9 (Meal Deals)
80. A rectangle has an area of
2
2
36 m and a width of 3 meters.
What is the number of meters in
the length of the rectangle?
Answer: 54 (meters)