Transcript 1. What is the value of ?

MATHCOUNTS
Countdown Round

1. Half of 12 is equal to what
number?
Answer: 6
2. What is the smallest positive
integer that can be added to 100
to make a multiple of 3?
Answer: 2
3. Five U.S. coins are worth a
total of 35 cents. How many of
the coins are dimes?
Answer: 2 coins
4. How much more than 42 is
3
3?
Answer: 11
5. What is the greatest common
factor of 40 and 48?
Answer: 8
6. What is the sum of the
number of faces and edges of a
triangular prism?
Answer: 14
7. The value of eight nickels
and six dimes is the same as four
nickels and how many dimes?
Answer: 8 dimes
8. Fred has 2 yellow, 2 red and
2 green tokens. One red token is
equal to 9 green tokens. One
yellow token is equal to 3 green
tokens. Fred converts all of his
tokens to green tokens. How
many green tokens does he have?
Answer: 26 tokens
9. If the last two digits of 9567
were interchanged, how much
larger would the new number be?
Answer: 9
10. The average of five numbers
is 10. Four of the numbers are
10, 10, 10 and 9. What is the
value of the fifth number?
Answer: 11
11. In the figure shown,
polygons ABCD, CDEF and
DEGH are squares. The length
of segment FG is 10 cm. How
many square centimeters
are in the area of
E
F
hexagon
C
ABFGHD?
D
B
A
G
H
Answer: 75 square centimeters
12. How many positive integers
are less than 10p?
Answer: 31 integers
1
6
13. In training, Petra runs of a
mile in 60 seconds. At this rate,
how many seconds does it take
Petra to complete a run of 1 mile?
Answer: 360 seconds
14. What is the remainder when
4697 is divided by 9?
Answer: 8
15. How many more boxes are
needed if 70 ornaments are
packaged in boxes that each hold
5 ornaments rather than boxes
that each hold 7 ornaments?
Answer: 4 boxes
16. What reduced fraction is
equivalent to 25%?
1
Answer:
4
16a.
The area of a square is
49 square centimeters. How
many centimeters are in the
length of a side of the square?
Answer: 7 centimeters
17. At which of the following
stores is the average cost per
pencil the least?
Store A: 17 pencils for $1.70
Store B: 7 pencils for $1.40
Store C: 5 pencils for $0.85
Answer: Store A
18. In any month with a “Friday
the 13th,” what day of the week is
the first day of the same month?
Answer: Sunday
19. Each side of pentagon
ABCDE has length less than or
equal to 7 units, AB = 5 units and
BC = 4 units. How many units
are in the greatest possible
perimeter of ABCDE?
Answer: 30 units
20. Two figures each have a
perimeter of 80 feet. One is a
square and one is a rectangle with
dimensions of 10 feet by 30 feet.
What is the positive difference in
the number of square feet of their
areas?
Answer: 100 square feet
21. What is the greatest integer
17
less than
?
4
Answer: 5
22. Using two distinct members
of the set {0, 1, 2, 3}, how many
different sums can be found?
Answer: 5 sums
23. How many integers between
20 and 90 are perfect squares?
Answer: 5 integers
24. What is the greatest two-digit
multiple of 4?
Answer: 96
25. Joshua’s restaurant bill is
$10. To calculate the tip, he
calculates 15% of the value of the
bill and then rounds up to the
nearest dollar. What was the
amount of his tip?
Answer: 2 dollars
26. What is the sum:
–4 + –3 + –2 + ... + 3 + 4 + 5 + 6?
Answer: 11
27. The ratio of x to 10 is equal
to the ratio of 12 to 30. What is
the value of x?
Answer: 4
28. What is the units digit of the
product of the first four positive
integers?
Answer: 4
29. Evaluate (x + y)(x – y)
when x = 15 and y = 5.
Answer: 200
30. How many degrees are in
each interior angle of an
equilateral triangle?
Answer: 60 degrees
31. If 75 seeds are planted and
25 of the seeds are germinating,
what is the ratio of seeds
germinating to seeds planted?
Express your answer as a reduced
fraction.
1
Answer:
3
32. The scale of a backpacker’s
map is “1 cm on the map =
240 meters on the ground.” How
many kilometers long is a hike
that measures 10 cm on the map?
Express your answer as a decimal
to the nearest tenth.
Answer: 2.4 kilometers
33. Mississippi was one of the
10 states to lose a Congressional
seat based on the 2000 Census.
What percent of the 50 states did
not lose a Congressional seat?
Answer: 80 percent
34. Let y = 2 + 3x. How much
greater is y when x = 3 than when
x = 2?
Answer: 3
35. Ben flips a fair nickel two
times. What is the probability
that Ben flips a Head and then a
Tail? Express your answer as a
reduced fraction.
Answer:
1
4
36. Mary jogs 12 miles in
2 hours. On average, how many
minutes does it take her to jog
one mile?
Answer: 10 minutes
37. With one skein of wool yarn,
Sharon can knit 3 inches of a
scarf that is 9 inches wide. What
is the least whole number of
skeins with which she can knit a
scarf that is 6 inches wide and
27 inches long?
Answer: 6 skeins
38. Two positive integers have a
sum of 28 and are in the ratio 3:4.
What is the least of these two
integers?
Answer: 12
39. Marie owns 11 department
stores. Each store has 12 shelves
for towels. What is the total
number of shelves for towels?
Answer: 132 shelves
40. When 5 is subtracted from
three times a particular number,
the result is 13. What is the
number?
3×
 5 = 13
Answer: 6
41. The Battling Hummingbirds
have won 40% of their first
60 games. If they win their next
12 games in a row, what percent
of all of their games will they
have won?
Answer: 50 percent
42. In box A, there are four more
pennies than in box B. The total
number of pennies in boxes A
and B is 34. What is the number
of pennies in box A?
Answer: 19 pennies
43. What is the sum of the first
five positive odd integers?
Answer: 25
44. What number is one hundred
less than one thousand thirtythree?
Answer: 933
45. Katrina can bicycle 50 miles
in four hours. At the same speed,
how many miles does she bicycle
in six hours?
Answer: 75 miles
46. What is the least positive
integer that has exactly three
distinct factors?
Answer: 4
47. The total value of 90 pennies,
20 dimes and 12 quarters is what
percent of the value of a
ten-dollar bill?
Answer: 59 percent
48. Solve for x: 18  x = 10 + x.
Answer: 4
49. What is the number of
degrees in the measure of
angle ABD in square ABCD?
A
B
D
C
Answer: 45 degrees
50. What is the units digit of 64?
Answer: 6
51. Triangle ABC is isosceles
with angle B congruent to
angle C. The measure of angle C
is four times the measure of
angle A. What is the number of
degrees in the measure of
angle B?
Answer: 80 degrees
52. What integer is closest
100
to
?
7
Answer: 14
53. What is the largest three-digit
multiple of 2?
Answer: 998
54. The Carters had a 10-foot by
10-foot patio built at a cost of
$2200. How many dollars per
square foot did the patio cost to
build?
Answer: 22 dollars per sq ft
55. What is the decimal
11
equivalent of
? Express
4
your answer to the nearest
hundredth.
Answer: 2.75
56. The ratio of the measures of
two complementary angles is 2:1.
What is the measure, in degrees,
of the larger angle?
Answer: 60 degrees
57. From a one-meter piece of
yarn, Chris cuts a 31.5 cm piece
and a 35.5 cm piece. In
centimeters, how much yarn is
left?
Answer: 33 centimeters
58. Simplify:
7  103 + 5  102  4  101 + 7  100.
Answer: 7467
59. A stair-step exercise machine
indicates that Leon burns
180 calories in 12 minutes. At
the same rate, how many calories
would Leon burn in a 4-minute
workout?
Answer: 60 calories
60. If y = x2  1, what is the
value of y when x = 1?
Answer: 0
61. Four friends are in line for
movie tickets. Rick is
somewhere behind Tom, but
ahead of Mark. James and Tom
are separated by one person.
Who is last in line?
Answer: Mark
62. Steven is making a scale
drawing of his living room. He is
using a scale of 1/4 in = 1 ft. In
the drawing, how many inches
will represent the length of a
6-foot long couch? Express your
answer as a decimal to the
nearest tenth.
Answer: 1.5 inches
63. The ages, in years, of the
eight people in the math club are:
12, 12, 12, 12, 13, 13, 14, 14.
What is the mode of the ages?
Answer: 12 years
64. What is the greatest prime
factor of 10!?
Answer: 7
65. Rebecca remembered the
first 6 digits of a friend’s 7-digit
phone number. If she randomly
selects a digit to fill the last digit
she can’t remember, what is the
probability she will dial the
correct number? Express your
answer as a common fraction.
Answer:
1
10
66. Fifty percent of what number
is 12?
Answer: 24
67. What is the number of square
centimeters in the area of a circle
with radius 4 cm? Express your
answer is terms of p.
Answer: 16p square centimeters
68. A candy company puts
21 candies in each bag. There
are only red and blue candies in
each bag. For every 2 red
candies in a bag there are 5 blue
candies. How many red candies
are in each bag?
Answer: 6 candies
69. What is the value of 52  32?
Answer: 16
70. How many triangles of any
size are in this figure?
Answer: 5 triangles
71. What is 150% of 26?
Answer: 39
72. In how many ways can a pair
of students be selected from a
group of four students?
Answer: 6 ways
73. In the formula d = rt, what is
the value of r if d = 60 and t = 4?
Answer: 15
74. On average, each American
consumes 286 eggs per year.
What is the number of years it
would take, at this rate, for an
American to eat 2000 eggs?
Express your answer to the
nearest whole number.
Answer: 7 years
75. Of the 80 students at camp,
40% of them are male. How
many female students are at
camp?
Answer: 48 female students
76. One fair standard six-sided
die is rolled. What is the
probability of rolling a number
greater than 4? Express your
answer as a reduced fraction.
Answer:
1
3
77. What is the positive
difference between 32 and 23?
Answer: 1
78. Jane turns 15 in the year
2008. In what year was she
born?
Answer: 1993
79. A printer prints 17 pages per
minute. How many minutes will
it take to print 200 pages?
Express your answer to the
nearest whole number.
Answer: 12 minutes
80. Jenna is at a fair with
4 friends. They all want to ride
the roller coaster, but only
3 people can fit in a car. How
many different groups of 3 can
the 5 of them make?
Answer: 10 groups
81. What is the value of the
following expression:
10 – 9 + 8 – 7 + … + 4 – 3 + 2 – 1?
Answer: 5
82. A three-digit integer will be
chosen at random from all
possible positive three-digit
integers. What is the probability
that the number’s units digit will
be less than 5? Express your
answer as a common fraction.
1
Answer:
2
83. If
value of
+ 5 = 18, what is the
+
?
Answer: 26
84. How many factors does 20
have?
Answer: 6 factors
85. Kaya ate 60 cookies over a
5-minute period. On average,
how many cookies did she eat
each minute?
Answer: 12 cookies
86. What is the average of
3, 4, 5 and 8?
Answer: 5
87. If two different numbers are
chosen from the set {0, 4, 6, 20},
and the smaller number is
subtracted from the larger
number, what is the smallest
possible result?
Answer: 2
88. The area of a circle is
49p square units. What is the
radius of the circle, in units?
Answer: 7 units
89. What is the least common
multiple of 3, 5 and 6?
Answer: 30
90. If 3 ×
+ 5 = 29, what
number must be placed in the
square?
Answer: 8
91. A hot air balloon is 10 feet
off the ground now and is rising
at a constant rate of 2 feet per
second. What is the height of the
balloon, in feet, after 25 more
seconds?
Answer: 60 feet
92. What fraction of 2 feet is
3 inches? Express your answer
as a reduced fraction.
1
Answer:
8
93. The three-digit integer 63_
is a multiple of 3. What is the
greatest possible digit that can be
placed in the blank?
Answer: 9
94. The probability that Asha
4
will lose the game is . What is
9
the probability Asha will not lose
the game? Express your answer
as a reduced fraction.
5
Answer:
9
95. What is the value of 5!?
Answer: 120
96. Robert reads 90 pages per
hour. How many 270-page
books can he read in six hours?
Answer: 2 books
97. Pencils come in a package
holding 10 pencils. Rina’s
teacher bought 23 packages of
pencils. How many pencils did
she buy?
Answer: 230 pencils
A
98. On a protractor,
ray BA goes
through the
85-degree mark
B
and ray BC goes through the
30-degree mark. What is the
measure, in degrees, of
angle ABC?
C
Answer: 55 degrees
99. What is the sum of the first
five positive even integers?
Answer: 30
100. Two sides of an isosceles
triangle are 15 cm and 10 cm.
What is the greatest possible
perimeter of this triangle, in
centimeters?
Answer: 40 centimeters
101. What is the sum of the
greatest possible three-digit
integer and the greatest possible
two-digit integer?
Answer: 1098
102. What is the ratio of one
interior angle of an equilateral
triangle to one interior angle of a
square? Express your answer as
a reduced fraction.
2
Answer:
3
103. What is the greatest
possible three-digit number that
is divisible by 3 and divisible
by 6?
Answer: 996
104. How many obtuse interior
angles are in an obtuse triangle?
Answer: 1 angle