Download 1. What is the greatest prime factor of 99?

2014 School
Compet i t i on
Count down Round
1. What is the greatest prime
factor of 99?
Answer: 11
2. A small square is
entirely contained in a
larger square, as shown. The side
length of the small square is
3 units and the side length of the
larger square is 7 units. What is
the number of square units in the
area of the black region?
Answer: 40 (units2)
3. Fifty ping-pong-balls are
numbered 1, 2, 3, ..., 49, 50. A
ball is chosen at random. What is
the probability that the number
on the selected ball is a multiple
of 5 or 7 or both? Express your
answer as a common fraction.
8
Answer:
25
4. How many zeros are at the
end of the product 25
     
Answer: 3 (zeros)
5. Following the directions of
the arrows, how many different
paths are there from A to C?
A
B
C
Answer: 5 (paths)
6. At 2:30 p.m. during a long
drive, Bobbi asks her parents,
“Are we there yet?” Her mother
responds, “We will be there in
7200 seconds.” If Bobbi’s
mother is correct, at what time in
the afternoon will they arrive at
their destination?
Answer: 4:30 (p.m.)
7. If 3x + 8 = 5x
     what is the value of
the product 10x ?
Answer: 70
8. How many prime numbers
are between 30 and 40?
Answer: 2 (numbers)
9. Triangle ABC is isosceles
with angle A congruent to
angle B. The measure of angle C
is 30 degrees more than the
measure of angle A. What is the
number of degrees in the measure
of angle C?
Answer: 80 (degrees)
10. In the NBA in 2003, Yao
Ming was one of the tallest
players at 7’5”. Earl Boykins
was the shortest player at 5’5”.
How many inches taller than
Boykins was Ming?
Answer: 24 (inches)
11. Simplify:
2
2
1 2
.
Answer: 3
12. Robin bought a four-scoop
ice cream cone having a scoop
each of vanilla, chocolate,
strawberry and cherry. In how
many orders can the four scoops
be stacked on the cone if they are
stacked one on top of the other?
Answer: 24 (orders)
13. How many integers n satisfy
2
?
n 5
Answer: 5 (integers)
14. In a 30-year period, what is
the maximum possible number of
leap years?
Answer: 8 (leap years)
15. Each pirate lied in making the
following statements:
Long: I stole the map.
John: Silver did not steal the map.
Silver: John stole the map.
Who stole the map?
Answer: Silver
16. What is the least prime factor
4
 
of 7   

Answer: 2
17. If x = 3y2, what is the value
of 4x in terms of y?
Answer: 12y2
18. What is the 2004th positive
odd integer?
Answer: 4007
19. Solve for x:
5  x  
Answer:  3
20. What is the greatest two-digit
whole number, the product of
whose digits is 8?
Answer: 81
21. The lengths of two sides of a
triangle are 33 units and 42 units.
The third side also has an
integral length. What is the least
possible number of units in the
perimeter of the triangle?
Answer: 85 (units)
22. The daily high temperatures
in degrees Celsius for Monday
through Friday were 3,
           an
d 2, respectively. What is the
arithmetic mean of these five
temperatures? Express your
answer as a decimal to the
nearest tenth.
Answer:  1.4 (degrees)
4 2
23. Compute: ( ) .
5
Express your answer as a
common fraction.
25
Answer:
16
24. One gallon of paint covers
400 square feet. If paint is only
sold in whole gallons, how many
gallons of paint do you have to
buy to paint a surface of
925 square feet?
Answer: 3 (gallons)
25. What is the units digit of the
product of all of the odd integers
between 0 and 12?
Answer: 5
26. You connect the points (0, 0)
and (9, 6) with a line segment.
1
Starting at (0, 0), you move
3
of the way along the segment.
What is the sum of the coordinates
of the point you land upon?
Answer: 5
27. Each of the six members
from the Skateer University
hockey team shakes hands with
each of the six members of the
Iceburg Tech team. How many
handshakes take place?
Answer: 36 (handshakes)
28. For x > 0, the area of the
triangle with vertices (0, 0), (x, 0)
and (x, 5) is 30 square units.
What is the value of x?
Answer: 12
29. The probability that a
randomly thrown dart will land
3
on a target is
. What is the
8
probability that the dart will not
land on the target? Express your
answer as a common fraction.
Answer:
5
8
30. What is the value of the 25th
term of the arithmetic sequence
2, 5, 8, ... ?
Answer: 74
31. The fine for an overdue
library book is 8 cents per day.
Pokey is 8 days late with each of
three books. How much is
Pokey’s fine in cents?
Answer: 192 (cents)
32. The congruent sides of an
isosceles triangle are each 5 cm
long, and the perimeter is 17 cm.
In centimeters, what is the length
of the base?
Answer: 7 (centimeters)
33. Solve for x: 2(3x) = 162
Answer: 4
34. The sum of two numbers is
12 and their product is 35. What
is the positive difference between
the numbers?
Answer: 2
35. Equilateral triangle ABC and
square BCDE are coplanar, as
shown. What is the number of
A
degrees in the measure of
angle CAD?
B
C
E
D
Answer: 15 (degrees)
36. At the Marian County
Antique Show, 202 tickets were
sold on Friday, 357 were sold on
Saturday, and 408 were sold
Sunday. How many dollars were
collected if the Friday tickets cost
$3 each, the Saturday tickets cost
$4 each, and the Sunday tickets
cost $5 each?
Answer: 4074 (dollars)
37. Five toppings for a pizza are
available at Polina’s Pizza. How
many combinations of two
different toppings are possible?
Answer: 10 (combinations)
38. Five friends raced each other.
Bill finished next to last. John
finished behind Bill. Al finished
after Clark and before Tony.
Which friend finished third?
Answer: Tony
39. How many positive integers
can be represented as the
difference of two distinct
members of the set
{1, 3, 5, 7, 9, 11, 13}?
Answer: 6 (integers)
40. Define a * b as 2a   b2.
If a * 5 = 9, what is the value
of a?
Answer: 17
41. Compute: 15 + 82   
Answer: 76
42. In a rectangular coordinate
system, what is the number of
units in the distance from the
origin to the point
(        
Answer: 17 (units)
10
10
x x x
43. Simplify:
10
x
if x    
10
Answer: 3
44. How many three-digit
positive integers are multiples
of 4?
Answer: 225 (integers)
45. The fair spinner shown is
spun once. What is the
probability of spinning an odd
number? Express your answer as
a common fraction.
23
15
14
Answer:
3
4
46. In square centimeters, what is
the area of triangle ABC?
A
10 cm
B
8 cm
C
Answer: 40 (square centimeters)
47. The sum of two numbers is
13, while their product is 36.
What is the sum of their
reciprocals? Express your
answer as a common fraction.
13
Answer:
36
x 10

48. Given
.
y 4
If y = 18, what is the value of x?
Answer: 45
49. What is the number of square
units in the area of a triangle
whose sides measure 5, 5 and
6 units?
Answer: 12 (units2)
50. For a world record, George
Adrian picked 15,832 pounds of
apples in 8 hours. Assuming he
maintained a constant rate of
picking, how many pounds of
apples did he pick in 3 hours?
Answer: 5937 (pounds)
51. What is the smallest positive
perfect cube that can be written
as the sum of three consecutive
integers?
Answer: 27
52. The perimeter of a square is
44 meters. How many square
meters are in the area of the
square?
Answer: 121 (square meters)
53. For how many positive
2
integers x is x + 6x + 9 between
20 and 40?
Answer: 2 (integers)
54. What is the least positive
integer such that it is a multiple
of 16 and the product of its digits
is a multiple of 12?
Answer: 64
55. At an average speed of
60 miles per hour, how many
miles does a car travel in six
hours and 30 minutes?
Answer: 390 (miles)
56. The area of rectangle ABCD
with vertices A(0, 0), B(0, 4),
C(x, 4) and D(x, 0) is 28 square
units. If x > 0, what is the value
of x?
Answer: 7
57. Sean had a temperature of
99.6°F at 3 p.m. Five hours later
his temperature was 102.4°F. By
how many degrees Fahrenheit did
his temperature rise during those
five hours? Express your answer
as a decimal to the nearest tenth.
Answer: 2.8 (degrees)
58. The coordinates of a
parallelogram are (5, 3), (6, 8),
(7, 4) and (x, y) and x > 7. What
is the value of x + y?
Answer: 17
59. The sequence 2, 7, 12, a, b,
27 is arithmetic. What is the
value of a + b?
Answer: 39
60. Express the value of
2

2 5
as a decimal to the
2
2 5
nearest tenth.
Answer: 1.5