Download A rectangular field is half as wide as it is long, and it

MATHCOUNTS
Countdown
Round
1. A rectangular field is half as
wide as it is long, and it is
completely enclosed by
54 meters of fencing. What is the
number of square meters in the
area of the field?
Answer: 162 (square meters)
2. What is the sum of the distinct
prime factors of 735?
Answer: 15
3. Compute:
12
5 5
3
9
 5  ...  5
10
5 .
Answer: 11
4. How many square inches are
in the area of a square inscribed
in a circle of radius 6 inches?
Answer: 72 (square inches)
5. If 7 is placed to the right of a
three-digit number to form a
four-digit number, the new
number is 7000 greater than the
original number. What was the
original number?
Answer: 777
6. What is the 87th odd positive
integer?
Answer: 173
2
7. Simplify:
n 4
 2 (2 )
n
n 3
2 (2 )
Express your answer as a
common fraction.
.
7
Answer:
8
8. A rectangle having integer
length and width has a perimeter
of 100 units. What is the number
of square units in the least
possible area?
Answer: 49 (square units)
9. What is the units digit of
20  21 22  23  24  25
?
1000
Answer: 2
10. The Badgers play the
Cougars in a series of seven
basketball games. Each team has
an equal chance of winning each
game. What is the probability
that the Badgers will win at least
four games? Express your
answer as a common fraction.
1
Answer:
2
11. How many prime numbers
less than 100 have a units digit
of 3?
Answer: 7 (numbers)
12. Brad is younger than 30. His
age is a multiple of 5, and next
year his age will be a multiple of
7. Brad is how many years old?
Answer: 20 (years)
13. How many prime numbers
between 30 and 65 have a prime
remainder when divided by 10?
Answer: 4 (numbers)
14. What is the smallest integer
value of n such that 2
n
1
?

1000
Answer: 10
15. The degree measures of the
interior angles of a pentagon
form an arithmetic sequence.
What is the middle term of this
sequence?
Answer: 108 (degrees)
16. How many numbers can be
expressed as the sum of two or
more distinct elements of the set
{0, 1, 2, 4, 8, 16} ?
Answer: 31 (numbers)
17. A photograph measuring
16 inches by 20 inches is reduced
uniformly so that the greater
measure becomes 5 inches. What
is the number of inches in the
perimeter of the reduced photo?
Answer: 18 (inches)
18. How many distinct,
natural-number factors does
3 4 2 have?
4 5  6
Answer: 135 (factors)
19. What is the sum of all
integers x that satisfy
1  (   1) x  10 ?
Answer: 10
20. Compute: 15  35  21 .
Answer: 105
21. A standard die is rolled six
times. What is the probability
that the result of each roll is odd?
Express your answer as a
common fraction.
1
Answer:
64
22. What is the sum of all values
of x that are solutions to the
2
equation x  7 x  12 ?
Answer: 7
23. What is the smallest fourdigit whole number divisible by 9
which has two even and two odd
digits?
Answer: 1089
24. If the endpoints of one side
of a square are at (2, 3) and
(5, 4), then how many square
units are in the area of the
square?
Answer: 58 (square units)
25. The lengths of the sides of
 ABC are 3 cm, 4 cm and 6 cm.
Determine the number of
centimeters in the least possible
perimeter of a triangle similar to
 ABC which has one side of
length 12 cm.
Answer: 26 (centimeters)