2006 Washington State Math Championship
Unless a particular problem directs otherwise, give an exact answer or one rounded
to the nearest thousandth.
Potpourri - Grade 5
−
−
+
=
1.
2. (88,888,888,888 + 88,888 − 8) ÷ 8 =
€
€
3. What is the last positive integer you count if you count backwards from 1000 by
7’s?
€
4. How many prime numbers have a remainder of 0 when divided by 2?
€
€
5. To keep the answers safe, the words were written with a secret code. In this code,
the number 26 stood for the letter “A”, the number 25 stood for “B”, and so on.
In this code, the seven numbers 24, 12, 9, 9, 22, 24, 7 stand for what word?
6. If 6 widgets = 24 fidgets, then how many widgets is 16 fidgets?
7. If the pattern of the first four letters in MATHMATHMATH… continues, then
what is the 503rd letter in the pattern?
8. Bob ran a 5km race where each kilometer his speed decreased 1km/hr. If he
averaged 5km/hr at first, then how many minutes did it take to finish?
9. How many revolutions does the second hand on a clock make in
eight hours?
10. What time is 1 hour and 31 minutes before 2 hours and 59
minutes after 1:41 P.M.
2006 Washington State Math Championship
Unless a particular problem directs otherwise, give an exact answer or one rounded
to the nearest thousandth.
Potpourri - Grade 6
1. How many prime numbers have a remainder of 0 when divided by 2?
2. To keep the answers safe, the words were written with a secret code. In this code,
the number 26 stood for the letter “A”, the number 25 stood for “B”, and so on.
In this code, the seven numbers 24, 12, 9, 9, 22, 24, 7 stand for what word?
3. If 6 widgets = 24 fidgets, then how many widgets is 16 fidgets?
4. If the pattern of the first four letters in MATHMATHMATH… continues, then
what is the 503rd letter in the pattern?
5. Bob ran a 5km race where each kilometer his speed decreased 1km/hr. If he
averaged 5km/hr at first, then how many minutes did it take to finish?
6. How many revolutions does the second hand on a clock make in
eight hours?
7. What time is 1 hour and 31 minutes before 2 hours and 59
minutes after 1:41 P.M.
8. How many positive integers are factors of 40?
9. If today is March 15th, then 2006 days from now what month will it be?
10. If one blue equals 3 greens, 6 reds equals 3 blues, and 3 yellows equals 9 red, then
10 yellows equals how many greens?
2006 Washington State Math Championship
Unless a particular problem directs otherwise, give an exact answer or one rounded
to the nearest thousandth.
Potpourri - Grade 7
1. If the pattern of the first four letters in MATHMATHMATH… continues, then
what is the 503rd letter in the pattern?
2. Bob ran a 5km race where each kilometer his speed decreased 1km/hr. If he
averaged 5km/hr at first, then how many minutes did it take to finish?
3. How many revolutions does the second hand on a clock make in
eight hours?
4. What time is 1 hour and 31 minutes before 2 hours and 59
minutes after 1:41 P.M.
5. How many positive integers are factors of 40?
6. If today is March 15th, then 2006 days from now what month will it be?
7. If one blue equals 3 greens, 6 reds equals 3 blues, and 3 yellows equals 9 red, then
10 yellows equals how many greens?
8. What is the largest power of 5 which divides evenly into the product of the first
100 positive integers: 1× 2 × 3...× 98 × 99 ×100 ?
9. What are the last three elements in the pattern: A, 2, B, 0, C, 2, D, 0, E, 3, F, 3,
G, 2, H, 4, I, 2, J, 2, K, 4, L, 2, M, 2, N, 2, O, 0, P, 1, Q, 1, R, 2, S, 2, T, 3, U, 2,
€
V, 2, W, 2, X, 4, Y, _____, ______, _______
10. Express 254(base 6) as a base 8 number.
2006 Washington State Math Championship
Unless a particular problem directs otherwise, give an exact answer or one rounded
to the nearest thousandth.
Potpourri - Grade 8
1. What time is 1 hour and 31 minutes before 2 hours and 59 minutes after 1:41 P.M.
2. How many positive integers are factors of 40?
3. If today is March 15th, then 2006 days from now what month will it be?
4. If one blue equals 3 greens, 6 reds equals 3 blues, and 3 yellows equals 9 red, then
10 yellows equals how many greens?
5. What is the largest power of 5 which divides evenly into the product of the first
100 positive integers: 1× 2 × 3...× 98 × 99 ×100 ?
6. What are the last three elements in the pattern: A, 2, B, 0, C, 2, D, 0, E, 3, F, 3,
G, 2, H, 4, I, 2, J, 2, K, 4, L, 2, M, 2, N, 2, O, 0, P, 1, Q, 0, R, 2, S, 2, T, 3, U, 2,
€
V, 2, W, 2, X, 4, Y, _____, ______, _______
7. Express 254(base 6) as a base 8 number.
8. There are seven circles of different sizes, arranged as shown, such that their
centers are aligned on a straight line. The total distance they spanned from end to
end is 60 centimeters. What is the exact sum of the circumferences of all the
circles. 9. A large gasoline tank has three inlet pipes and one outlet pipe. One inlet pipe,
colored red takes 2 hours to fill the tank. Another inlet pipe, colored blue, takes 3
hours to fill the tank. The third inlet pipe, colored green, takes 4 hours to fill the
tank. The outlet pipe empties the whole tank in 12 hours. If the tank is initially
empty, how many hours would it take to fill the tank if all the pipes are fully in
operation?
Start
10. Consider the flow chart:
N=1
X=2
Y = 100
Y = Y - XN
No
Is N an
odd number
Is N ≤ 5
No
Stop
What is the value of Y when you reach “Stop”?
Yes
Yes
Y = Y + XN
N=N+1