Ergogenic Aids
MATHCOUNTS
2008 State Sprint Round
1. John saw an ad for tomato soup at 24¢ per can. At the price 1. advertised, what is the greatest number of whole cans of soup John could buy for $1.00?
2. Yvonne purchased a jacket at Right Price, and the lowest 2. price on the tag was $4. This was the sale price, which was calculated by taking 75% off of the original price.
What was the original price of Yvonne’s jacket?
3. What is the greatest number of interior right angles a convex 3. octagon can have?
4. Tamara knows that the arithmetic mean of her five quiz scores 4. is 95%. However, she has misplaced one of these quizzes.
The ones she can find have scores of 100%, 100%, 99% and 98%.
What is her score on the misplaced quiz?
5. How many integers between 100 and 300 have both 11 and 8 5. as factors?
6. One-half of a road construction 6. project was completed by 6 workers in 12 days. Working at the same rate, what is the smallest number of workers needed to finish the rest of the project in exactly four days?
7. The trisectors of angles B and C of scalene A7. triangle ABC meet at points P and Q, as shown. Angle A measures 39 degrees and angle QBP measures 14 degrees. What is the Q measure of angle BPC? P
B C
8. What non-zero, real value of x satisfies ? 8.
Express your answer as a common fraction.
9. A clock loses 5 seconds every 12 minutes. 9.
At this rate, how many minutes will the clock lose in a 24-hour period?
10. Elliott Farms has a silo for storage. 10.
The silo is a right circular cylinder topped by a right circular cone, both having the 27m same radius. The height of the cone is half the height of the cylinder. The diameter of the base of the silo is 10 meters and the height of the entire silo is 27 meters.
What is the volume, in cubic meters, of the silo?
Express your answer in terms of .
11. For how many non-negative real values of x is 11.
an
2008 State Sprint Round
1. John saw an ad for tomato soup at 24¢ per can. At the price 1. advertised, what is the greatest number of whole cans of soup John could buy for $1.00?
2. Yvonne purchased a jacket at Right Price, and the lowest 2. price on the tag was $4. This was the sale price, which was calculated by taking 75% off of the original price.
What was the original price of Yvonne’s jacket?
3. What is the greatest number of interior right angles a convex 3. octagon can have?
4. Tamara knows that the arithmetic mean of her five quiz scores 4. is 95%. However, she has misplaced one of these quizzes.
The ones she can find have scores of 100%, 100%, 99% and 98%.
What is her score on the misplaced quiz?
5. How many integers between 100 and 300 have both 11 and 8 5. as factors?
6. One-half of a road construction 6. project was completed by 6 workers in 12 days. Working at the same rate, what is the smallest number of workers needed to finish the rest of the project in exactly four days?
7. The trisectors of angles B and C of scalene A7. triangle ABC meet at points P and Q, as shown. Angle A measures 39 degrees and angle QBP measures 14 degrees. What is the Q measure of angle BPC? P
B C
8. What non-zero, real value of x satisfies ? 8.
Express your answer as a common fraction.
9. A clock loses 5 seconds every 12 minutes. 9.
At this rate, how many minutes will the clock lose in a 24-hour period?
10. Elliott Farms has a silo for storage. 10.
The silo is a right circular cylinder topped by a right circular cone, both having the 27m same radius. The height of the cone is half the height of the cylinder. The diameter of the base of the silo is 10 meters and the height of the entire silo is 27 meters.
What is the volume, in cubic meters, of the silo?
Express your answer in terms of .
11. For how many non-negative real values of x is 11.
an