MATHCOUNTS. 2003 @ School Competition i Sprint Round Problems 1-30 Name, DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO. This section of the competition consists of 30 problems. You will have 40 minutes to complete all the problems ‘You are not allowed to use calculators, slide rules, books or other aids during this round. Calculations may be done on soratch paper. All answers must be complete, legible and simplified to lowest terms. Record only final answers in the blanks in the right-hand column of the competition booklet. If you complete the problems before time is, called, use the remaining time to check your answers. Total Correct Scorer’s Initials 1] Founding Sponsors National Sponsors CCNA Foundation CConocaPhilins National Society of Profesional Engineers The Dow Chemical Company Foundation National Counel of Teacher of Mathematics General Motors Foundation Lockheed Manin National Aeronautics and Space Adrnistation Texas Instroments neorporated 2M Foundation (©2002 MATHCOUNTS Foundation, 1420 king Steet, Alexandria, VA 220141. What is the greatest positive integer m such that 1° is less than 1 95? 2. The marks on this thermometer are equally spaced. How many 2 degrees warmer is the temperature measuring A degrees than the temperature measuring B degrees? Express your answer as, a decimal to the nearest tenth g £ 3. In March 2000, Jake Euget, a high school senior in Fargo, 3 North Dakota, won his school’s annual x memorization contest by reciting 5,005 digits of m. He recited the digits in 55 minutes. On average, how many digits did he recite each minute? 4, What is the sum of the number of faces, edges — 4 3 and vertices of a hexagonal prism? 5. Using each digit only once, place the digits 7, 8 and 9, one in 5. each box, so that the product is as close to 6 as possible. What is the product ([_]}.})( 0.[)? Express your answer as a decimal to the nearest hundredth. 6. Of the 2400 jellybeans in a jar, + are purple. Lucia then 6 removes 150 purple jellybeans from the jar. What fraction of the jellybeans left in the jar are purple? Express your answer as a common fraction. (©2002 MATHCOUNTS Foundation: 2003 School Sprint Round7. An antique dealer buys a chair for $20 and sells it for $85. The dealer later buys back the same chair for $110 and sells it for $135. How many dollars total profit did the dealer make on this chair? SIA 8. If 6$-x=1, then what is the value of x? Express your answer as a common fraction. 9. A water tank in the shape of a right circular eylinder has a base radius of 30 meters and a volume of 2700 cubic meters. What is the number of meters in the height of the tank? 10. The game of Ibish is played in rounds. In the first round, you cam 0, 10 or 11 points; in the second round, you earn 0, 10, 11 or 12 points; in the third round, you earn 0, 10, 11, 12 or 13 points, and so on, including the next greatest integer in the possible point values. What is the fewest number of rounds after which your total score can have a 9 in the units digit? 11. When this net of six squares is folded to make a cube, which face will be opposite face S? pie 12, What is the least three-digit positive integer that has 2, 5 and 7 as factors? (©2002 MATHCOUNTS Foundation: 2003 School Sprint Round 10. u13, The rectangular stage at Radio City Music Hall in New York 13 City measures 144 feet wide and 60 feet deep. What is the number of square yards in its area? 14, One-fourth of one-third of a number is one-half, What is the 14. number? 15, Following the arrows, how many different routes are there from A to D? 16. There are only six red, four blue and eight brown buttons in a 16. jar. A button is randomly selected from the jar. What is the probability that the button selected is not blue? Express your answer as a common fraction. 17. An airline reported a total of 2500 flight departures and, of 17. those, 1760 departed on time. What percent of the airline's flight departures were on time? Express your answer to the nearest tenth. 18. What is the greatest three-digit multiple of 19? 18. ©2002 MATHCOUNTS Foundation: 2003 School Sprint Round19. A racing car has a fuel capacity of 35 gallons of 19. fuel and an average mileage of 2.0 miles per gallon, A family car has a fuel capacity of 17 gallons of fuel and an average mileage of 28 miles per gallon. What is the positive difference, in miles, between the average distance possible for each of these two vehicles if each one starts with one full tank of fuel? 20, Let N be the product of all integers from 1 through 10 that are 20, not divisible by 5. What is the units digit of N? 21, What is the value of the following sum: 21. 100+ -99 +98 +... + 108 + 109 + 110? 22. Bill has 4 as much money as Bonnie, Bonnie has ? as much 2 money as Fran, Bonnie has $480, What is the total amount of money, in dollars, that Bill and Fran have together? 23. A composite mamber is a number that has two or more prime 23. factors. The number 87 can be expressed as the sum of two composite numbers in many ways, What is the minimum positive difference between two such numbers? 24, The five concentric circles shown have radii of 1, 2, 3 5 centimeters. What is the number of square centimeters in the total area of the three shaded regions? Express your answer in terns of ©) ©2002 MATHCOUNTTS Foundation: 2003 School Sprint Round 4and 24,25. 26. 27. 28, 29. 30, For how many digits C is the positive three-digit number 1C3 a multiple of 3? What is the distance, in units, between the points (-3, 4) and (4, -5)? Express your answer in simplest radical form. The sum of two integers is 20 more than their difference. What must the value of one of these two integers be? ‘The trees in a peach orchard were arranged in a square array with N’ columns and N rows. To enlarge the orchard by one row and one column to make a larger square, the owner bought and planted 29 more peach trees. How many trees are in the orchard after the enlargement? A student spins the spinner twice and records the number that. the spinner lands on each time. What is the probability that the ‘sum of the two recorded numbers is less than 4, if the probability of spinning each number is}? Express your answer as a common fraction. (Te) A Lem. 1 em square is cut from each of the four comers of a square piece of cardboard with area 64 square centimeters. The sides are then folded up to make a rectangular box. What is the volume in cubic centimeters of the box? | lee 25. 26, 21. 29, 30, [©2002 MATHCOUNTS Foundation: 2003 School Sprint Round