ࡱ> GIFU%` bnbjbjNN Mz,,```t<7<7<7<77t8L8888 $hVDi`xb xxD88KRZZZx88`8ZxZZH`Z8|8 `x<7(ZÜ0ZggZg`ZgZ DDJxxxxtttd).dttt.ttt MATHCOUNTS 2005 State Sprint Round 1. In octagon ABCDEFGH, every side is perpendicular to 1. each of its adjacent sides. What is the perimeter of ABCDEFGH? A H E D 8 4 6 G F B 10 C 2. The difference between two prime numbers is 17. 2. What is their sum? 3. What is the sum of the two perfect square integers 3. that are closest to 2005? 4. In February 2005, the Smiths watched TV for three 4. hours every Monday, Wednesday and Friday; they watched TV for four hours every Tuesday and Thursday; and they never watched TV on weekends. How many hours of TV did they watch that month? 5. The chart below gives the air distance in miles 5. between selected world cities. If two different cities from the chart are chosen at random, what is the probability that the distance between them is less than 7000 miles? Express your answer as a common fraction. BankokCape TownHonoluluLondonBankok6,3006,6095,944Cape Town630011,5355,989Honolulu660911,5357,240London59445,9897,240 6. When a water tank is 30% full, it contains 27 6. gallons less than when it is 20% empty. How many gallons of water does the tank hold when it is full? 7. Each of the letters A, B, C and D represents a 7. different odd integer between two and ten. What is the least possible value of  EMBED Equation.DSMT4 ? Express your answer as a common fraction. 8. At a malls food court, Crystal has $7.50 to buy a meal 8. (one entre, one drink and one dessert). The table below lists Crystals choices and their prices including sales tax. How many distinct possible meals can she afford to buy? Entres Drinks Desserts Pizza $3.50 Lemonade $1.50 Frozen Yogurt $3.00 Corn Dog $2.50 Soda $1.25 Cookies $2.00 Fish & Chips $3.50 Fried Rice $4.75 9. The points (x, y) represented in this table lie on a 9. straight line. When the equation of this line is written in the form y =Ax + B, what is the value of A + B? x y 2 7 t 2 v t v + 6 10. When Roslyn writes her name repeatedly in a 5 by 5 10. table as shown, the bottom right corner contains the letter R. If she repeats the process in a 20 by 20 table, what letter would occupy the bottom right corner?  R O S L Y N R O S L Y N R O S L Y N R O S L Y N R 11. The number 210 is the product of two consecutive 11. positive integers and is also the product of three consecutive integers. What is the sum of those five integers? 12. A 12-diameter pizza and a 16-diameter pizza are 12. each cut into eight congruent slices. Jane ate three slices of the 12 pizza. Mark ate three slices of the 16 pizza. How many more square inches of pizza than Jane did Mark eat? Express your answer as a common fraction in terms of . 13. In how many patterns can a 2-by-5 rectangle be tiled 13. with five white rectangular 2-by-1 tiles? The two examples shown below are considered to be different tiling patterns. 1  2 5 14. For each plumbing repair job, Mr. Wrench charges N 14. dollars for coming out to the house plus x dollars per hour that he works at the house. He charged $97 for a one-hour repair job and $265 for a five-hour repair job. What is his charge for a two-hour repair job? 15. Regions I, II and III are bounded by squares. The 15. perimeter of region I is 12 units and the perimeter of region II is 24 units. What is the ratio of the area of region I to the area of region III? Express your answer as a common fraction.  I III II 16. What is the positive difference between the 2000th 16. term and the 2005th term of the arithmetic sequence "8, "2, 4, 10, ... ? 17. The ratio of teachers to students in a particular school 17. is 1 to 11. The ratio of female students to the total number of students is 4 to 9. If there are 396 female students, how many teachers are there? 18. A juice company sells its product in either a 48-ounce 18. size or a 32-ounce size. It charges $3.90 for the 48-ounce size. How much should it charge for the smaller size if it wants the price per ounce to be 25% more than the price per ounce of the larger size? 19. A stack of 45 dimes is divided into three piles in the ratio 19.  EMBED Equation.DSMT4 . How many dimes are in the pile with the least number of dimes? 20. Rectangle ABCD is folded in half to form rectangle 20. AEFD, which is then folded in half to form rectangle AGHD. The perimeter of rectangle AGHD is 23 cm and the perimeter of ABCD is 47 cm. What is the area of rectangle ABCD? B C E F G H A D A D A D 21. How many positive three-digit integers with each 21. digit greater than 4 are divisible by 6? 22. The sum of four positive integers that form an 22. arithmetic sequence is 46. Of all such possible sequences, what is the greatest possible third term? 23. For the data whose frequency histogram is shown, 23. by how many days is the mean number of days missed per student greater than the median number of days missed per student for the 15 students? Express your answer as a common fraction. Number of School Days Missed  by Mr. Clarks Students 5 4 3 2 1  0 1 2 3 4 5 # of Days of School Missed 24. There are only red marbles and green marbles in a 24. bag. The ratio of red marbles to green marbles in the bag is 4:7. Julia then adds 90 red marbles and 36 green marbles to the bag, which makes the probability of selecting a red marble from the bag on a random draw equal to  EMBED Equation.DSMT4 . How many total marbles are in the bag after Julia has added the 126 marbles? 25. What is the area of the region bounded by the three 25. lines with equations 2x + y = 8, 2x " 5y = 20 and x + y = 10? 26. Yesterday, 28 students took a test. The arithmetic mean 26. of those 28 scores was 72 points. 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