S RoundTime - 40 minutes
30 questions | Direction: The real competition of Sprint round consists of 30 questions. You will have 40 minutes to complete all the questions. You are NOT allowed to use calculators, books or other aids during the round. | 1. How many knots are needed to connect 16 short ropes into a circular rope? 2. A natural number divided by another natural number N has a remainder of 4. What is the smallest value N could be? 3. If it takes 5 minutes to cut a log into 6 pieces, how many minutes will it take to cut the log into 28 pieces? 4. The product of two whole numbers is 10. If neither of the numbers contains the digit zero, what is the smaller number? 5. In a chess tournament, there are 5 players. Each player will play a game with each other. How many games will be played in total? 6. Two salesmen had combined total sales of $386 on a certain day. If one of them gave $16 to the other person, each would have the same amount of the sales. What was the difference in the sales between the two salesmen(in dollars)? 7. There are 41 marbles in a red bag and 37 marbles in a blue bag. How many marbles need to be moved from the red bag to the blue bag, so that there will be twice as many marbles in the blue bag as in the red bag? 8. How many triangles can you count in the figure below? 9. A box of pencils can be distributed equally among 2, 3, 4, 5 or 6 children with no pencils left. What is the smallest number of pencils that the box could have? 10. Mary has a total of 22 $5 and $100 bills with a total value of $1060. How many $5 bills does Mary have? 11. Both Jessica and Joe have a certain number of cards. If Joe gave Jessica 25 of his cards, they would have the same number of cards. However if Jessica gave Joe 20 of her cards instead, then Joe would have three times as many cards as Jessica would have. How many cards do they have in total? 12. Jay planned to work after school. If he worked 8 weeks, he would earn $158 and a trip to Disney. If he worked 7 weeks at the fixed weekly rate, he would earn $130 and the trip. What was the fixed weekly rate (in dollars) for the job? 13. There are 30 tables numbered 1-30 which are equally spaced around a round garden in the number order. What is the number of the table directly across from the table numbered 10? 14. In three math exams, Alice's scores are 81, 71, and 95. What score will Alice need to get on the fourth exam in order to have an average score of 82 for all four exams? 15. John has the following coins in his pocket: 3 pennies, 1 nickel, and 3 dimes. He takes out two coins, records the sum of their values, and then puts them back with the other coins. He continues to take out two coins, records the sum of their values, and puts them back. How many different sums can he record at most? 16. Two buses leave a station at 9:00 AM. One heads east at 43 MPH while the other heads west at 37 MPH. How many miles apart are the two buses at 2:00 PM of the same day? 17. The product of two whole numbers is 150 and their quotient is 6. What is the smaller number? 19. A 12-hour chime clock strikes 1 chime at 1 o'clock, 2 chimes at 2 o'clock, 3 chimes at 3 o'clock,..., and 12 chimes at 12 o'clock. The clock also strikes 1 chime in the middle of every hour. What is the maximum total number of chimes the clock will strike in a 530-minutes period? 20. One third of a number is equal to 32 less than three times the number. What is the number? 21. Smith has a certain amount of money to spend on 3 types of gifts, and their prices are $7, $8, and $9 each respectively. If he spends all the money on any single type of gifts, there will all be $2 left. The amount of money Smith has is more than $9. At least, how much (in dollars) money does Smith have? 22. There are 368 students in a school. At least how many students have the same birthday as someone else? Assume that none was born on Feb. 29. 23. The total cost of 9 packs of a snack is less than $6. However, the total cost of 11 packs of the same snack is more than $6. At most, how many cents could a single pack of the snack cost? 24. Nick has the following coins in his pocket: 2 pennies, 2 nickels, 1 dime, 2 quarters, 2 half-dollars, and 2 dollars. 9 of these coins are taken out of the pocket and the sum of their values is recorded. How many different sums are possible? 25. A whole number has two factors A and B. If factor A increases by 7 and factor B doesn't change, then the product increases by 182. If factor A doesn't change, and factor B decreases by 9, then the product decreases by 270. Find the original whole number. 26. The distance from place A to place B is 495 miles. Two cars start out from place A to place B at the same time. One car drove at 54 mph; the other car drove at 45 mph. When the faster car got to the place B, it went back immediately. How many hours did it take for them to meet again? 27. The average of 6 numbers was 24. After one of the numbers was removed, the average of the remaining 5 numbers became 23. After another number was removed, the average of the remaining 4 numbers became 22. What were the two numbers which were removed? Type only the numbers separated by a space or a comma. 28. If you write down all the odd numbers from 1 to 471 inclusively, how many times will the digit 7 appear? 29. What is the largest two-digit number that has a remainder of 1 when 1002 is divided by this two-digit number? |