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. 7 people are holding hands each other to make a human circle. How many hands are being held each other? 2. How many "5"s are there if you write down the natural numbers from 30 through 100? 3. Here are the Roman numerals and their corresponding value: I(1), V(5), X(10), L(50), C(100), D(500), M(1000). What is the value of the Roman numeral string "LXXXVI"?
(Note that when a smaller Roman numeral is on the left of another Roman numeral that is larger in value, the smaller Roman numeral value needs to be subtracted. For example, XIV = 10 + 5 − 1). 4. How many triangles can you count in the figure below? 5. Laura has a total of 12 $1 and $5 bills with a total value of $24. How many $1 bills does Laura have? 6. Laura and Eric are 39 miles apart and Eric is in front of Laura. Both are trying to get the same destination which is still many hours away. Laura bicycled at 15 mph, and Eric walked at 2 mph. In how many hours will Laura catch up with Eric? 7. When Emily opens her math book, two pages face her and the sum of the two page numbers is 337. What is the number of the very next page? 8. Among 15 students, at least how many students were born in the same month as someone else? 9. Rene had 57 Yu-Gi-Oh cards, and Hillary had none. Rene can move exactly 7 cards to Hillary at a time, and Hillary can move exactly 2 cards to Rene at a time. At least how many moves are needed to move all Rene's cards to Hillary? 10. In the natural numbers from 1 to 100, how many times does digit '5' show up? 11. What is the missing number to make the following equation to be true?
1 + 3 + 5 + 7 + 9 + ... + 1539 = 2 + 4 + 6 + 8 + 10 + ... + 1540 - (?) 12. John stopped at a restaurant for dinner. There are 13 kinds of main dishes and 8 kinds of soup. How many possible combinations can be made from the menu (Each with one main dish and one soup)? 13. Kevin and Anne start together and race their bikes around a circular trial at constant speeds. It will take Kevin 6 minutes to go 1 lap, and it will take Anne 4 minutes for a lap. How long will it take Anne to be exactly 1 lap ahead of Kevin (in minutes)? 15. In a chess tournament, there are 44 players. Every 4 people form a group. In each group, all players will play a game with each other. How many games will be played in total? 16. If a@b=(a × b) − (a + b), how much larger is 12@13 than 6@6? 17. A man made a 2-hour up-hill trip at 38 mph (miles per hour). On the return down-hill trip, he traveled at 57 mph. What was the his average speed in mph for the entire trip? 18. Steve has $510 in his wallet. The money consists only of $5 and $10 bills. If the number of $5 bill is 4 times the number of $10 bills, how many $5 bills are there in his wallet? 19. Ben can paint a room in 6 hours, and his sister Niconia can paint it in 7 hours. If Ben paints for 1 hour and then leaves, and his sister takes over, how many hours will it take his sister to finish the painting? (Express your answer as a mixed number in the lowest terms). 20. The product of two whole numbers is 512 and their quotient is 8. What is the sum of the two numbers? 21. When a natural number is multiplied by itself, the result is a square number. Such as 1, 4, 9, 16, and 25. How many square numbers are there between 4000 and 5000 inclusively? 22. 5 students were working on a project as a group at the same rate. They finished of the project in 5 hours. On the following day, only one student can continue to work on it. How many hours will be needed for him to finish the remaining project at the same rate as before? 23. What is the probability of tossing a coin twice with the outcome of 1 tail up and 1 head up regardless of the order? Express your answer as a fraction in lowest terms. 24. What is the sum of 10 consecutive numbers with the first number being 23? 25. A bike and a helmet together cost $139 before a discount. During a sales event, bikes are at 20% discount and helmets are at 15% discount. If the total cost of the bike and helmet is $112.65 after the discount, what was the original price of the bike (in dollars)? 26. A certain number of candy bars are distributed to children in a kindergarten. If they are only distributed to the children in class A, each child in the class will get 18 candy bars. If they are distributed to the children in both class A and class B, each child will get 6 candy bars. If they are only distributed to class B, how many candy bars will each child in class B get? 28. Steve has a pile of pennies, nickels, and dimes with a total of $2.80. The number of pennies is 5 times the number of nickels and the number of nickels is 6 times the number of dimes. How many dimes are there in the pile? 29. Consecutive numbers are natural numbers that follow in order, while the cube of a number is the product of three of the same number. The difference between the cube of the average of the three consecutive numbers and the product of the three consecutive numbers is 23. What is the smallest number in the three consecutive numbers? 30. A whole number A is 4 more than another whole number B. The product of the two numbers is 45. What is number A? |