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. 3 people are holding hands each other to make a human circle. How many hands are being held each other? 2. How many "6"s are there if you write down the natural numbers from 40 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 "XLIII"?
(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. Susan has a total of 13 $1 and $5 bills with a total value of $41. How many $1 bills does Susan have? 6. Alice and Richard are 36 miles apart and Richard is in front of Alice. Both are trying to get the same destination which is still many hours away. Alice bicycled at 12 mph, and Richard walked at 3 mph. In how many hours will Alice catch up with Richard? 7. When Nancy opens her math book, two pages face her and the sum of the two page numbers is 221. 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. Curtis had 74 Yu-Gi-Oh cards, and Nancy had none. Curtis can move exactly 8 cards to Nancy at a time, and Nancy can move exactly 3 cards to Curtis at a time. At least how many moves are needed to move all Curtis's cards to Nancy? 10. In the natural numbers from 1 to 100, how many times does digit '0' show up? 11. What is the missing number to make the following equation to be true?
1 + 3 + 5 + 7 + 9 + ... + 1099 = 2 + 4 + 6 + 8 + 10 + ... + 1100 - (?) 12. Smith stopped at a restaurant for dinner. There are 17 kinds of main dishes and 10 kinds of soup. How many possible combinations can be made from the menu (Each with one main dish and one soup)? 13. Michael and Susan start together and race their bikes around a circular trial at constant speeds. It will take Michael 6 minutes to go 1 lap, and it will take Susan 4 minutes for a lap. How long will it take Susan to be exactly 1 lap ahead of Michael (in minutes)? 15. In a chess tournament, there are 40 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 13@11 than 7@5? 17. A man made a 6-hour up-hill trip at 36 mph (miles per hour). On the return down-hill trip, he traveled at 54 mph. What was the his average speed in mph for the entire trip? 18. Tom has $250 in his wallet. The money consists only of $5 and $10 bills. If the number of $5 bill is 3 times the number of $10 bills, how many $5 bills are there in his wallet? 19. Jay can paint a room in 8 hours, and his sister Jennifer can paint it in 9 hours. If Jay 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 216 and their quotient is 6. 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 7000 and 8000 inclusively? 22. 5 students were working on a project as a group at the same rate. They finished of the project in 7 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 4 times with the outcome of 1 head up and 3 tails up regardless of the order? Express your answer as a fraction in lowest terms. 24. What is the sum of 12 consecutive numbers with the first number being 20? 25. A bike and a helmet together cost $163 before a discount. During a sales event, bikes are at 20% discount and helmets are at 25% discount. If the total cost of the bike and helmet is $129.00 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 60 candy bars. If they are distributed to the children in both class A and class B, each child will get 12 candy bars. If they are only distributed to class B, how many candy bars will each child in class B get? 28. Smith has a pile of pennies, nickels, and dimes with a total of $2.00. The number of pennies is 3 times the number of nickels and the number of nickels is 5 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 17. What is the smallest number in the three consecutive numbers? 30. A whole number A is 2 more than another whole number B. The product of the two numbers is 99. What is number A? |