S Round**Time - 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 make in order to connect 7 line sections into a longer line?**2. ** There are 6 sisters in a family and each of them has 4 brothers and 5 sisters. How many kids are there in this family?**3. **Larry's father and mother married 13 years ago. The sum of their ages was 73 when they married . This year, the age sum of Larry and his parents is 109 years old. How old is Larry this year?**4. **Steve is 1.53 meters tall. He casts a shadow of 107.1 centimeters, at the same time a tower is casting a shadow of 21.7 meters. How tall is the tower (in meters)? Note that: one meter = 100 centimeters.**5. **Below is a calendar in a certain month of a certain year. Each cell on the calendar is a 1x1 square. There are 24 possible 2x2 grids (Do not count the title row of the grid). What is the largest sum of the numbers in a 2x2 grid (If a cell has no number, assume it will be a 0)? SUN | MON | TUE | WED | THU | FRI | SAT | |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | | | | | | **6. **Using digits 1, 2, 3, 4, and 5 (Each digit can be used as many times as you want), how many 2-digit odd numbers can you make?**7. **X and Y are positive integers and X is larger than Y. If the remainder of (X ÷ Y) is 5, what is the smallest possible dividend X?**8. **Nancy is 3 times the age of David who is 3 years older than Susan. If the total age of the three is 52, how old is Susan?**9. **How many triangles can you count in the figure below? **10. **How many multiples of 5 are between 14 and 206?**11. **Joe drove his car at 50 mph to a planned destination that was far away. 1 hour after he started out, his brother tried to catch up with him from behind at the speed of 70 mph. How many hours would it take for Joe's brother to catch up with him?**12. **There are 14 students. At least one student was born in each month. At most, how many students have a birthday in the same month as someone else?**13. **A 12-hour digital clock shows time in digits with accuracy to seconds. What is the largest possible sum of all the digits?**14. **Hillary's weight is doubled over the past two years, and her weight is 54 pounds plus half the weight of her two years ago. How many pounds does she weigh now?**15. **The students lined up in rows to do some exercises. If 30 students are in each row, 5 students are left; if 25 students are in each row, 5 students are left; if 32 students are in each row, there are still 5 students left. At least how many students are there?**16. **In how many ways can you make up 29 cents using coins(quarter, dime, nickel, and penny)?**17. **In a series math quizzes during a school year, a student was awarded 21 points for each math quiz he passed, and was reduced 21 points for each math quiz he failed. At the end of the school year, the student had passed 8 times as many quizzes as he had failed, and received 735 points. How many quizzes did the student fail in the school year?**18. ** M and N are two numbers, and M**♦**N represents . What is the value of 8**♦**(24**♦**64).**19. **9 dollars were exchanged for nickels and dimes. The number of nickels to the number of dimes was 3:1. How many nickels were there in the change?**20. ** The numbers 2, 4, 6, and 8 are a set of four consecutive even numbers. Suppose the sum of 11 consecutive even numbers is 594. What is the smallest number among these 11 numbers?**21. **John bought a HDTV for $1400.80 after a 15% discount, with a 3% sales tax included. What was the original price of the HDTV (Before discount and the tax) in dollars?**22. **The ratio of the number of candies in three bags (A, B, C) is 6:9:5. If 66 candies are taken out from bag B and equally split, and then put into bag A and bag C respectively, the number of candies in bag A and bag B are equal. How many candies in total are there in all three bags?**23. **One pump can fill a swimming pool in 5 hours, and another pump can fill it in 9 hours, and one drain can empty it in 7 hours. If all three are opened at the same time, how many hours will it take to fill the pool?(Express your answer as a mixed number in the lowest terms).**24. **The sum of the digits in a two-digit number is 9. If the two digits exchange places, we get a new two-digit number. The new number is 45 more than the old number. What is the old number?**25. **In an one-mile running race, Hillary was able to run at 9 MPH for the 1st half, but was only able to run at 1 MPH for the remaining half. What was her average speed (in MPH) for the entire race?**26. **In the six-digit number D3131C, D and C represent the first and last digits respectively. The six-digit number is divisible by 88. Can you write down the entire number? Note that D and C don't have to be different.**27. **There are 4 cards with numbers 0, 1, 2, and 3 on them. These 4 cards were put in a box. You are asked to randomly pick up two cards each time to form a two-digit number (Cards are then put back). How many different two-digit numbers can you form?**28. **Anne added 55 pounds to of Kevin's weight. Nancy tripled Kevin's weight and then subtracted 55 pounds. If Anne and Nancy ended up with the same number, how many pounds does Kevin weigh?**29. **Jackson wants to exchange $4.00 for quarters, dimes, nickels, and pennies. He wants the same number of quarters and dimes, the same number of nickels and pennies, as well as the largest number of quarters possible. How many quarters can he get?**30. **There are three natural numbers a, b, and c. ab=12, bc=28, ca=21. What is abc =? |