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 make in order to connect 8 pieces of rope into a circular rope? 2. It takes 12 minutes to cut a log into 4 pieces. How long will it take for each cut (in minutes)? 3. Suppose numbers 1 through 93 are written on a piece of paper. How many times will digits 2 and 5 appear on the paper in total? 4. When a positive integer is divided by 4, 6, or 8, the remainder is 1 . What is the least possible value for the number? 5. One side of a triangle is 17 inches longer than its shortest side. Another side of the triangle is 16 inches longer than its shortest side. If the perimeter of the triangle is 48 inches, how long is the longest side in inches? 6. Martha has a total of 11 $5 and $20 bills with a total value of $115. How many $5 bills does Martha have? 7. A group of 22 people went to a trip, some by cars and some by bus. When they were going, 13 people rode on a bus and 3 people rode in each car. When they were coming back, 4 people rode in each car. How many people came back home by bus? 8. The sum of two numbers is 259. The larger number is 19 more than 3 times the smaller number. What is the bigger number? 9. How many triangles can you count in the following figure? 10. In the arithmetic sequence below, 253, 250, 247, 244, 241, ... What is the 82nd term? 11. A drawer contains 2 red socks, 8 brown socks, 7 gray socks, 2 blue socks, and 26 black socks. If you are blindfolded, what is the fewest number of socks you need to pick from the drawer in order to make sure that you either pick a pair of blue socks or a pair of black socks? 12. A 5-digit whole number is added to a 2-digit whole number. There is a largest possible sum and a smallest possible sum. What is the difference between those two sums? 13. The ratio of male to female people in a city is 48.9 to 51.1. If the population of the city is 72000, how many more female residents than male residents are there in the city? 14. M is the sum of 6 consecutive whole numbers. If the smallest number among the 6 numbers ends with 4, what is the ones digit of M? 15. Using digits 1, 2, 3, 4, and 5 (Each digit can be used as many times as you want in a number), how many 3-digit odd numbers can you make? 16. If you are asked to write down the natural numbers from 1 to 250, how many digits in total will be written? 17. A is a two-digit number. When 214 is divided by this number , there is a remainder of 5. What is the smallest possible value for A? 18. Some toys are distributed to children. If each child is given 4 toys, 3 toys are left. If each child is given 5 toys, 6 more toys are needed. How many children are there? 19. A 12-hour digital clock shows time in digits with accuracy to seconds. What is the largest possible product of its non-zero digits? 20. What is the sum of the first 9 multiples of 9? 21. = + , where A is less than B and both are whole numbers. What is the largest possible value for B? 22. Julia went shopping. She spent half of her money in the 1st store. She went to a second store where she spent one-third of what remained, and then had $40 left. How much money (in dollars) did she have before she went to the 1st store? 24. Alice has 60 stamps, and Edward has 48 stamps. In each exchange, Alice gives 9 stamps to Edward, and Edward gives 11 stamps back to Alice. After how many exchanges will Alice have twice the number of stamps that Edward has? 25. Suppose the sum of 7 consecutive even numbers is 308. If each number is reduced by the smallest number among these 7 numbers, what will be the sum of these new 7 numbers? 26. Natural numbers are randomly selected, and the difference between any two selected natural numbers is calculated. How many different natural numbers are needed to be picked in order to make sure that there is at least one calculated difference which is a multiple of 5? 27. There are three continuous natural numbers. The difference between the product of the last two numbers and the product of the first two numbers is 62. What is the average of the three numbers? 28. Kevin biked from his home to his high school at 6.6 miles per hour. When he returned home from school, using the same route, he biked at 3.4 miles per hour. If the total round trip took 25 minutes, what was the distance from his home to his school (in miles)? 29. Select 5 digits from 1, 2, 3, 4, 5, and 6 to make a 5-digit number which is a multiple of 3. How many different such 5-digit numbers can you make? 30. When a natural number is multiplied by all the natural numbers less than itself, the result is a factorial number, such as 1!=1(1), 2!=1 × 2(2), 3!=1 × 2 × 3(6), 4!=1 × 2 × 3 × 4(24), ... with 1, 2, 6, 24, being factorial numbers. If you multiply the first 15 factorial numbers (starting from 1!) together, how many prime factors of 2 will be in the product? |