Math Olympiad 4( Week 46 Quiz 9) 1. If a∧b = (a+b)+(a-b), what is the value of 7∧(8∧3)? 2. If a⊥b=(a+b)+(a-b), then what is the value of 16⊥14? 3. Richard was paid $8 per hour plus a bonus of $16.50 per day. On a certain day Richard was paid $40.50. How many hours did he work on that day? 4. A twin prime is a prime number that differs from another prime number by two, such as (3,5) or (5,7). How many pairs of twin primes are there within 20? 5. John was paid $5.50 per hour plus a bonus of $13.50 a day if he works more than 4 hour for the day. On a certain day John was paid $41.00. How many hours did he work on that day? 6. Mother bought some candies. The children ate 3 more than half of the candies on the first day, and 7 more than half of the remaining on the second day. Now there are 8 candies left. How many candies did the mother buy? 7. People are sorted by their last name in lots of cases. A school is trying to be fair, so students are sorted with various systems in different occasions. One of the systems is based on a calculated index of their first name. Let A=1, B=2, C=3, ..., Y=25 and Z=26. The calculated index is determined by adding the value of all letters in the name. Can you sort the following names based on the system in ascending index value (if both names have the same index value, keep their original order)? You need to type the names exactly as they are shown below with the first character in upper case. Before sort: Susan, Eric, Mary. After sort: , , . 8. In a group of 50 high school students, 21 of them took Economics, 29 of them took Science, and 13 took both subjects. How many of them took neither Economics nor Science? 9. Out of 110 people, 25 can ski, 97 can swim, and 26 can both swim and ski. How many people cannot swim nor ski? 10. If a@b means , then what will 20@(11@14) = ? 11. If m and n are positive integers and 5m + 5n = 40, what is the sum of all possible values of n? 12. Some toys are distributed to children. If each child is given 5 toys, 7 toys are left. If each child is given 6 toys, 8 more toys are needed. How many toys are there? 14. The cost of mailing a first-class letter is 34 cents for the first ounce and 23 cents for each additional ounce. A letter mailed had a total cost of $1.26. How many ounces does the letter weigh? 15. There are 24 tables numbered 1-24 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 8? |