Math Olympiad 5( Week 52 Final Exam) 1. If a@b = |a+b|+|a-b|, what is the value of 10@(4@9)? 2. If a∀b = a2 + 2b, what is the value of (3∀5)∀4? 3. If a♦b = (a − 1) + ab + (b − 1)2, what is the value of (3♦1)♦4? 4. Edward is 8 times the age of Emily who is 3 years older than John. If the total age of the three is 47, how old is John? 7. If 1⊜5 = 1+11+111+1111+11111, 2⊜4 = 2+22+222+2222, 3⊜3 = 3+33+333, and 4⊜2 = 4+44, what is the value of 5⊜3? 8. There are 24 hours a day, 60 minutes in an hour and 60 seconds in a minute. There are even smaller time units, such as millisecond (10 −3 second), microsecond (10 −6 second), nanosecond (10 −9 second). How many seconds are in 9 hours 19 minutes? 9. If 4 days before yesterday was Friday, what day of the week will it be 10 days from today? 10. There are 12 triangles. Each triangle has exact one shared side with another triangle. How many sides are there in total? 12. Consecutive numbers are whole numbers that follow in order such as 2, 3, 4, 5 and 6. There are seven consecutive numbers whose sum is 70. What is the smallest number among the consecutive numbers? 13. Below is a bar chart showing the profit (in millions) of a company in the last 4 quarters.
What was the average quarter profit in millions during 1999? 14. All the customers to the restaurant ordered either hamburgers or fries or both in some day. 38 customers ordered hamburgers, 39 ordered fries, and 19 ordered both. What was the total number of customers in the day to the restaurant? 15. If 9 × = 11, what is the value of 385 × ? 16. If 5m = 8, what is the value of 10m − 5? 17. M is a set of numbers whose median is 3. N is a set that is generated by tripling each number in M. What is the median of the numbers in set N? 18. After a holiday season, a department store gave a 25% discount on the suits which were less than $70, while gave a 30% discount on the suits which were $70 or more. What is the price (in dollars) after discount if a suit was $110 originally? 19. The average age of 8 people is 30. None of them are younger than 25 years old. How old is the oldest possible age in the group? 20. How many two-digit numbers are there in which the tens digit is less than or equal to the ones digit? |