Math Olympiad 5( Week 52 Final Exam) 1. If a♣b = |a − 2b|, what is the value of (7♣3)♣8? 2. If a♠b = a2 − ab + b2, what is the value of (1♠5)♠4? 3. If a♥b = a + ab + b2, what is the value of (3♥4)♥3? 4. Josh is 7 times the age of Hillary who is 2 years older than Rene. If the total age of the three is 115, how old is Rene? 7. If a⊛b = a2 − 2ab + b2, which of the following has the smallest value? 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 1 hour 48 minutes? 9. If 4 days before yesterday was Friday, what day of the week will it be 60 days from today? 10. There are 20 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. 54 customers ordered hamburgers, 46 ordered fries, and 24 ordered both. What was the total number of customers in the day to the restaurant? 15. If 7 × = 5, what is the value of 100 × ? 16. If 3m = 5, what is the value of 9m − 10? 17. M is a set of numbers whose median is 1. 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 20% discount on the suits which were less than $100, while gave a 25% discount on the suits which were $100 or more. What is the price (in dollars) after discount if a suit was $80 originally? 19. The average age of 6 people is 22. None of them are younger than 14 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 greater than the ones digit? |