Math Olympiad 5

1. 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?

2. Below is a pie chart showing a company's revenue distribution from different regions.

If the total revenue is 900 million, what is the revenue from "Asia-Pacific" in millions?

3. What is the median of the following number set {5, 9, 4, 7, 12, 7, 3, 9, 4}?

5. Which set of the numbers below has the same value for the average, median, and the mode?

	Take school bus	Not take school bus	Total
Boys			486
Girls	431
Total		116	994

The table above, showing the summary of students transportation in Liston Middle School, is partially filled in. Base on the information in the table, how many boys are taking buses?

7. The average of 12 and a is 24, and the average of 12, a, and b is 40. If the average of 12, a, b, and c is 54, then what is the value of c?

8. The average (arithmetic mean) weight of 5 kids in a group is 105 pounds. If a new kid is added to the group and the average weight of the group decreases to 102 pounds. What is the weight, in pounds, of the new added kid?

9. The average (arithmetic mean) of three positive numbers, a, b, and c, is 17. When the smallest of these numbers is subtracted from the sum of the other two, the result is 43. If a < b, which of the following pairs of equations could correctly express the information above?

a + b + c = 17

a + c − b = 43

a + b + c = 51

b − (a + c) = 43

a + b + c = 51

b + c − a = 43

a + b + c = 17

a + b − c = 43

a + b + c = 51

a + c − b = 43

10.

A seven-segment display is a form of electronic display device for displaying decimal numerals. Above figure shows the numbers from 0 to 9 that are displayed with seven-segment display. Number 8 uses all the seven segments, while number 1 uses only two segments. If each number from 0 to 9 are displayed with the seven-segment displays, what is the median number of segments to display those numbers?