Math Olympiad 4( Week 52 Final Exam) 1. Below are the numbers from 0 to 9, + − and = signs made of line segments.
Please correct the following equation by adding Only one segment to the equation and write your corrected equation (only one is needed) in the blank (such as 1+2=3).
3. It takes 6 minutes to cut a piece of wood into 2 pieces. How many minutes will it take to cut the wood into 8 pieces? 4. Here are the Roman numerals and their corresponding value: I(1), V(5), X(10), L(50), C(100), D(500), M(1000). What is the value of the Roman numeral string "CCCLXVI"?
(Note that when a smaller Roman numeral is on the left of another Roman numeral that is larger in value, the smaller Roman numeral value needs to be subtracted from the sum). 5. What is the largest possible remainder of (X ÷ 9) ? (X is a whole number). 6. A farmer has ducks, geese, and hens. He feeds them with a certain amount bird food every day. A duck eats twice as much as a hen and a goose eats 3 times as much as a hen. Half of the food is fed to 3 ducks and 5 geese, and another half is fed to hens. How many hens does the farmer have? 7. The length of a rectangle is 3 times its width. If the perimeter is 40 inches, what is the area of the rectangle(in square inches)? 8. Write down the first 5 common multiples of 4 and 6. Separate each number with a comma. 9. Determine which of the following number(s) are divisible by 9. Type the number(s) in the blank, and separate each number with a comma if necessary.| | 14 | 983 | 4695 | 51013 | 262734 | 3007647 |
10. What is the multiple of 2 between 800 and 899 inclusively with the largest digits sum? 11. The sum of the three angles of any triangle must be 180 degrees. In the triangle XYZ, angle X has a measure of 20 degrees. Angle Y is 4 times as large as angle X. What is the measure (in degrees) of angle Z 12. There are 16 pens and 19 pencils that are distributed evenly to a group of students with exactly one pen and one pencil left. What is the greatest possible number of students in the group? 13. A teacher brings 54 cards and 42 pencils to the class. The cards and pencils are evenly distributed to all the students and each student get the same number of cards and the equal number of the pencils. No cards and pencils are left. At most, how many students are in the class? 14. Type all the multiples of 6 between 100 and 199, and their digits sum also are multiples of 6. Separate two numbers with a comma. 15. 10 and 21 are two examples of the numbers that have a digit sum less or equal to 3 (1 + 0 ≤ 3 and 2 + 1 ≤ 3). How many two-digit numbers have the sum of the digits less or equal to 2? 16. Hillary is 7 years older than Rene who is 7 years older than Laura. If their ages add up to 27, how old is Laura? 17. How many triangles can you count in the figure below? 18. Determine which of the following number(s) are divisible by 4. Type the number(s) in the blank, and separate each number with a comma if necessary. 19. If a∎b = ab − a + b, which of the following has the greatest value? 20. Hillary has 15 different pairs of socks in a drawer. At most, how many socks can she take out from the drawer before finding a pair of socks? |