Math Olympiad 4( Week 26 Mid-Term 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 3 pieces. How many minutes will it take to cut the wood into 10 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 "DL"?
(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 ÷ 6) ? (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 5 ducks and 3 geese, and another half is fed to hens. How many hens does the farmer have? 7. The length of a rectangle is twice its width. If the perimeter is 18 inches, what is the area of the rectangle(in square inches)? 8. Express 64 as a product of prime numbers. Type * for multiplication symbol ×. 9. Write down the first 5 common multiples of 4 and 7. Separate each number with a comma. 11. The sum of the three angles of any triangle must be 180 degrees. In the triangle XYZ, angle X has a measure of 30 degrees. Angle Y is 2 times as large as angle X. What is the measure (in degrees) of angle Z 12. There are 13 pens and 16 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 60 cards and 39 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 600 and 699, 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 9? 16. There are 10 red balls and 14 green balls in a bag. At least how many balls do you need to pick from the bag (without putting balls back) in order to make sure that you have balls of different colors? 17. If a number is divisible by 6 and 7, is the number also divisible by 42? 18. 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 Roman numeral with a value of 99? 19. Jennifer is jogging through a trail at a speed of 2.05 mph. If the trail is 0.82 miles long, how many minutes will it take her to go through the trail? 20. All the numbers are from 6 to 11 and each number is only allowed to be used once. Fill in the blanks with the remaining numbers within the range so that the sums of the three numbers in each side are the same.
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