Math Olympiad 4

Math Olympiad 4( Week 15 Quiz 3)

1. 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 "LXXXV"?
(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).

2. 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 decimal value of the following Roman numeral equation: LXXVIII - LVI =?
(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. For example, XIV = 10 + 5 − 1).

3. The length of a rectangle is 4 times its width. If the perimeter is 40 inches, what is the area of the rectangle(in square inches)?

4. 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 2 times as large as angle X. What is the measure (in degrees) of angle Z

5. A teacher brings 88 cards and 64 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?

6. Jane has 12 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?

7. 9 gal 1 qt + 7 gal 3 qt = gal qt.

8. 4 × (8 gal 2 qt) = gal qt.

9. There are ounces, pounds and tons used in the U.S. customary weight system.

1 pound (lb.) = 16 ounces (oz.)

1 ton (t.) = 2000 pounds

How many ounces are in 12 pounds?

10. Susan and Ed has a total of $84 together, and what Susan has is twice as what Ed has. How much money do they have respectively?(Separate the answers by a comma.)

11. American customary system weight unit conversion.

2 pounds = ounces

1 ton = pounds

12000 pounds = tons

1 pound = 16 ounces

1 ton = 2000 pounds

12. Time unit conversion.

4 quarters = months

2 years = quarters

3 decades = years

3 centuries = decades

4 millenniums = centuries

36000 months = millenniums

1 quarter = 3 months

1 year = 4 quarters

1 decade = 10 years

1 century = 10 decades

1 millennium = 10 centuries

13. Michael and his brother made some money by working during the summer. Michael earned $30 less than 4 times of what his brother earned. If the total amount they made was $170, how much money did Michael earn (in dollars)?

14. There are 18 balls of 6 colors with 3 balls per each color in a bag. At least how many balls need to be picked to make sure that there are three balls of the same color?

15. Ben weighs 4 times as much as Josh, and their total weight is 170 pounds. How much does Ben weigh (in pounds)?

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