Federal Way Math Contest 2009

Team Test

1)

B

a) 27 b) 16 c) 20 d) 25 e) NOTA

2) A college student drove his compact car 120 miles home for the weekend and averaged 30 miles per gallon. On the return trip the student drove his parents’ SUV and averaged only 20 miles per gallon. What was the average gas mileage in miles per gallon for the round trip?

a) 22 b) 24 c) 25 d) 26 e) NOTA

3) Find the sum of the first fifteen terms of this sequence

1, 2, 4, 8, 16 …

a) 32767 b) 33777 c) 32777 d) 32757 e) NOTA

4) A cook makes pudding in a triangular pan having sides of 10 inches by 10 inches by 16 inches and 2 inches deep. If each of her guests will have 8 cubic inches per serving and there are no leftovers, how many guests will she have?

a) 16 b) 24 c) 12 d) 18 e) NOTA

5) The length of Jimmy’s backyard is 15 feet more than three times its width in feet. If the width is increased by 5 feet and the length is increased by 10 feet, the area is increased by 1000 square feet. What is the perimeter of the original lot in square feet?

a) 430 b) 350 c) 310 d) 270 e) NOTA

6) The positive integer 4 can be represented as a sum of 1’s or 2’s in five ways, such as 1+2+1 and 1+1+2. In how many ways can the positive integer 5 be represented as a sum of 1’s or 2’s?

a) 6 b) 7 c) 8 d) 9 e) NOTA

7) What is the value of (a + b – c) Given that a = , b = and c =

a) b) c) d) e) NOTA

8)

a) 30 b) 33 c) 29 d) 27 e) NOTA

9) Larry flips five fair coins. What is the probability that he gets more heads than he does tails?

a) b) c) d) e) NOTA

10) A zoo exhibit contains polar bears and penguins. If one can count fourteen eyes and twenty-four feet, how many penguins are contained in the exhibit?

a) 4 b) 7 c) 2 d) 5 e) NOTA

11) Ten students were surveyed to see which fruit was most popular. The results showed that 5 people liked apples, 3 people liked oranges, 5 people liked cherries, 1 person liked both apples and oranges, 1 person liked both oranges and cherries, 2 liked both apples and cherries, and 1 liked none of them. How many people liked all three fruits?

a) 0 b) 1 c) 2 d) 3 e) NOTA

12) What is the sum of the smallest eleven positive perfect cubes?

a) 4356 b) 4456 c) 4366 d) 4256 e) NOTA

13) A ball is initially dropped from a height of 10 meters. After each bounce, it attains 80% of its previous height. What total vertical distance has the ball traveled after five bounces?

a) 57.132 b) 57.222 c) 57.232 d) 57.322 e) NOTA

14) When two-digit integer MM, with equal digits, is multiplied by the one-digit integer M, the result is the three-digit integer NPM. What is the greatest possible value of NPM?

a) 376 b) 385 c) 386 d) 396 e) NOTA

15) The three angles of a triangle ABC have the properties that the degree measure of is three times the degree measure of , and the sum of the degree measure of and the supplement of the degree measure of is twice the degree measure of . Find the degree measure of the complement of .

a) 60 b) 65 c) 70 d) 75 e) NOTA

16) The letters of the alphabet are given numeric values based on the two conditions below.

- Only the numeric values of –2,-1,0,1,2 are used

-  Starting with A and going through Z, a numeric value is assigned to each letter according to the following pattern:

1, 2, 1, 0, -1, -2, -1, 0, 1, 2, 1, 0, -1, -2, -1, 0, …

Two complete cycles of the pattern are shown above. The letter A has a value of 1, B has a value of 2, F has a value of –2 and Z has a value of 2. What is the sum of the numeric values of the letters in the word “numeric?”

a) -1 b) -2 c) 1 d) 2 e) NOTA

17) What is the arithmetic mean (average) of the following set of numbers?
51, 65, 57, 94, 101, 156, 357, 248, 651, 9980

a) 1776 b) 1178 c) 1176 d) 1276 e) NOTA

18) There are three sisters, Betty, Bertha, and Betsy. One is swimming at Fort Flagler, a second is at Seattle, and the third is in Tacoma. One is playing tennis, one is swimming, and the other is playing golf. Betty is not at Fort Flagler, Betsy is not at Seattle, and the sister who plays golf is not at Tacoma. If Betsy is not the swimmer, who is playing golf and at what city?

a) Betty at Seattle b) Betsy at Fort Flagler c) Bertha at Fort Flagler d) Bertha at Tacoma e) NOTA

19) In a mixture of red and blue marbles, the ratio of red to blue is 2:3. With half as many red and 3 more blue marbles, the ratio of red to blue is 3:10. The number of marbles in the first mixture is…

a) 36 b) 45 c) 32 d) 42 e) NOTA

20) Carla does not know what to wear one day. If she has three shirts, four pants, and ten pairs of different socks, how many different outfits can she have if her socks match?

a) 100 b) 120 c) 160 d) 60 e) NOTA