20. Two box-like building face each other and are 240 feet apart. A flagpole stands between the buildings. An observer standing on the top of the first building near the front has his eyes 180 feet from the ground. The observer sees the top of the flagpole in line with the base of the second building. Similarly, an observer on top of the second building has his eyes 270 feet above the ground and sees the top of the flagpole in line with the base of the first building. What is the height of the flagpole in feet?
(A) 96
(B) 108
(C) 120
(D) 124
(E) Insufficient information has been given.


PAGE 10 OF 12 - PART I HONORS MATH CONTEST 2008
21. Two buildings are 60 feet apart. A bird is perched 48 feet up on one building. The bird flies to the ground between the buildings, and then flies to a nest 32 feet up on the second building. What is the shortest distance in feet that the bird could have flown?
(A) 72
(B) 80
(C) 100
(D) 108
(E) 140


22. Consider a frustum of a right circular cone. Let the radius of the upper base be a, the radius of the lower base be b, and the distance between the bases be h. What is the volume of the frustum?
(A) π(a²+b²)h/2
(B) π(a²+b²)h/3
(C) π(a²+b²)h/6
(D) (a²+b²)h/2
(E) π(a²+ab+b²)h/3

PAGE 11 OF 12 - PART I HONORS MATH CONTEST 2008
23. Fix a triangle with base 100 meters and two sides equal to 150 meters. Consider all the inscribed rectangles with their bases on the base of the triangle. What is the maximum area in square meters of these rectangles?
(A) 7500
(B) 3750
(C) 2500√2
(D) 3000
(E) 2000


24. There are 12 books standing on a shelf. How many ways are there to choose five of them so that no two of the chosen books stand next to each other on the shelf?
(A) 24
(B) 35
(C) 56
(D) 70
(E) 120

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