How many positive integers not exceeding 2001 are multiples of 3 or 4 but not 5?
(A) 768 (B) 801 (C) 934 (D) 1067 (E) 1167
ANSWER: B
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Problem 39
A box contains exactly five chips, three red and two white. Chips are randomly removed one at a time without replacement until all the red chips are drawn or all the white chips are drawn. What is the probability that the last chip drawn is white?
(A) 3/10 (B) 2/5 (C) 1/2 (D) 3/5 (E) 7/10
ANSWER: D
Problem 38
A right circular cylinder with its diameter equal to its height is inscribed in a right circular cone. The cone has diameter 10 and altitude 12, and the axes of the cylinder and cone coincide. Find the radius of the cylinder.
(A) 8/3 (B) 30/11 (C) 3 (D) 25/8 (E) 7/2
ANSWER: B
Problem 37
Pat wants to buy four donuts from an ample supply of three types of donuts: glazed, chocolate, and powdered. How many different selections are possible?
(A) 6 (B) 9 (C) 12 (D) 15 (E) 18
ANSWER: D
Problem 36
The mean of three numbers is 10 more than the least of the numbers and 15 less than the greatest. The median of the three number is 5. What is their sum ?
(A) 5 (B) 20 (C) 25 (D) 30 (E) 36
ANSWER: D
Problem 35
A street has parallel curbs 40 feet apart. A crosswalk bounded by two parallel stripes crosses the street at an angle. The length of the curb between the stripes is 15 feet and each stripe is 50 feet long. Find the distance, in feet, between the stripes ?
(A) 9 (B) 10 (C) 12 (D) 15 (E) 25
ANSWER: C
Problem 34
A charity sells 140 benefit tickets for a total of $2001. Some tickets sell for full price (a whole dollar amount), and the rest sells for half price. How much money is raised by the full-price tickets ?
(A) $782 (B) $986 (C) $1158 (D) $1219 (E) $1449
ANSWER: A
Problem 33
Suppose that n is the product of three consecutive integers and that n is divisible by 7. Which of the following is not necessarily a divisor of n ?
(A) 6 (B) 14 (C) 21 (D) 28 (E) 42
ANSWER: D
Problem 32
If x,y,and z are positive with xy=24,xz=48,and yz=72, then x+y+z is
(A) 18 (B) 19 (C) 20 (D) 22 (E) 24
ANSWER: D
Problem 31
Wanda, Darren, Bratrice, and Chi are tutors in the school math club. Their schedule is as follows: Darren works every third school day, Wanda works every fourth school day, Beatrice works every sixth school day, and Chi works every seventh school day. Today they are all working in the math club. In how many school days from today will they next be together tutoring in the lab ?
(A) 42 (B) 84 (C) 126 (D) 178 (E) 252
ANSWER: B