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Andy’s lawn has twice as much area as Beth’s lawn and three times as much as Carlos’ lawn.Carlos’ lawn mower cuts half as fast as Beth’s mower and one third as fast as Andy’s mower. If they all start to mow their lawns at the same time, who will finish first?
(A) Andy (B) Beth (C) Carlos (D) Andy and Carlos tie for first
(E) All three tie
ANSWER: B
Four distinct circles are drawn in a plane. What is the maximum number of points where at least two of the circles intersect?
(A) 8 (B) 9 (C) 10 (D) 12 (E) 16
ANSWER: D
The positive integers A,B,A-B,and A+B are all prime numbers. The sum of these four primes is
(A) even (B) divisible by 3 (C) divisible by 5 (D) divisible by 7 (E) prime
ANSWER: E
The product of three consecutive positive integers is 8 times their sum. What is the sum of the squares?
(A) 50 (B) 77 (C) 110 (D) 149 (E) 194
ANSWER: B
Using the letters A,M,O,S,and U, we can form five-letter “words”. If these “words” are arranged in alphabetical order, then the “word” USAMO occupies position
(A) 112 (B) 113 (C) 114 (D) 115 (E) 116
ANSWER: D
Suppose July of year N has five Mondays. Which of the following must occur five times in the August of year N? (Note: Both months have 31 days)
(A) Monday (B) Tuesday (C) Wednesday (D) Thursday (E) Friday
ANSWER: D
The arithmetic mean of the nine numbers in the set {9,99,999,9999,…,999999999} is a 9-digit number M, all of whose digits are distinct. The number M does not contain the digit
(A) 0 (B) 2 (C) 4 (D) 6 (E) 8
ANSWER: A
Tina randomly selects two distinct numbers from the set {1,2,3,4,5}, and Sergio randomly selects a number from the set {1,2,…,10}. What is the probability that Sergio’s number is larger than the sum of the two numbers chosen by Tina ?
(A) 2/5 (B) 9/20 (C) 1/2 (D) 11/20 (E) 24/25
ANSWER: A
Points A,B,C, and D lie on a line, in that order, with AB=CD and BC=12. Point E is not on the line, and BE=CE=10. The perimeter of triangle AED is twice the perimeter of triangle BEC. Find AB.
(A) 15/2 (B) 8 (C) 17/2 (D) 9 (E) 19/2
ANSWER: D
A set of tiles numbered 1 through 100 is modified repeatedly by the following operation: remove all tiles numbered with a perfect square, and renumbered the remaining tiles consecutively starting with 1. How many times must the operation be performed to reduce the number of tiles in the set to one ?
(A) 10 (B) 11 (C) 18 (D) 19 (E) 20
ANSWER:C