When 15 is appended to a list of integers, the mean is increased by 2. When 1 is appended to the enlarged list, the mean of the enlarged list is decreased by 1. How many integers were in the original list?
(A) 4 (B) 5 (C) 6 (D) 7 (E) 8
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Problem 62
Riders on a Ferris Wheel travel in a circle in a vertical plane. A particular wheel has radius 20 feet and revolves at the constant rate of one revolution per minute. How many seconds does it take a rider to travel from the bottom of the wheel to a point 10 vertical feet above the bottom?
(A) 5 (B) 6 (C) 7.5 (D) 10 (E) 15
ANSWER: D
Problem 61
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
Problem 60
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
Problem 59
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
Problem 58
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
Problem 57
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
Problem 56
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
Problem 55
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
Problem 54
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