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Logic
Geometry
Word Problems
Equations
Probability/ Miscellaneous
100
The ratio (10^2000+10^2002)/(10^2001+10^2001) is closest to which of the following numbers? a. .2 b. .2 c. 1 d. 5 e. 10
What is d, 5?
100
A 45 degree arc of circle A is equal in length to a 30 degree arc of circle B. What is the ratio of circle A's area and circle B's area? a. 4/9 b. 2/3 c. 5/6 d. 3/2 e. 9/4
What is a, 4/9?
100
From a starting number, Cindy was supposed to subtract 3, and then divide by 9, but instead, Cindy subtracted 9, then divided by 3, getting 43. If the correct instructions were followed, what would the result be? a. 15 b. 34 c. 43 d. 51 e. 138
What is a, 15?
100
What is the value of (3x-2)(4x+1)-(3x-2)4x+1 when x=4? a. 0 b. 1 c. 10 d. 11 e. 12
What is d, 11?
100
For how many positive integers n is n^2-3n+2 a prime number? a. none b. one c. two d. more than two but finitely many e. infinitely many
What is b, one?
200
Given that a, b, and c are non-zero real numbers, define (a, b, c) = (a/b)+(b/c)+(c/a). Find (2, 12, 9). a. 4 b. 5 c. 6 d. 7 e. 8
What is c, 6?
200
Given a triangle with side lengths 15, 20, and 25, find the triangle's smallest height. a. 6 b. 12 c. 12.5 d. 13 e. 15
What is b, 12?
200
Jamal wants to save 30 files onto disks, each with 1.44 MB space. 3 of the files take up 0.8 MB each, 12 of the files take up 0.7 MB each, and the rest take up 0.4 MB each. It is not possible to split a file onto 2 different disks. What is the smallest number of disks needed to store all 30 files? a. 12 b. 13 c. 14 d. 15 e. 16
What is b, 13?
200
There are 3 numbers A, B, and C, such that 1001C - 2002A = 4004, and 1001B + 3003A = 5005. What is the average of A, B, and C? a. 1 b. 3 c. 6 d. 9 e. not uniquely determined
What is b, 3?
200
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
What is d, 115?
300
According to the standard convention for exponentiation, 2^2^2^2=2(^2(^2^2))=2^16=65,536. If the order in which the exponentiations are performed is changed, how many other values are possible? a. 0 b. 1 c. 2 d. 3 e. 4
What is b, 1?
300
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
What is d, 12?
300
Mr. Earl E. Bird leaves home every day at 8:00 AM to go to work. If he drives at an average speed of 40 miles per hour, he will be late by 3 minutes. If he drives at an average speed of 60 miles per hour, he will be early by 3 minutes. How many miles per hour does Mr. Bird need to drive to get to work exactly on time? a. 45 b. 48 c. 50 d. 55 e. 58
What is b, 48?
300
What is the sum of all of the roots of (2x + 3) (x - 4) + (2x + 3) (x - 6) = 0? a. 7/2 b. 4 c. 5 d. 7 e. 13
What is a, 7/2?
300
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
What is b, 77?
400
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 d. 8
What is a, 0?
400
Spot's doghouse has a regular hexagonal base that measures one yard on each side. He is tethered to a vertex with a two-yard rope. What is the area, in square yards, of the region outside of the doghouse that Spot can reach? a. 2pi/3 b. 2pi c. 5pi/2 d. 8pi/3 e. 3pi
What is e, 3pi?
400
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
Who is b, Beth?
400
Suppose that a and b are nonzero real numbers, and that the equation x^2+ax+b=0 has solutions a and b. Then the pair (a,b) is a. (-2, 1) b. (-1, 2) c. (1, -2) d. (2, -1) e. (4, 4)
What is c, (1, -2)?
400
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 three c. divisible by five d. divisible by seven e. prime
What is e, prime?
500
For how many positive integers m is there at least 1 positive integer n such that mn is less than or equal to m + n? a. 4 b. 6 c. 9 d. 12 e. infinitely many
What is e, infinitely many?
500
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
What is d, 9?
500
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
What is d, 10?
500
Let a + 1 = b + 2 = c + 3 = d + 4 = a + b + c + d + 5. What is a + b + c + d? a. -5 b. -10/3 c. -7/3 d. 5/3 e. 5
What is b, -10/3?
500
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
What is a, 2/5?