Arithmetic & Algebra
What is the value of (20-1+52+0)-1 x 5?
A) -125 B) -120 C) 1/5 D) 5/24 E) 25
C) 1/5
A circle of radius 5 is inscribed in a rectangle as drawn on the board. The ratio of the length of the rectangle to its width is 2:1. What is the area of the rectangle?
A) 50 B) 100 C) 125 D) 150 E) 200
E) 200
In a Science Olympiad team, there are three officer positions to be filled: president, vice president, and treasurer. If Abigail, Bacon, Chris, Dan, and Elisa are interested in running for a position, how many different "sets" of officer members are possible? (A set includes a president, vice president, and treasurer.)
A) 5 B) 15 C) 30 D) 60 E) 120
D) 60
How many integer values of x satisfy |x|<3π? (π ≈ 3.14)
A) 9 B) 10 C) 18 D) 19 E) 20
D) 19
Each third-grade classroom at Pearl Creek Elementary has 18 students and 2 pet rabbits. How many more students than rabbits are there in all 4 of the third-grade classrooms?
A) 48 B) 45 C) 64 D) 72 E) 80
C) 64
Tony works 2 hours a day is paid $0.50 per hour for each full year of his age. During a six month period Tony worked 50 days and earned $630. How old was Tony at the end of the six month period?
A) 9 B) 11 C) 12 D) 13 E) 14
D) 13
The ratio of the length of the width of a rectangle is 4:3. If the rectangle has diagonal of length d, then the area may be expressed as kd2 for some constant k. What is k?
A) 2/7 B) 3/7 C) 12/25 C) 16/25 E) 3/4
C) 12/25
Two different numbers are selected at random from {1, 2, 3, 4, 5} and multiplied together. What is the probability that the product is even?
A) 0.2 B) 0.4 C) 0.5 D) 0.7 E) 0.8
D) 0.7
The least common multiple of a positive integer n and 18 is 180, and the greatest common divisor of n and 45 is 15. What is the sum of the digits of n?
A) 3 B) 6 C) 8 D) 9 E) 12
B) 6
Amelia needs to estimate the quantity a/b - c, where a, b, and c are large positive integers. She rounds each of the integers so that the calculation will be easier to do mentally. In which of these situations will her answer necessarily be greater than the exact value of a/b - c?
A) She rounds all three numbers up.
B) She rounds a and b up, and she rounds c down.
C) She rounds a and c up, and she rounds b down.
D) She rounds a up, and she rounds b and c down.
E) She rounds c up, and she rounds a and b down.
D) She rounds a up, and she rounds b and c down.
What is the value of (22014+22012)/(22014-22012)?
A) -1 B) 1 C) 5/3 D) 2013 E) 24024
C) 5/3
Convex quadrilateral ABCD has AB = 3, BC = 4, CD = 13, AD = 12, and ∠ABC = 90°, as shown. What is the area of the quadrilateral? (draw on board)
A) 30 B) 36 C) 40 D) 48 E) 58.5
B) 36
At a gathering of 30 people, there are 20 people who all know each other and 10 people who know no one. People who know each other hug, and people who do not know each other shake hands. How many handshakes occur?
A) 240 B) 245 C) 290 D) 480 E) 490
B) 245
Which of the following numbers is a perfect square?
A) (14!x15!)/2 B) (15!x16!)/2 C) (16!x17!)/2 D) (17!x18!)/2 E) (18!x19!)/2
D) (17!x18!)/2
A unit of blood expires after 10! = 10x9x8x...x1 seconds. Yasin donates a unit of blood at noon on January 1. On what day does his unit of blood expire?
A) January 2 B) January 12 C) January 22 D) February 11 E) February 12
E) February 12
Integers x and y with x>y>0 satisfy x+y+xy=80. What is x?
A) 8 B) 10 C) 15 D) 18 E) 26
Points A and B lie on a circle centered at O, and ∠AOB = 60°. A second circle is internally tangent to the first and tangent to both line segments OA and OB. What is the ratio of the area of the smaller circle to that of the larger circle?
A) 1/16 B) 1/9 C) 1/8 D) 1/6 E) 1/4
B) 1/9
Larry and Julius are playing a game, taking turns throwing a ball at a bottle sitting on a ledge. Larry throws first. The winner is the first person to knock the bottle off the ledge. At each turn the probability that a player knocks the bottle off the ledge is 1/2, independently of what has happened before. What is the probability that Larry wins the game?
A) 1/2 B) 3/5 C) 2/3 D) 3/4 E) 4/5
C) 2/3
In the equation below, A and B are consecutive positive integers, and A, B, and A+B represent number bases: 132A + 43B = 69A+B.
What is A+B?
A) 9 B) 11 C) 13 D) 15 E) 17
C) 13
A) 71 B) 76 C) 80 D) 82 E) 91
C) 80
Define a sequence recursively by F0 = 0, F1 = 1, and Fn = the remainder when Fn-1 + Fn-2 is divided by 3 for all n≥2. Thus the sequence starts 0, 1, 1, 2, 0, 2, .... What is F2017 + F2018 + F2019 + F2020 + F2021 + F2022 + F2023 + F2024?
A) 6 B) 7 C) 8 D) 9 E) 10
C) 8
The five small shaded squares inside this unit square are congruent and have disjointed interiors. The midpoint of each side of the middle square coincides with one of the vertices of the other four small squares as shown. The common side length is (a-√2)/b, where a and b are positive integers. What is a+b?
A) 7 B) 8 C) 9 D) 10 E) 11
E) 11
Let N be a positive multiple of 5. One red ball and N green balls are arranged in a line in random order. Let P(N) be the probability that at least 3/5 of the green balls are on the same side of the red ball. Observe that P(5) = 1 and that P(N) approaches 4/5 as N grows large. What is the sum of the digits of the least value of N such that P(n) < 321/400?
A) 12 B) 14 C) 16 D) 18 E) 20
A) 12
A five-digit palindrome is a positive integer with respective digits abcba, where a is not zero. Let S be the sum of all five-digit palindromes. What is the sum of the digits of S?
A) 9 B) 18 C) 27 D) 36 E) 45
B) 18
In the eight-term sequence A, B, C, D, E, F, G, H, the value of C is 5 and the sum of any three consecutive terms is 30. What is A+H?
A) 17 B) 18 C) 25 D) 26 E) 43
C) 25