Algebra
3/5=M/45=60/N, what is M + N?
What is 127?
How many square yards of carpet are required to cover a rectangular floor that is 12 feet long and 9 feet wide?
What is 12?
Each edge of a cube is colored either red or black. Every face of the cube has at least one black edge. The smallest number possible of black edges is?
What is 3?
The eighth grade class at Lincoln Middle School has 93 students. Each student takes a math class or a foreign language class or both. There are 70 eighth graders taking a math class, and there are 54 eighth graders taking a foreign language class. How many eighth graders take only a math class and not a foreign language class?
What is 39?
What is the probability that any two randomly chosen chords on a circle intersect?
What is 1/3?
If a, b and c are positive integers, how many integers are strictly between the product abc and (a+1) (b+1)(c+1)? For example, there are 35 integers strictly between 24 = 2 * 3 * 4 and 60 = 3 * 4 * 5. Give your answer in terms of a, b, and c.
What is ab+ac+bc+a+b+c?
Which of the following triangles cannot exist?
(A) An acute isosceles triangle
(B) An isosceles right triangle
(C) An obtuse right triangle
(D) A scalene right triangle
(E) A scalene obtuse triangle
What is (C) an obtuse right triangle?
How many whole numbers between 100 and 400 contain the digit 2?
What is 138?
After Euclid High School's last basketball game, it was determined that 1/4 of the team's points were scored by Alexa and 2/7 were scored by Brittany. Chelsea scored 15 points. None of the other 7 team members scored more than 2 points. What was the total number of points scored by the other 7 team members?
What is 11?
100 ants are placed in random directions of a one dimensional log that is one meter long. At t=0, every ant begins running at speed 1 meter/minute in the direction they are facing. Every time two ants collide, they instantly change directions and begin running in opposite directions. What is the longest possible time it can take for the ants to all walk off the log? Assume ants are point-like objects.
What is one minute?
A store increased the original price of a shirt by a certain percent and then lowered the new price by the same amount. Given that the resulting price was 84% of the original price, by what percent was the price increased and decreased?
What is 40?
Liquid & does not mix with water. Unless obstructed, it spreads out on the surface of water to form a circular film 0.1cm thick. A rectangular box measuring 6cm by 3cm by 12cm is filled with liquid X. Its contents are poured onto a large body of water. What will be the radius, in centimeters, of the resulting circular film?
What is sqrt(2160/pi).
The 120 permutations of AHSME are arranged in dictionary order as if each were an ordinary five-letter word. The last letter of the 86th word in this list is?
What is E?
A palindrome is a number that has the same value when read from left to right or from right to left. (For example 12321 is a palindrome.) Let N be the least three-digit integer which is not a palindrome but which is the sum of three distinct two-digit palindromes. What is the sum of the digits of N?
What is 2?
One side of the bottom layer of a triangular pyramid has 11 balls. How many are there in the whole pyramid? Note that the pyramid is equilateral and solid.
What is 286?
If S is the set of points & in the complex plane such that (3 + 4i) z is a real number, then S is a:
(A) right triangle
(B) circle
(C) hyperbola
(D) line
(E) parabola
What is a line?
The large circle has diameter AC. The two small circles have their centers on AC and just touch at O, the center of the large circle. If each small circle has radius 1, what is the value of the ratio of the area of the shaded region to the area of one of the small circles?
(I will draw what the shaded region is)
What is 1
How many line segments have both their endpoints located at the vertices of a given cube?
What is 28?
What is the tens digit in the sum 7! + 8! + 9! + ... + 2006!
What is 4?
An explorer walks one mile due south, turns and walks one mile due east, turns again and walks one mile due north. He finds himself back where he started. He shoots a bear. What color is the bear?
What is white?
Find x^2 + y^2 if x and y are positive integers such that
xy + x + y = 71,
х^2*y + x*y^2 = 880.
What is 146?
A cylindrical hole six inches long has been drilled straight through the center of a solid sphere. What is the volume remaining in the sphere?
What is 36pi?
Find the number of positive integers with three not necessarily distinct digits, abc, with a != 0 and c != 0 such that both abc and cba are multiples of 4.
What is 40?
Two farmers agree that pigs are worth 300 dollars and that goats are worth 210 dollars. When one farmer owes the other money, he pays the debt in pigs or goats, with "change" received in the form of goats or pigs as necessary. (For example, a 390 dollar debt could be paid with two pigs, with one goat received in change.) What is the amount of the smallest positive debt that can be resolved in this way?
What is 30?
What is (((((2!)!)!)!)+e^(ipi)-1)!)^2?
What is 1?