Algebra
How many feet long is the shadow of a 20-foot flagpole if a 6-foot woman standing at the base of the flagpole has a shadow that is nine feet long?
What is 30
Bekah has four brass house number digits: 2, 3, 5 and 7, and only has one of each number. How many distinct numbers can she form using one or more of the digits?
What is 64
In rectangle ABMC, AB= 5 and BM= 8. If point X is the midpoint of side AC, what is the area of triangle XCM?
What is 10
How many positive factors of 96 are also multiples of 12?
What is 4
Suppose that we roll two fair 6-sided dice. What is the probability that the two numbers rolled sum to 4?
What is 1/12?
Jan is as old now as Gary was 15 years ago. Six years from now, Gary will be twice as old as Jan will be then. How old is Gary now?
What is 24
At Beaumont High School, there are 20 players on the basketball team. All 20 players are taking at least one of biology or chemistry. (Biology and chemistry are two different science courses at the school.) If there are 8 players taking biology and 4 players are taking both sciences, how many players are taking chemistry?
What is 16
A rectangular garden 50 feet long and 10 feet wide is enclosed by a fence. To make the garden larger, while using the same fence, its shape is changed to a square. By how many square feet does this enlarge the garden?
What is 400
How many distinct prime factors does the sum of the positive divisors of 400 have?
What is 1
Krishanu and Shaunak each pick an integer at random between 1 and 10, inclusive. What is the probability that the product of their numbers is more than 10? Express your answer as a common fraction.
73/100
Round tables seating 8 people and rectangular tables seating 12 people are being used at a banquet for 8th graders. The ratio of round tables to rectangular tables is 2 to 1. How many tables are used to seat 336 students at the banquet, if no table has an empty seat?
What is 36
Find the number of times the digit 9 appears in the list of all integers from 1 to 500. (The number 99, for example, is counted twice, because 9 appears two times in it.)
What is 100
A right cylindrical tank with circular bases is being filled with water at a rate of 20pi cubic meters per hour. As the tank is filled, the water level rises four meters per hour. What is the radius of the tank, in meters? Express your answer in simplest radical form.
What is sqrt(5)
A palindrome is a number that is the same when read forwards and backwards, such as 43234. What is the smallest five-digit palindrome that is divisible by 11?
10901
One fair die has faces 1, 1, 2, 2, 3, 3, and another has faces 4, 4, 5, 5, 6, 6. The dice are rolled and the numbers on the top faces are added. What is the probability that the sum will be odd?
What is 5/9?