Tuesday, September 30, 2008

September 30, 2008

Each principal of Lincoln High School serves exactly one 3-year term. What is the maximum number of principals this school could have during an 8-year period?

Interactive version of problem and solution.

Monday, September 29, 2008

September 29, 2008

How many whole numbers lie in the interval between 5/3 and 2π ?

Interactive version of problem and solution.

Friday, September 26, 2008

September 26, 2008

What is the difference between the sum of the first 2003 even counting numbers and the sum of the first 2003 odd counting numbers?

Interactive version of problem and solution.

Thursday, September 25, 2008

September 25, 2008

How many pairs of positive integers (a, b) are there such that a and b have no common factors greater than 1 and (a/b) + (14b/9a) is an integer?

Interactive version of problem and solution.

Wednesday, September 24, 2008

September 24, 2008

A pyramid with a square base is cut by a plane that is parallel to its base and is 2 units from the base. The surface area of the smaller pyramid that is cut from the top is half the surface area of the original pyramid. What is the altitude of the original pyramid?

Interactive version of problem and solution.

Tuesday, September 23, 2008

September 23, 2008

Let n denote the smallest positive integer that is divisible by both 4 and 9, and whose base-10 representation consists of only 4's and 9's, with at least one of each. What are the last four digits of n?

Interactive version of problem and solution.

Monday, September 22, 2008

September 22, 2008

Which of these numbers is less than its reciprocal?

(A) –2 (B) –1 (C) 0 (D) 1 (E) 2

Interactive version of problem and solution.

Friday, September 19, 2008

September 19, 2008

Isabella's house has 3 bedrooms. Each bedroom is 12 feet long, 10 feet wide, and 8 feet high. Isabella must paint the walls of all the bedrooms. Doorways and windows, which will not be painted, occupy 60 square feet in each bedroom. How many square feet of walls must be painted?

Interactive version of problem and solution.

Thursday, September 18, 2008

September 18, 2008

Sarah pours four ounces of coffee into an eight-ounce cup and four ounces of cream into a second cup of the same size. She then transfers half the coffee from the first cup to the second and, after stirring thoroughly, transfers half the liquid in the second cup back to the first. What fraction of the liquid in the first cup is now cream?

Interactive version of problem and solution.

Wednesday, September 17, 2008

September 17, 2008

Suppose A, B, and C are three numbers for which 1001C – 2002A = 4004 and 1001B +3003A = 5005. The average of the three numbers A, B, and C is...?

Interactive version of problem and solution.

Tuesday, September 16, 2008

September 16, 2008

For how many positive integers m does there exist at least one positive integer n such that m·nm+n?

Interactive version of problem and solution.

Monday, September 15, 2008

September 15, 2008

Aunt Anna is 42 years old. Caitlin is 5 years younger than Brianna, and Brianna is half as old as Aunt Anna. How old is Caitlin?

Interactive version of problem and solution.

Friday, September 12, 2008

September 12, 2008

Cindy was asked by her teacher to subtract 3 from a certain number and then divide the result by 9. Instead, she subtracted 9 and then divided the result by 3, giving an answer of 43. What would her answer have been had she worked the problem correctly?

Interactive version of problem and solution.

Thursday, September 11, 2008

September 11, 2008

Exercise your mind daily with a problem from the AMC-8, AMC-10, or AMC-12.

While eating out, Mike and Joe each tipped their server $2. Mike tipped 10% of his bill and Joe tipped 20% of his bill. What was the difference, in dollars, between their bills?

Interactive version of problem and solution.