Tuesday, September 29, 2009

September 29, 2009

A piece of cheese is located at (12, 10) in a coordinate plane. A mouse is at (4,-2) and is running up the line y = -5x + 18. At the point (a, b) the mouse starts getting farther from the cheese rather than closer to it. What is a + b ?

Interactive version of problem and solution.


Friday, September 25, 2009

September 25, 2009

If a is a nonzero integer and b is a positive number such that ab2 = log10 b, what is the median of the set {0, 1, a, b, 1/b} ?




Thursday, September 24, 2009

September 24, 2009

Find the number of ordered pairs of real numbers (a, b) such that (a + bi)2002 = a – bi.

Interactive version of problem and solution.


Wednesday, September 23, 2009

September 23, 2009

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?



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Monday, September 21, 2009

Friday, September 18, 2009

September 18, 2009

A piece of cheese is located at (12, 10) in a coordinate plane. A mouse is at (4,-2) and is running up the line y = -5x + 18. At the point (a, b) the mouse starts getting farther from the cheese rather than closer to it. What is a + b ?

Interactive version of problem and solution.


Thursday, September 17, 2009

September 17, 2009

The set {3; 6; 9; 10} is augmented by a fifth element n, not equal to any of the other four. The median of the resulting set is equal to its mean. What is the sum of all possible values of n ?


Wednesday, September 16, 2009

Tuesday, September 15, 2009

September 15, 2009

A five-legged Martian has a drawer full of socks, each of which is red, white or blue, and there are at least five socks of each color. The Martian pulls out one sock at a time without looking. How many socks must the Martian remove from the drawer to be certain there will be 5 socks of the same color?

Interactive version of problem and solution.


Monday, September 14, 2009

September 14, 2009

Big Al, the ape, ate 100 bananas from May 1 through May 5. Each day he ate six more bananas than on the previous day. How many bananas did Big Al eat on May 5?



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Friday, September 11, 2009

Thursday, September 10, 2009

September 10, 2009

How many three-digit numbers are composed of three distinct digits such that one digit is the average of the other two?

Interactive version of problem and solution.



Wednesday, September 9, 2009

September 9, 2009

Triangles ABC and ADE have areas 2007 and 7002, respectively, with B = (0, 0), C = (223, 0), D = (680, 380), and E = (689, 389). What is the sum of all possible x-coordinates of A?

Interactive version of problem and solution.



Thursday, September 3, 2009

September 3, 2009

A rectangular box P is inscribed in a sphere of radius r. The surface area of P is 384, and the sum of the lengths of its 12 edges is 112. What is r?

Interactive version of problem and solution.


Wednesday, September 2, 2009

September 2, 2009

A wooden cube n units on a side is painted red on all six faces and then cut into n3 unit cubes. Exactly one-fourth of the total number of faces of the unit cubes are red. What is n?



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Tuesday, September 1, 2009

September 1, 2009

On a twenty-question test, each correct answer is worth 5 points, each unanswered question is worth 1 point and each incorrect answer is worth 0 points. Which of the following scores is NOT possible?

(A) 90
(B) 91
(C) 92
(D) 95
(E) 97

Interactive version of problem and solution.


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