November 26, 2008

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 ?


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November 25, 2008

Mindy made three purchases for $1.98, $5.04 and $9.89. What was her total, to the nearest dollar?

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November 24, 2008

The year 2002 is a palindrome (a number that reads the same from left to right as it does from right to left). What is the product of the digits of the next year after 2002 that is a palindrome?

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November 21, 2008

How many non-congruent triangles with perimeter 7 have integer side lengths?

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November 20, 2008

Let x and y be two-digit integers such that y is obtained by reversing the digits of x. The integers x and y satisfy x² – y² = m² for some positive integer m. What is x + y + m?

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November 19, 2008

A teacher gave a test to a class in which 10% of the students are juniors and 90% are seniors. The average score on the test was 84. The juniors all received the same score, and the average score of the seniors was 83. What score did each of the juniors receive on the test?

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November 18, 2008

A game is played with tokens according to the following rule. In each round, the player with the most tokens gives one token to each of the other players and also places one token into a discard
pile. The game ends when some player runs out of tokens. Players A, B, and C start with 15, 14, and 13 tokens, respectively. How many rounds will there be in the game?

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November 17, 2008

Granny Smith has $63. Elberta has $2 more than Anjou and Anjou has one-third as much as Granny Smith. How many dollars does Elberta have?

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November 14, 2008

For how many values of a is it true that the line y = x + a passes through the vertex of the parabola y = x² + a²?

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November 13, 2008

Kate rode her bicycle for 30 minutes at a speed of 16 mph, then walked for 90 minutes at a speed of 4 mph. What was her overall average speed in miles per hour?

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November 12, 2008

A parabola with equation y = x² + bx + c passes through the points (2, 3) and (4, 3). What is c?

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November 11, 2008

Which of the following numbers has the smallest prime factor?

a) 55
b) 57
c) 58
d) 59
e) 61

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November 10, 2008

Connie multiplies a number by 2 and gets 60 as an answer. However, she should have divided the number by 2 to get the correct answer. What is the correct answer?

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November 7, 2008

Josh and Mike live 13 miles apart. Yesterday Josh started to ride his bicycle toward Mike's house. A little later Mike started to ride his bicycle toward Josh's house. When they met, Josh had ridden for twice the length of time as Mike and at four-fifths of Mike's rate. How many miles had Mike ridden when they met?

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November 6, 2008

Alicia earns $20 per hour, of which 1.45% is deducted to pay local taxes. How many cents per hour of Alicia's wages are used to pay local taxes?

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November 5, 2008

Twelve fair dice are rolled. What is the probability thatthe product of the numbers on the top faces is prime?

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November 4, 2008

A set of tiles numbered 1 through 100 is modified repeatedly by the following operation: remove all tiles numbered with a perfect square, and renumber the remaining tiles consecutively starting with 1. How many times must the operation be performed to reduce the number of tiles in the set to one?

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November 3, 2008

Jamie counted the number of edges of a cube, Jimmy counted the number of corners, and Judy counted the number of faces. They then added the three numbers. What was the resulting sum?

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