June 30, 2009

Sally has five red cards numbered 1 through 5 and four blue cards numbered 3 through 6. She stacks the cards so that the colors alternate and so that the number on each red card divides evenly into the number on each neighboring blue card. What is the sum of the numbers on the middle three cards?

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June 29, 2009

Ms. Hamilton's eighth-grade class wants to participate in the annual three-person-team basketball tournament. After Sally takes 20 shots, she has made 55% of her shots. After she takes 5 more shots, she raises her percentage to 56%. How many of the last 5 shots did she make?

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June 26, 2009

Gage skated 1 hr 15 min each day for 5 days and 1 hr 30 min each day for 3 days. How long would he have to skate the ninth day in order to average 85 minutes of skating each day for the entire time?

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June 25, 2009

Circles of radius 2 and 3 are externally tangent and are circumscribed by a third circle, as shown in the figure. Find the area of the shaded region.

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June 24, 2009

Harold tosses a nickel four times. The probability that he gets at least as many heads as tails is what?

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June 23, 2009

How many whole numbers between 99 and 999 contain exactly one 0?

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June 22, 2009

Ali, Bonnie, Carlo and Dianna are going to drive together to a nearby theme park. The car they are using has four seats: one driver's seat, one front passenger seat and two back seats. Bonnie and Carlo are the only two who can drive the car. How many possible seating arrangements are there?

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June 19, 2009

Last year Mr. John Q. Public received an inheritance. He paid 20% in federal taxes on the inheritance, and paid 10% of what he had left in state taxes. He paid a total of $10,500 for both taxes. How many dollars was the inheritance?

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June 18, 2009

Suppose that 4^a = 5, 5^b = 6, 6^c = 7, and 7^d = 8. What is a x b x c x d?

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June 17, 2009

Team A and team B play a series. The first team to win three games wins the series. Each team is equally likely to win each game, there are no ties, and the outcomes of the individual games are independent. If team B wins the second game and team A wins the series, what is the probability that team B wins the first game?

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June 16, 2009

Antonette gets 70% on a 10-problem test, 80% on a 20-problem test and 90% on a 30-problem test. If the three tests are combined into one 60-problem test, which percent is closest to her overall score?

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June 15, 2009

For his birthday, Bert gets a box that holds 125 jellybeans when filled to capacity. A few weeks later, Carrie gets a larger box full of jellybeans. Her box is twice as high, twice as wide and twice as long as Bert's. Approximately, how many jellybeans did Carrie get?

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June 12, 2009

How many positive integers n satisfy the following condition:

(130n)⁵⁰ > n¹⁰⁰ > 2²⁰⁰ ?

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June 11, 2009

Suppose a, b, and c are positive integers with a + b + c = 2006, and a!b!c! = m x 10ⁿ, where m and n are integers and m is not divisible by 10. What is the smallest possible value of n ?

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June 10, 2009

How many non-similar triangles have angles whose degree measures are distinct positive integers in arithmetic progression?

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June 9, 2009

Homer began peeling a pile of 44 potatoes at the rate of 3 potatoes per minute. Four minutes later Christen joined him and peeled at the rate of 5 potatoes per minute. When they finished, how many potatoes had Christen peeled?

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June 8, 2009

Keiko tosses one penny and Ephraim tosses two pennies. The probability that Ephraim gets the same number of heads that Keiko gets is what?

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June 5, 2009

Oscar buys 13 pencils and 3 erasers for $1.00. A pencil costs more than an eraser, and both items cost a whole number of cents. What is the total cost, in cents, of one pencil and one eraser?

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June 3, 2009

Six trees are equally spaced along one side of a straight road. The distance from the first tree to the fourth is 60 feet. What is the distance in feet between the first and last trees?

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June 2, 2009

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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June 1, 2009

Ms. Hamilton's eighth-grade class wants to participate in the annual three-person-team basketball tournament. The losing team of each game is eliminated from the tournament. If sixteen teams compete, how many games will be played to determine the winner?

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Buy Martin Gardner's Mathematical Games