State_2015_CDR.ppt - 2015 State Competition Countdown Round Please note that videotaping photographing reproducing or publishing the following questions

State_2015_CDR.ppt - 2015 State Competition Countdown Round...

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2015 State Competition Countdown Round
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Please note that videotaping, photographing, reproducing or publishing the following questions or answers is strictly prohibited. A sample question follows that you are allowed to reproduce.
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A 3-ounce can of tomato sauce costs $1.68. In cents, what is the price per ounce? Sample Question
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Answer: 56 (cents) Sample Question
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2015 State Competition Countdown Round
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1. The number is what percent of ? 4 5 5 6
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Answer: 96 (percent)
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2. If a > b > 1 and a m b n = ( a −2 b 5 )( a 6 b −2 ), what is the value of the product mn ?
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Answer: 12
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3. The average of a , b and c is 60, and the average of a and b is 90. What is the value of c ?
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Answer: 0
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4. Two equilateral triangles of side length 6 cm share a side as shown. In centimeters, what is the radius of the smallest circle that encloses both triangles? Express your answer in simplest radical form.
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Answer: 3 (cm) 3
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5. In the seven-pointed star shown here, what is the mean degree measure of the seven vertex angles? Express your answer as a common fraction.
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Answer: (degrees) 180 7
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6. Mary and Fred purchased sandwiches for a luncheon. Mary spent $29.95 on 3 medium sandwiches and 2 large sandwiches. Fred spent $28.45 on 4 medium sandwiches and 1 large sandwich. What would it cost to buy 1 medium sandwich and 1 large sandwich?
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Answer: ($) 12.28
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7. A ball thrown upward from a height of 4 feet with an initial velocity of v feet per second will be vt – 16 t 2 + 4 feet above the ground after t seconds. What is the minimum value of v for which the ball reaches a height of at least 20 feet?
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Answer: 32 (ft/s)
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8. If the sum of the first 42 positive odd numbers is reduced by 1, what is the sum of the prime factors of the result?
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