State_2014_CDR.ppt - 2014 State Competition Countdown Round Please note that videotaping photographing reproducing or publishing the following questions

State_2014_CDR.ppt - 2014 State Competition Countdown Round...

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2014 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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2014 State Competition Countdown Round
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1. What is the least possible denominator of a common fraction that lies strictly between and ? 1 3 1 2
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Answer: 5
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2. In a list of 30 integers, 18 of the integers are multiples of 5. If 10 of the multiples of 5 are odd integers, then what is the maximum number of even integers in the list?
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Answer: 20 (even integers)
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3. What is the largest possible area, in square units, of a triangle with perimeter 6 units? Express your answer in simplest radical form.
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Answer: (units 2 ) 3
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4. A library system with 6 branches employs 60 workers. If no branch has fewer than 7 workers and no more than 11 workers, what is the minimum number of total workers in any two of the branches?
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Answer: 16 (workers)
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5. At a school, grade point averages are calculated by making an A worth 4 points, a B worth 3, etc., and all courses are equally weighted. After 20 courses, Zach has a grade point average of exactly 3.9. If he can get As in all of his future classes, how many more classes must Zach take to raise his average to exactly 3.95?
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Answer: 20 (classes)
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6. A rectangle of area 9 ft 2 is made by placing square A next to half of square B, as shown. In feet, what is the side length of square A? Express your answer in simplest radical form. B A
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Answer: (feet) 3
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7. If b = , where a ≠ 0 and b ≠ 1, then = ka . What is the value of k ? 3 a 3 1 a b
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Answer: −1
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8. How many positive integers divide 6 2014 but not 6 2013 ?
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