MATHCOUNTS  2002 Chapter Competition Countdown Round

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Transcript of MATHCOUNTS  2002 Chapter Competition Countdown Round

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  • MATHCOUNTS 2002 Chapter Competition Countdown Round
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  • 1.What is the sum of the number of faces, vertices and edges in a triangular prism?
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  • Answer: 20
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  • 2.One-third of a 30-student class is absent today. One-half of those were also absent yesterday. What percent of the class has been absent for two straight days? Express your answer to the nearest whole number.
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  • Answer: 17 (percent)
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  • 3.Compute:
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  • Answer: 680
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  • 4.Two of Mr. Bernards classes took the same test. His class of 20 students had an average score of 80. His other class of 30 students had an average of 70. What was the average score for all 50 students?
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  • Answer: 74
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  • 5.The radius of a circle is increased by 100%. By what percent is the area of the circle increased?
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  • Answer: 300 (percent)
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  • 6.Compute:
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  • Answer: 1
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  • 7.What is the least common multiple of 12, 18 and 30?
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  • Answer: 180
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  • 8.In any given year, the dates (represented as month/day) 4/4, 6/6, 8/8, 10/10 and 12/12 all fall on the same day of the week. June 3, 2020 is a Wednesday. What day of the week is December 15, 2020?
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  • Answer: Tuesday
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  • 9.Taylor wants to buy cases to hold her 86 compact discs. Each case holds 9 discs. How many cases does she need to buy?
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  • Answer: 10 (cases)
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  • 10.A board whose length is 84 inches is cut into three pieces in the ratio 1:2:3. What is the number of inches in the length of the shortest piece?
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  • Answer: 14 (inches)
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  • 11.How many integers can be represented as a difference of two distinct members of the set {1, 2, 3}?
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  • Answer: 4 (integers)
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  • 12.At what time is the sum of the digits which represent the hours and minutes on a 12-hour digital watch the greatest?
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  • Answer: 9:59
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  • 13.What is the sum of the coordinates of the midpoint of the segment with endpoints (6, 12) and (0, -6)?
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  • Answer: 6
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  • 14.A refrigerator was originally priced at $250. It was then put on sale for 20% off. What is the number of dollars in the final price of the refrigerator if an additional 15% is taken off of the sale price?
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  • Answer: 170 (dollars)
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  • 15.What is the sum of all the prime numbers less than 10?
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  • Answer: 17
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  • 16.Sixteen is 64% of what number?
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  • Answer: 25
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  • 17.Molly has seven U.S. coins with a total value of 88 cents. She does not have any half-dollars. How many dimes does Molly have?
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  • Answer: 1 (dime)
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  • 18.What is the number of square units in the area of a triangle whose sides are 3, 4 and 5 units?
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  • Answer: 6 (square units)
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  • 19.The point A(-7, 4) is reflected across the x-axis onto point B. Point B is reflected over the y-axis onto point C. What is the sum of the coordinates of point C?
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  • Answer: 3
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  • 20.If x = 3 and y = 2, then what is the value of ?
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  • Answer: 7
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  • 21.What is the value of ?
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  • Answer: 32
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  • 22.Set A has 16 elements and set B has 37 elements. The union of sets A and B has 43 elements. How many elements are in the intersection of sets A and B?
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  • Answer: 10 (elements)
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  • 23.TV screens are described by the lengths of their diagonals. A 19" TV has a rectangular screen with a diagonal length of 19 inches. The screen of a 20" TV is 12 inches tall. How many inches wide is the screen?
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  • Answer: 16 (inches)
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  • 24.Jonathan drove at an average rate of 48 miles per hour. How many miles did he travel in 40 minutes?
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  • Answer: 32 (miles)
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  • 25.For what value of n does ? Express your answer as a common fraction.
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  • Answer:
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  • 26.What part of 15 hours is 15 seconds? Express your answer as a common fraction.
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  • Answer:
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  • 27.What is the ratio of 1 pound, 4 ounces to 3 pounds, 10 ounces? Express your answer as a common fraction.
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  • Answer:
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  • 28.The cost of the daily school lunch increased from $1.50 to $1.95. What was the percent increase?
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  • Answer: 30 (percent)
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  • 29.For class president, Tom received 50% of the votes, John received 30% of the votes and Alana received the remaining 88 votes. How many votes did Tom receive?
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  • Answer: 220 (votes)
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  • 30.Compute: (2 + 12 + 22 + 32) + (8 + 18 + 28 + 38).
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  • Answer: 160
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  • 31.The average of nine consecutive integers is 13. What is the sum of the least and greatest of these integers?
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  • Answer: 26
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  • 32.If the sides of a triangle are tripled, then the new area is what percent of the original area?
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  • Answer: 900 (percent)
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  • 33.Ervin made 37.5% of the shots he took during his basketball game. If he took exactly 40 shots during the game, how many shots did he make?
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  • Answer: 15 (shots)
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  • 34.The numbers 1 through 999, inclusive, are printed on a piece of paper. How many digits are printed on the paper?
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  • Answer: 2889 (digits)
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  • 35.How many pairs of prime numbers have a sum of 40?
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  • Answer: 3 (pairs)
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  • 36.What is the sum of the first 6 positive odd integers?
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  • Answer: 36
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  • 37.What is the greatest real number that is at least as large as its square?
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  • Answer: 1
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  • 38.The Catch The Spirit group is conducting a raffle. Each ticket costs $2, and the total expenses are $500. What is the minimum number of tickets that must be sold to yield a profit of $2000?
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  • Answer: 1250 (tickets)
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  • 39.What is the sum of the reciprocals of all the positive divisors of 8? Express your answer as a mixed number.
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  • Answer:
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  • 40.If, what is the value of x ?
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  • Answer: 19
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  • 41.Solve for n:.
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  • Answer: 2
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