4. _________How many factors of 1000 can be divided by 20 without a remainder? 5. _________ The square shown is divided into 4 congruent rectangles. If the perimeter of the square is 144 units, what is the perimeter of one of the four congruent rectangles? 6. _________ Two integers have a difference of −18 and a sum of 2. What is the product of the two integers? 7. _________ The median of a set of consecutive odd integers is 138. If the greatest integer in the set is 145, what is the smallest integer in the set? 8. _________ Among all three-digit integers from 100 to 400, how many have exactly one digit that is an 8? 9. _________ Ben and Dan are two of the members on the school’s chess team. In a tournament against their rival team, Ben played exactly 1 out of every 4 games. Dan, who played more games, played 14 games. What is the largest number of games the team could have played? 10. ________ Peter Pedals rode his bike a total of 500 miles in five days. Each day he rode 10 more miles than he had ridden on the previous day. How many miles did Peter ride on just the fifth day? sq in Outcome # of Occurrences 1 14 2 5 3 9 4 7 5 7 6 8 % units miles $ factors integers games
MATHCOUNTS 2008-2009 24 Warm-Up 2 1. _________ A pattern of equilateral triangles will be made from matchsticks, as shown. One whole matchstick is used per side on each triangle. If the pattern is extended and uses exactly 77 matchsticks, how many triangles will be formed? 2. _________ The ratio of the length of a rectangular room to its width is 5:3. The perimeter of the room is 48 feet. What is the area of the room? 3. _________What is the greatest perfect square that is a factor of 7! ? 4. _________ A standard six-sided die with its faces numbered 1 to 6 is rolled once, and a dime is tossed once. What is the probability of rolling a number less than 3 and tossing a tail? Express your answer as a common fraction. 5. _________ In a recent survey of 300 students, 152 students had at least one dog, 120 students had at least one cat, and 46 students had at least one cat and at least one dog. How many of the surveyed students did not have either a cat or a dog? 6. _________ Alicia’s average score on her five tests is 88 points. The score range for each test is 0 points to 100 points, inclusive. What is the lowest possible score that Alicia could have earned on one of the five tests? 7. _________ The numerical value of a particular square’s area is equal to the numerical value of its perimeter. What is the length of a side of the square? 8. _________ When converted to be in the same unit of measure, what is the ratio of 4 cm to 1 km? Express your answer as a common fraction.
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