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MATH COUNTS. . 2004 School Competition Countdown Round. 1. Marie owns 103 department stores. Each store has 106 shelves for towels. What is the total number of shelves for towels?. Answer: 10,918 (shelves).

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MATHCOUNTS

2004 School Competition

Countdown Round


1. Marie owns 103 department stores. Each store has 106 shelves for towels. What is the total number of shelves for towels?


Answer 10 918 shelves
Answer: 10,918 (shelves) 106 shelves for towels. What is the total number of shelves for towels?



Answer 4
Answer: 4 result is 7. What is the number?


3. The Battling Hummingbirds have won 40% of their first 60 games. If they win their next 12 games in a row, what percent of all of their games will they have won?


Answer 50 percent
Answer: 50 (percent) 60 games. If they win their next 12 games in a row, what percent of all of their games will they have won?


4. A 3-foot tall flower-stand casts a 9-foot shadow. At the same time, a nearby tree casts a 51-foot shadow. How many feet tall is the tree?


Answer 17 feet
Answer: 17 (feet) same time, a nearby tree casts a 51-foot shadow. How many feet tall is the tree?


5. Two boxes, A and B, contain pennies. In box A, there are nine more pennies than in box B. The total number of pennies in boxes A and B is 41. What is the number of pennies in box A?


Answer 25 pennies
Answer: 25 (pennies) nine more pennies than in box B. The total number of pennies in boxes A and B is 41. What is the number of pennies in box A?


6 what is the sum of the first five positive odd integers
6. What is the sum of the first five positive odd integers? nine more pennies than in box B. The total number of pennies in boxes A and B is 41. What is the number of pennies in box A?


Answer 25
Answer: 25 nine more pennies than in box B. The total number of pennies in boxes A and B is 41. What is the number of pennies in box A?


7. Trae is searching for a treasure on the beach. From point A, he is told to walk two meters north, three meters east, and then two meters north to point B. In meters, what is the length of ?


Answer 5 meters
Answer: 5 (meters) point A, he is told to walk two meters north, three meters east, and then two meters north to point B. In meters, what is the length of ?


8. Mr. Cole is driving at his favorite speed of 55 miles per hour. He is 125 miles from his destination. His goal is to arrive at his destination in two hours. How many miles per hour faster than his preferred speed must he drive to meet his goal? Express your answer as a decimal to the nearest tenth.


Answer 7 5 miles per hour
Answer: 7.5 (miles per hour) hour. He is 125 miles from his destination. His goal is to arrive at his destination in two hours. How many miles per hour faster than his preferred speed must he drive to meet his goal? Express your answer as a decimal to the nearest tenth.



Answer 933
Answer: 933 thirty-three?


10. What is the degree measure of the angle between the hour hand and the minute hand of a clock at exactly 2:30 p.m. on a 12-hour analog clock?


Answer 105 degrees
Answer: 105 (degrees) hand and the minute hand of a clock at exactly 2:30 p.m. on a 12-hour analog clock?


11. Katrina can bicycle 50 miles in four hours. At the same speed, how many miles does she bicycle in six hours?


Answer 75 miles
Answer: 75 (miles) speed, how many miles does she bicycle in six hours?



Answer 41
Answer: 4 three distinct factors?



Answer 9
Answer: 9 three distinct factors?


14. In a state senate, there are 24 Democrats, 32 Republicans, and 4 Independents. If one senator is selected at random, what is the probability that the senator is a Republican? Express your answer as a common fraction.


Answer
Answer: Republicans, and 4 Independents. If one senator is selected at random, what is the probability that the senator is a Republican? Express your answer as a common fraction.


15. The sum of Republicans, and 4 Independents. If one senator is selected at random, what is the probability that the senator is a Republican? Express your answer as a common fraction.x and y is 11 and the positive difference between x and y is 3. What is the value of the product of x and y?


Answer 28
Answer: 28 Republicans, and 4 Independents. If one senator is selected at random, what is the probability that the senator is a Republican? Express your answer as a common fraction.


16. The total value of 90 pennies, 20 dimes and 12 quarters is what percent of the value of a ten-dollar bill?


Answer 59 percent
Answer: 59 (percent) is what percent of the value of a ten-dollar bill?


17 solve for x 18 x 10 x
17. Solve for is what percent of the value of a ten-dollar bill?x: 18 - x = 10 + x.


Answer 42
Answer: 4 is what percent of the value of a ten-dollar bill?


18. An 8 cm by is what percent of the value of a ten-dollar bill?N cm rectangle has a diagonal of length 10 cm. What is the number of centimeters in the perimeter of this rectangle?


Answer 28 centimeters
Answer: 28 (centimeters) is what percent of the value of a ten-dollar bill?


19. The histogram shows the numbers of types of the 50 pets reported by the 7th graders in a school. What percent of the pets are cats?

20

15

10

5

Dogs

Cats

Fish

Birds


Answer 40 percent
Answer: 40 (percent) reported by the 7th graders in a school. What percent of the pets are cats?


20. What is the sum of the reciprocals of the distinct positive factors of 8? Express your answer as a mixed number.


Answer1
Answer: positive factors of 8? Express your answer as a mixed number.


21 what is the number of degrees in the measure of angle abd in square abcd
21. What is the number of degrees in the measure of positive factors of 8? Express your answer as a mixed number.angle ABD in square ABCD?


Answer 45 degrees
Answer: 45 (degrees) positive factors of 8? Express your answer as a mixed number.


22 what is the units digit of 6 2004
22. What is the units digit of 6 positive factors of 8? Express your answer as a mixed number.2004?


Answer 6
Answer: 6 positive factors of 8? Express your answer as a mixed number.


23. Triangle ABC is isosceles with angle B congruent to angle C. The measure of angle C is four times the measure of angle A. What is the number of degrees in the measure of angle B?


Answer 80 degrees
Answer: 80 (degrees) angle C. The measure of angle C is four times the measure of angle A. What is the number of degrees in the measure of angle B?


24 what integer is closest to
24. What integer is closest angle C. The measure of angle C is four times the measure of angle A. What is the number of degrees in the measure of angle B?to ?


Answer 14
Answer: 14 angle C. The measure of angle C is four times the measure of angle A. What is the number of degrees in the measure of angle B?



Answer 100
Answer: 100 What is the number?



Answer 120
Answer: 120 What is the number?


27. The Carters had a 10-foot by 10-foot patio built at a cost of $2200. How many dollars per square foot did the patio cost to build?


Answer 22 dollars per square foot
Answer: 22 (dollars per cost of $2200. How many dollars per square foot did the patio cost to build? square foot)


28. Jenna has $1.75 in nickels and dimes. She has twice as many dimes as nickels. How many dimes does Jenna have?


Answer 14 dimes
Answer: 14 (dimes) many dimes as nickels. How many dimes does Jenna have?


29 what is the decimal equivalent of express your answer to the nearest hundredth
29. What is the decimal many dimes as nickels. How many dimes does Jenna have? equivalent of ? Expressyour answer to the nearest hundredth.


Answer 2 75
Answer: 2.75 many dimes as nickels. How many dimes does Jenna have?


30. The ratio of the measures of two complementary angles is 7:11. What is the measure, in degrees, of the larger angle?


Answer 55 degrees
Answer: 55 (degrees) 7:11. What is the measure, in degrees, of the larger angle?



Answer2
Answer: fraction.


32. From a one meter piece of yarn, Chris cuts a 31.5 cm piece and a 35.5 cm piece. In centimeters, how much yarn is left?


Answer 33 centimeters
Answer: 33 (centimeters) piece and a 35.5 cm piece. In centimeters, how much yarn is left?


33 simplify 7 10 3 5 10 2 4 10 1 7 10 0
33. Simplify: piece and a 35.5 cm piece. In centimeters, how much yarn is left?7 ´ 103 + 5 ´ 102 - 4 ´ 101 + 7 ´ 100.


Answer 7467
Answer: 7467 piece and a 35.5 cm piece. In centimeters, how much yarn is left?


34. A stair-step exercise machine indicates that Leon burns 180 calories in 12 minutes. At the same rate, how many calories would Leon burn in a 4-minute workout?


Answer 60 calories
Answer: 60 (calories) 180 calories in 12 minutes. At the same rate, how many calories would Leon burn in a 4-minute workout?


35 if f x x 2 1 what is the value of f 1
35. If 180 calories in 12 minutes. At the same rate, how many calories would Leon burn in a 4-minute workout?f (x) = x2- 1, what is the value of f (-1)?


Answer 0
Answer: 0 180 calories in 12 minutes. At the same rate, how many calories would Leon burn in a 4-minute workout?


36. Four friends are in line for movie tickets. Rick is behind Tom, but ahead of Mark. James and Tom are separated by one person. Who is last in line?


Answer mark
Answer: Mark behind Tom, but ahead of Mark. James and Tom are separated by one person. Who is last in line?


37. When the expression behind Tom, but ahead of Mark. James and Tom are separated by one person. Who is last in line?7 + 4(x + 5) - 8(3 - x) is simplified, what is the value of the coefficient of the x-term?


Answer 12
Answer: 12 behind Tom, but ahead of Mark. James and Tom are separated by one person. Who is last in line?


38. Steven is making a scale drawing of his living room. He is using a scale of one-quarter inch to one foot. In the drawing, how many inches will represent the length of a 72-inch long couch? Express your answer as a decimal to the nearest tenth.


Answer 1 5 inches
Answer: 1.5 (inches) is using a scale of one-quarter inch to one foot. In the drawing, how many inches will represent the length of a 72-inch long couch? Express your answer as a decimal to the nearest tenth.


39. The ages, in years, of the ten people in the math club are: 12, 12, 12, 12, 13, 13, 13, 14, 14, 39. What is the mode of the ages?


Answer 12 years
Answer: 12 (years) are: 12, 12, 12, 12, 13, 13, 13, 14, 14, 39. What is the mode of the ages?


40 what is the greatest prime factor of 10
40. What is the greatest prime factor of 10!? are: 12, 12, 12, 12, 13, 13, 13, 14, 14, 39. What is the mode of the ages?


Answer 7
Answer: 7 are: 12, 12, 12, 12, 13, 13, 13, 14, 14, 39. What is the mode of the ages?



Answer 45
Answer: 45 What is the lesser number?


42. Rebecca remembered the first six digits of a friend’s 7-digit phone number. If she randomly selects a digit to replace the last digit she can’t remember, what is the probability she will dial the correct number? Express your answer as a common fraction.


Answer3
Answer: 7-digit phone number. If she randomly selects a digit to replace the last digit she can’t remember, what is the probability she will dial the correct number? Express your answer as a common fraction.


43 given what is the value of the ratio express your answer as a common fraction
43. Given: . What is the 7-digit phone number. If she randomly selects a digit to replace the last digit she can’t remember, what is the probability she will dial the correct number? Express your answer as a common fraction.value of the ratio ? Expressyour answer as a common fraction.


Answer4
Answer: 7-digit phone number. If she randomly selects a digit to replace the last digit she can’t remember, what is the probability she will dial the correct number? Express your answer as a common fraction.


44. The categories and percentages for 536 million juvenile books are given in the table. Of these juvenile books, how many books were Nonfiction?

Fiction 55%

Nonfiction 25%

Educational 10%

Other 10%


Answer 134 000 000 books
Answer: 134,000,000 (books) books are given in the table. Of these juvenile books, how many books were Nonfiction?


45 twenty five percent of what number is 12
45. Twenty-five percent of what number is 12? books are given in the table. Of these juvenile books, how many books were Nonfiction?


Answer 48
Answer: 48 books are given in the table. Of these juvenile books, how many books were Nonfiction?


46. What is the number of square centimeters in the area of a circle with radius 4 cm? Express your answer is terms of p.


Answer 16 p square centimeters
Answer: 16 a circle with radius 4 cm? Express your answer is terms of p (square centimeters)


47. A candy company puts 21 candies in each bag. There are only red and blue candies in each bag. For every two red candies in a bag there are five blue candies. How many red candies are in each bag?


Answer 6 candies
Answer: 6 (candies) are only red and blue candies in each bag. For every two red candies in a bag there are five blue candies. How many red candies are in each bag?




49 express the value of as a common fraction
49. Express the value of 11?as a common fraction.



50. Joshua flips three coins. What is the probability that they are neither all heads nor all tails? Express your answer as a common fraction.


Answer6
Answer: they are neither all heads nor all tails? Express your answer as a common fraction.


51 how many distinct prime factors does 5 2 3 2 have
51. How many distinct prime factors does 5 they are neither all heads nor all tails? Express your answer as a common fraction.2- 32have?


Answer 1 factor
Answer: 1 (factor) they are neither all heads nor all tails? Express your answer as a common fraction.


52 how many triangles of any size are in this figure
52. How many triangles of any size are in this figure? they are neither all heads nor all tails? Express your answer as a common fraction.


Answer 5 triangles
Answer: 5 (triangles) they are neither all heads nor all tails? Express your answer as a common fraction.


53 what is 150 of 26
53. What is 150% of 26? they are neither all heads nor all tails? Express your answer as a common fraction.


Answer 39
Answer: 39 they are neither all heads nor all tails? Express your answer as a common fraction.


54. Each bottle of perfume at The Perfume Parlor contains ounces of perfume. How many of these bottles of perfume could be made from 96 ounces of perfume?


Answer 512 bottles
Answer: 512 (bottles) ounces of perfume. How many of these bottles of perfume could be made from 96 ounces of perfume?



Answer 10 ways
Answer: 10 (ways) a group of five students?


56 in the formula d rt what is the value of r if d 60 and t 4
56. In the formula a group of five students?d = rt, what is the value of r if d = 60 and t = 4?


Answer 15
Answer: 15 a group of five students?


57. On average, each American consumes 286 eggs per year. What is the number of years it would take, at this rate, for an American to eat 2000 eggs? Express your answer to the nearest whole number.


Answer 7 years
Answer: 7 (years) What is the number of years it would take, at this rate, for an American to eat 2000 eggs? Express your answer to the nearest whole number.


58. Of the 80 students at camp, 37.5% of them are male. What is the number of students at camp who are female?


Answer 50 students
Answer: 50 (students) What is the number of students at camp who are female?


59. One fair standard six-sided die is rolled. What is the probability of rolling a number greater than 4? Express your answer as a common fraction.


Answer7
Answer: probability of rolling a number greater than 4? Express your answer as a common fraction.


60. There are 16 boys in Mr. Smith’s class of 34 students. What is the ratio of boys to girls? Express your answer as a common fraction.


Answer8
Answer: What is the ratio of boys to girls? Express your answer as a common fraction.


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