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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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MATH COUNTS

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Math counts

MATHCOUNTS

2004 School Competition

Countdown Round


Math counts

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)


2 when 5 is subtracted from three times a number the result is 7 what is the number

2.When 5 is subtracted from three times a number, the result is 7. What is the number?


Answer 4

Answer: 4


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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)


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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)


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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)


6 what is the sum of the first five positive odd integers

6.What is the sum of the first five positive odd integers?


Answer 25

Answer: 25


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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)


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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)


9 what number is one hundred less than one thousand thirty three

9.What number is one hundred less than one thousand thirty-three?


Answer 933

Answer: 933


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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)


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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)


12 what is the least positive integer that has exactly three distinct factors

12.What is the least positive integer that has exactly three distinct factors?


Answer 41

Answer: 4


13 the cube of what integer is closest to 800

13.The cube of what integer is closest to 800?


Answer 9

Answer: 9


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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:


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15.The sum of 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


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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)


17 solve for x 18 x 10 x

17.Solve for x: 18 - x = 10 + x.


Answer 42

Answer: 4


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18.An 8 cm by 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)


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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)


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


Answer1

Answer:


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 angle ABD in square ABCD?


Answer 45 degrees

Answer: 45 (degrees)


22 what is the units digit of 6 2004

22.What is the units digit of 62004?


Answer 6

Answer: 6


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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)


24 what integer is closest to

24.What integer is closest to ?


Answer 14

Answer: 14


25 sixty percent of a number is 40 less than the number what is the number

25.Sixty percent of a number is 40 less than the number. What is the number?


Answer 100

Answer: 100


26 what is the least positive three digit multiple of 24

26.What is the least positive three-digit multiple of 24?


Answer 120

Answer: 120


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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 square foot)


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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)


29 what is the decimal equivalent of express your answer to the nearest hundredth

29.What is the decimal equivalent of ? Expressyour answer to the nearest hundredth.


Answer 2 75

Answer: 2.75


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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)


31 simplify express your answer as a common fraction

31.Simplify: . Express your answer as a common fraction.


Answer2

Answer:


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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)


33 simplify 7 10 3 5 10 2 4 10 1 7 10 0

33.Simplify: 7 ´ 103 + 5 ´ 102 - 4 ´ 101 + 7 ´ 100.


Answer 7467

Answer: 7467


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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)


35 if f x x 2 1 what is the value of f 1

35.If f (x) = x2- 1, what is the value of f (-1)?


Answer 0

Answer: 0


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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


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37.When the expression 7 + 4(x + 5) - 8(3 - x) is simplified, what is the value of the coefficient of the x-term?


Answer 12

Answer: 12


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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)


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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)


40 what is the greatest prime factor of 10

40.What is the greatest prime factor of 10!?


Answer 7

Answer: 7


41 two numbers are in the ratio of 5 7 their sum is 108 what is the lesser number

41.Two numbers are in the ratio of 5:7. Their sum is 108. What is the lesser number?


Answer 45

Answer: 45


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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:


43 given what is the value of the ratio express your answer as a common fraction

43.Given: . What is thevalue of the ratio ? Expressyour answer as a common fraction.


Answer4

Answer:


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

Fiction55%

Nonfiction25%

Educational10%

Other10%


Answer 134 000 000 books

Answer: 134,000,000 (books)


45 twenty five percent of what number is 12

45.Twenty-five percent of what number is 12?


Answer 48

Answer: 48


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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: 16p (square centimeters)


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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)


48 how many positive three digit integers are multiples of 11

48.How many positive three-digit integers are multiples of 11?


Answer 81 integers

Answer: 81 (integers)


49 express the value of as a common fraction

49.Express the value of as a common fraction.


Answer5

Answer:


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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:


51 how many distinct prime factors does 5 2 3 2 have

51.How many distinct prime factors does 52- 32have?


Answer 1 factor

Answer: 1 (factor)


52 how many triangles of any size are in this figure

52.How many triangles of any size are in this figure?


Answer 5 triangles

Answer: 5 (triangles)


53 what is 150 of 26

53.What is 150% of 26?


Answer 39

Answer: 39


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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)


55 in how many ways can a pair of students be selected from a group of five students

55.In how many ways can a pair of students be selected from a group of five students?


Answer 10 ways

Answer: 10 (ways)


56 in the formula d rt what is the value of r if d 60 and t 4

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


Answer 15

Answer: 15


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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)


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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)


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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:


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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:


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