San Diego Junior High Math Field Day 2012

Math Bowl - 7

1.Write 2012 using Roman numerals.

2.What is the largest prime factor of 2012?

3.Find the value of x in the figure at the right. /

4.In Mrs. Koenig’s math class, 1/3 of the number of girls is equal to 1/5 of the total number of students. What is the ratio of the number of boys to the number of girls in the class??

5.The sum of Hermione’s number and Ron’s number is 30% more than 7. If you take Ron’s number and add one, this new number, when tripled, is five times Hermione’s number. What is the difference between Ron’s number and Hermione’s number?

6.What is the ratio of 5 ft.2 to 27 in.2? Express your answer as a common fraction.

7.If A is a multiple of 6 and B is a multiple of 8, how many multiples of both A and B are less than 100?

8.I am thinking of a number. Double my number, then subtract 1. If you triple this result, the answer will be 1 fewer than 25. What is my number?

9.You decide to do a tandem parachute jump from an airplane at a height of 1.75 miles. The parachute allows you to descend at an average rate of 15 feet per second. At this rate, how many seconds will pass until you reach the ground?

10.What are the last two digits (tens and units) of the product of all the positive prime numbers less than 100?

11.At Star Farms, Zuke Skywalker selects organic apples out of an enormous contaner filled with 1500 red and green apples. He picks apples in this order: 2 red, 3 green, 2 red, 3 green. If he continues to select apples in this order, what color is his 1226th apple?

12.Frodo’s house is now worth 27 percent more than he paid for it 10 years ago. It is currently worth $167,640. How much did he pay for it 10 years ago?

13.During lunch, students like to trade their food. The following exchange rates are used in the cafeteria: 3 candy bars can be traded for 2 pieces of pizza, and 1 piece of pizza can be traded for 4 lollipops. Using this exchange rate, how many lollipops would should Hershey accept for one candy bar?

14.In the figure at the right, line segment AC has a midpoint at B. Line segment BD, which is perpedincular to AC is 3 inches long. Line segment BD is divided into three subsegments, each of equal length.
In terms of area, what fraction of the region inside ΔADC is ΔAFC? /

15.How many triangles can be found in the figure in question 14?

16.If 1 # 2 = 2 and 3 # 5 = 34 and 6 # 9 = 117 and 10 # 14 = 296, what is the value of 15 # 19?

17.A certain product is sold as either a liquid or a powder. Consumers were interviewed, and a survey revealed that 1/5 do not use the product, 1/3 do not use the powder form, 427 use both the liquid and powder form, and 2/7 do not use the liquid form. How many consumers were interviewed for the survey?

18.Tom and Ted decide to walk over to one another’s homes at the same time. Their homes are 616 yards apart. Tom is walking 2 miles per hour, and Ted is walking 1.5 miles per hour. In how many minutes will they meet?

19.If and 1 are the lengths of the legs of a right triangle, then what is the length of the hypotenuese?

20.What is the 1002nd letter in the following pattern:

M A T H I S F U N M A T H I S F U N M A T H I S F U N …

21.What is the largest two-digit number that you can obtain from a product of two distinct prime numbers?

22.When school ends at 2:30 pm, Bella starts to walk at a rate of 3 miles per hour. If Edward leaves school 5 minutes later and walks at a rate of 3.6 miles per hour, at what time does Edward catch up with Bella?

23.At a bookstore, Harry Potter and the Sorcerer’s Stone and Harry Potter and the Chamber of Secrets cost $45 together. Two copes of The Sorcerer’s Stone and three copies of The Chamber of Secrets cost a total of $125. How much does one copy of The Sorcerer’s Stone cost?

24.McQueen can travel 25 miles on one gallon of gasoline, and Mater can travel 20 miles on one gallon of gasoline. They want to take a trip together. How many miles can they travel if they have $225 to spend on gasoline, which costs $2.50 per gallon?

25.What is the units digit of 82012?

26.The product of three consecutive odd numbers is 357,627. What is the smallest of the three factors?

27.If , then find f (2).

28.What is the y-intercept of the line represented by the equation ?

29.Evaluate:

30.If , then what is the value of y in the following coordinate pair: (27, y)?

31.The product of the diagonals of a certain square is 18 square units. How many units long is the square’s perimeter?

32.What is the distance between point A(-1, -3) and point B(19, -18)?

33.I have picked a number between 0 and 20. If I multiply my number by or add my number to , the product and the sum will be the same. What is the number that I picked?

34.Find the difference between the least and greatest prime factors of 33,660.

35.Small pieces of cheese are placd over each of twelve numbers on the face of a circular clock. A mouse eats the cheese over the number 1 and walks clockwise around the clock, eating every other piece of cheese. He continues walking around the clock until only one piece of cheese remains. What is the number under the last piece of cheese remaining in the clock?

36.A girl who is four and a half feet tall is standing next to a telephone pole. At 1:00 pm, the girl casts a shadow 8 feet long, and the telephone pole casts a shadow 36 feet long. How many inches tall is the telephone pole.

37.The mean of a set of five numbers is 9.4. If four of the numbers in the set are 7, 11, 15, and 19, what is the fifth number in the set?

38.If the first day of the year 2005 was a Saturday, one what day of the week did the fourth of July fall that year?

39.An eager little ant is able to move at a constant rate of 1 inch per second along a tile floor. What is the rate of this ant in terms of miles per hour?

40.A woman bought a plane ticket for herself and each of her four children. If she paid a total of $678 for all five tickets and each child’s ticket cost half of the adult’s ticket, how much did each child’s ticket cost?

41.Find the sum: 5 + 7 + 9 + 11 + … + 1003

42.A group of 6 women and 12 men weigh a total of 3090 pounds. If the women in the group weigh an average of 125 pounds, what is the avereage weight, in pounds, of the men in the group?

43.Express the number 193 (base ten) in binary.

44.A big sale is happening today at Quality Quidditch Supply. Fred and George buy two brooms. The first broom is 20% off the original price of $80. The second broom is 40% off the original price of $120. What is the percent discount on the combined purchase of the two brooms (assuming no taxes are collected).

45.The front wheels of a certain tractor have a diameter of 2 feet. The back wheels have a diameter of 3 feet. If the tractor travels 1 mile, how many more complete rotations will a front wheel make than a back wheel?

46.If the surface area of a sphere is 2916 square centimeters, what is its radius, in centimeters?

47.A Super Ball rebounds half the height from the height it is dropped. If Mr. Galileo drops a Super Ball from the roof of the Physics Building, which is 32 feet off of the ground, what is the total distance (up and down) that the ball will have traveled when it strikes the ground for the sixth time?

48.The ratio of the measures of two complementary angles is 4 to 5. The smallestmeasure is increased by 10%. By what percent must the larger measure be decreased so that the two angles remain complementary?

49.You have one each of a $1, $5, $10, and $20 bill in your dresser drawer. You close your eyes and select one of the bills. What is the probability that the sum of the remaining bills is greater than $30? Express your answer as a percent.

50.If a 4-inch tall right cylinder has a volume of 144π, how many inches long is the diameter of its base?

51.Stupid Human Tricks magazine states that 99% of people can’t like their own elbows, and 90% of the people who read that statistic will try to do it. Of 1000 randomly selected people who read that statistic, how many people can we assume will try to lick their own elbow and be able to do it?

52.What is the slope of the line containing the points (–3, –8) and (–5, 7)?

53.Two positive integers have a sum of 30 and a product of 144. Find the sum of the reciprocals of the two integers.

54.Mr. Wesley buys a new car that comes with five new tires, one for each wheel, and one spare tire. He decided to be economical by using the spare tire as much as the other four tires. If he drives 68,000 miles, what will be the wear in miles on each tire?

55.Four coins are tossed in the air. What is the probability that they all land heads up? Express your answer as a common fraction.

56.Doug is working on a mathematics problem in class. By mistake, he multiplies by 10 then divides by 5 instead of multiplying by 5 and then dividing by 10. If the incorrect answer is 3, what is the correct answer?

57.On a coordinate grid, the triangle is translated from position A to position B. What is the value of x + y? /

58.What is the integer value of x that minimizes the absolute value of (6x2 – 2x)?

59.At Avengers Assemble restaurant, a 15% tip is automatically added to Tony Stark’s bill because there are more than six people in his party. On his check, the tip is $81. What is the total cost of the check, including the tip?

60.The surface of Lake Michigan is 22,300 square miles. If the surface of Lake Michigan were a perfect cirfular region, whar woul its circumference be? Express your answer to the nearest mile.

THE END
NAMESCHOOL

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Score:

KEY

MMXXII

252,000

195 (pounds)

25(degrees)

11000001

1000 (miles)

32 (%)

1.525

280(rotations)

80/3

27 (cm)

94 (feet)

8 (%)

616 (seconds)

/ /

50 (%)

12 (inches)

12 (units)

$132,000

25 (units)

–15/2

3 (lollipops)

5/24

54,400 (miles)

15 (triangles)

1/256

243 (inches)

.75 or 3/4

735 (consumers)

–5

6 (minutes)

Monday

25 (units)

5/88(mph)

$621

$113

529 (miles)