Mathcounts Practice Contest Answers

MATHCOUNTS Practice Competition Sprint Round 1. mes 14 Raquel has collected $3.80 in nickels and dimes. She has exactly 48 nickels. How many dimes does she have? 2. 60 % At a certain middle school, there are 16 seventh graders and 24 eighth graders enrolled in algebra this term. What percent of the students enrolled in algebra are eighth graders? 3. 8 What positive integer is 56 less than its square? 4. 4 feet Each year, a certain tree doubled in height. At the end of 6 years, the height of the tree was 32 feet. What was the height of the tree at the end of 3 years? 5. 80 blespoons 1/7 If a certain recipe requires 5 tablespoons of üour for every 2 ounces of butter, how many tablespoons of üour are needed if 2 pounds of butter are used? There are 16 ounces of butter in one pound. 6. unds 3 The number of rounds of golf played by each golfer of an amateur golf association is shown in the chart. What is the average number of rounds played by each golfer? Express your answer to the nearest whole number. 7. $ 9 A book company charges a shipping fee of $3 for the ûrst item in a package, $2 for the second item and $1 for each additional item in the package. For example, the shipping fee charged for one package of four items is $3 + $2 + $1 + $1 = $7. How many dollars are saved by shipping 10 items in two packages of ûve items each, rather than ûve packages of two items each? 8. 73 Algebra exam scores for 27 students are given in the stem-and-leaf plot shown. What is the arithmetic mean of the median and mode of the given scores? 9. 16 25 One stamp is randomly selected from a 10-by-10 sheet of 100 stamps. What is the probability that the stamp selected is not along an outer edge? Express your answer as a common fraction. 10. 120 groups The WNBA champions have a twelve-player roster that includes two superstars. If a group of ûve starting players for this team must include the two superstars, how many different groups of ûve starting players are there? 11. 1.15 nts Two pencils and one pen cost $0.80, and one pencil and two pens cost $1.15. How many cents would three pencils cost? 12. 25 iles per day There are 8 furlongs in a mile. There are 2 weeks in a fortnight. The British cavalry traveled 2800 furlongs in a fortnight. How many miles per day did the cavalry average? 13. 1 4 Two cubes have edge lengths of 6 inches and 12 inches. What is the ratio of the surface area of the smaller cube to the surface area of the larger cube? Express your answer as a common fraction. 14. $ 2000000 Phil Lanthropist won a great deal of money in a contest. He gave 20% of his winnings to his parents, 25% of the remaining money to his children, and the remaining $900,000 to his favorite charity. What was the total number of dollars that Phil won? 15. 5 9 Two circles with spinners at their centers are divided into three equal regions, as shown. When both spinners are spun, what is the probability that the product of the two values is negative? Express your answer as a common fraction. 16. 132 ays Cheldelin Middle School has 12 doors to enter or leave the building. In how many ways is it possible to enter the building by one door and leave the building by a different door? 17. 11 years old Sue is four times as old as Tom is now, and she is as old as Tom will be in 7 years. How many years old was Tom three years ago? 18. 6 rows By hitting a target, Juanita can score 16, 17, 23, 26, 29 or 40 points with each arrow she shoots. What is the fewest arrows she can shoot to score exactly 100 points? 19. $ 180 Twenty students bought tickets for a school party. All of the money received for these 20 tickets was used to purchase beverages. Then, an additional 10 students bought tickets. Rather than use this additional money to buy more refreshments, all 30 students received a $3.00 refund. How many dollars were used to buy beverages? 20. ue marbles 9 A jar contains 10 red, 7 blue and 5 yellow marbles. What is the least number of blue marbles that must be added to the jar so that the probability of randomly selecting a blue marble is greater than 21. $ ? 350 Terry is purchasing a bike that is on sale for 40% off the original price. After a coupon is applied that reduces the sale price by 20%, Terry’s ûnal cost for the bike is $168. What was the original price of the bike Terry is purchasing? 22. 12 3 units Two cylindrical cans have the same volume. The height of one can is triple the height of the other. If the radius of the narrower can is 12 units, how many units are in the length of the radius of the wider can? Express your answer in simplest radical form. 23. 35 rms How many terms of the arithmetic sequence 88, 85, 82, … appear before the number −17 appears? 24. 26 people In the chess club, there are 15 eighth graders, 6 of whom wear glasses. Nine students in the chess club wear glasses. Eight students in the chess club are neither eighth graders nor wear glasses. How many people are in the chess club? 25. 3 In a sequence, each term after the ûrst is four more than three times the previous term. The ûfth term of this sequence is 403. What is the ûrst term? 26. 26 The average value of nine consecutive integers is 13. What is the sum of the smallest and largest of these integers? 27. 72 es A 24-foot by 72-foot rectangular dance üoor is completely tiled with 1-foot by 1-foot square tiles. Two opposite corners of the dance üoor are connected by a diagonal. This diagonal passes through the interior of exactly how many tiles? 28. 28 aths Starting at the M and moving left, right, up or down to an adjoining letter, how many distinct paths can be followed to spell the word MATH? Time Remaining: 6:46 Problems Answered: 30/30 Status: Answers Saved q 29. 15 Given that 30. × × × = , what is the value of ? 1199976 Camy made a list of all distinct ûve-digit positive even integers whose ûve digits are 1, 3, 4, 5 and 9. What is the sum of the integers on Camy’s list? 7/7