Gauss School and Gauss Math Circle
2016 Gauss Math Tournament
Grade 3-4 (Sprint Round 50 minutes)
1. Aunt Mary is years old. Brenda is years younger than Zoe, and Zoe is half as old as Aunt Mary. How old is Brenda?
2. How many whole numbers lie in the interval between 5/3 and ?
3. Jeff's shop class is making a golf trophy. He has to paint 300 dimples on a golf ball. If it takes him 2 seconds to paint one dimple, how many minutes will he need to do his job?
4. A circle and two distinct lines are drawn on a sheet of paper. What is the largest possible number of points of intersection of these figures?
5. How many different combinations of $5 bills and $2 bills can be used to make a total of $17? Order does not matter in this problem.
6. Amanda counted the number of edges of a cube, James counted the numbers of corners, and Judy counted the number of faces. They then added the three numbers. What was the resulting sum?
7. One map, a -centimeter length represents kilometers. How many kilometers does a -centimeter length represent?
8. Kyle bought five folders from Pay-A-Lot at a cost of each. Pay-A-Lot had a 20%-off sale the following day. How much could Kyle have saved on the purchase by waiting a day?
9. A class who has 60% boys goes on a field trip. If 30% of the girls, or 6 of the girls forgot to hand in their permission slip, how many students are in the class?
10. The Gauss soccer team entered a tournament where there were 6 teams, and each team plays each other once in a round robin. How many games are played in total?
11. In a national math competition, 75% of the contestants are eliminated the first round. Then in the second round, the 75% of the remaining contestants are eliminated. Then, in the third and final round, 75% of the remaining contestants are eliminated once again. To the nearest percent, what percentage of the original contestants have not been eliminated from the competition?
12. How many positive integers less than 100 are divisible by 2 and 3, 3 and 5, or 2 and 5, but not 2, 3, and 5?
13. A 5th grader writes his English essay, however, he spells the word “apple” incorrectly. How many different ways could he have misspelled this word?
14. The Fibonacci sequence is defined as 1, 1, 2, 3, 5, 8, … , where the next number is the sum of the two preceding numbers. Besides 1, what is the first Fibonacci number that is also a perfect square?
15. Jimmy shared his cookies with Ronald and Donald. He gave half of his cookies to Ronald, and the half of what was left to Donald. Jimmy ended up with 6 cookies for himself. How many cookies did he originally have?
16. Right triangle ABC and right triangle DEF are similar, with a ratio of 2:1. Right triangle DEF has side 3, 4, and 5. What is the area of the circle circumscribed around triangle ABC?
17. Raymond starts off with a collection of 2016 jelly beans. Each day, he gives away 4x jelly beans, where x is the number of jelly beans he gave away the previous day. If he gave away 1 jelly bean the first day, how many jelly beans does he have at the end of the 6th day?
18. At Harvard University, each dorm room either has 2 or 4 students. If there are 316 students and 128 dorm rooms, how many dorm rooms have 4 people?
19. Alfred runs toward the library from his school at 4 feet per second while Bobby runs toward the library from his school at 8 feet per second. If they both left the school at the same time, and Bobby gets to the library while Alfred is still 96 feet away. In feet, how far is the library from the school?
20. A machine fills 150 bottles of water every 8 minutes at a constant rate. In minutes, how long does it take the machine to fill 675 bottles of water?
21. A large 4x4 square is cut with lines to show 16 1x1 squares. In the described figure, how many squares are there in total?
22. The perimeter of a square A is three times the perimeter of the square B. What is the ratio of the area of A to the area of B?
23. The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children attended?
24. If the total amount that Tim paid for lunch was $50.50, and that price included a 20% tip, how much did Tim spend on the lunch itself? (Round your answer to the nearest cent)
25. What is the smallest positive integer that is both a perfect square and divisible by both 3 and 7?
26. When a positive number is multiplied by the sum of twice the number and half the number, the result is the original number. What is the original number?
27. John gave half of his stamps to Jim. Jim gave gave half of his stamps to Carla. Carla gave 1/4 of the stamps given to her to Thomas and kept the remaining 12. How many stamps did John start with?
28. Little John had $8.50. He spent $1.25 on sweets and gave to his two friends $1.20 each. How much money was left?
29. Boxes that are 12 inches tall are being stacked next to boxes that are 18 inches tall. What is the shortest height at which the two stacks will be the same height?
30. There are 30 kids on the tennis team or basketball team, 20 kids on the tennis team, and 12 kids on the basketball team. How many kids are on both the basketball and tennis team?
31. The truck driver Bill drives 30 mph for 44 miles, and then drives another 44 miles at speed of 20mph. What is his total average speed?
32. Timmy enters the local deli. He can choose to have 0,1,2 slices of meat, one choice of cheese, and one sauce. The choice for meat are salami, turkey, and beef. The choices for cheese consisted of provolone and swiss. He could add mustard, ketchup, or bbq sauce. How many different sandwiches can Tim make?
33. The arithmetic sequence begins with these three terms: 4, 7.25, 10.5 … What is the 29th term?
34. x-y= 6; x+y=2. What is X^2- Y^2?
35. How many multiples of 4 or 5 are from 1-100 inclusive?
36. Sara begins arrives to work at 7:00. She has a long meeting for 210 minutes, and then works in her office for an hour. She takes a lunch break for some minutes, and then calls her boss and yells at her co-workers for a good 3 hours. She then immediately goes home. She gets home at 3:30. Assume that it takes 0 minutes for Sara to drive from her home to her workplace. How long is her lunch time?
37. How many ways can you arrange the letters c,o,c,c,y,x ?
38. Kyle drives a car with 4 tires. He keeps 2 spare tires in the back. He drives 6,000 miles Assuming that he rotates the tires so that each tire has been used the same amount of miles, how many miles has each tires been used?
39. Sadie’s house is three blocks east, four block north of the park. She wants to get to her house from the library by walking only seven blocks. How many ways can she does this?
40. The mean of 10, 4, 1, x and 1 is equal to the median. What is the smallest possible value of x?
Sprint Round Ends
Gauss School and Gauss Math Circle
2016 Gauss Math Tournament
Grade 3-4 (Target Round 20 minutes)
1. Mike eats 200 jelly beans in four days. On each day, he ate 14 more than the previous day. How many cookies did he eat the first day?
2. A square with side length 5 has four 30-60-90 triangles attached to each side, with the hypotenuse of the triangle on the square’s side. What is the total area?
3. There is a box with left hand gloves and right hand gloves. How many gloves should you choose to ensure that you have at least two gloves of the same hand?
4. The surface area of a cube is 49 units squared. What is its volume?
5. What is the minimum value of a/b+b/a if a and b are real numbers?
6. There is a 50 percent chance that it rains Saturday, and a 20 percent chance that it rains Sunday. What is the probability that it rains at least once this weekend?
7. The large circle has diameter AC. The two small circles have their centers on AC and just touch at O, the center of the large circle. If each small circle has radius 1, what is the area of the shaded region?
8. School eats lunch at three different times. Three friends want to sit together at lunch, but the teachers decide when the students eat. Given that the teachers chose randomly for the students, what is the probability that they all eat lunch at the same time?
Target Round Ends
Name: ______Grade:______
Sprint Round Answers:
1 / 212 / 22
3 / 23
4 / 24
5 / 25
6 / 26
7 / 27
8 / 28
9 / 29
10 / 30
11 / 31
12 / 32
13 / 33
14 / 34
15 / 35
16 / 36
17 / 37
18 / 38
19 / 39
20 / 40
Target Round Answers:
1 / 52 / 6
3 / 7
4 / 8
G3-4 Answer Keys:
Sprint Round Answers
1. 16
2. 5
3. 10
4. 5
5. 2
6. 26
7. 102
8. $2.50
9. 50
10. 15
11. 42%
12. 23
13. 59
14. 144
15. 24
16. 25
17. 651
18. 30
19. 192 feet
20. 36 minutes
21. 30
22. 9:1
23. 1500 children
24. $42.08
25. 441
26. ⅖ or 0.4
27. 64
28. $4.85
29. 36 inches
30. 2 kids
31. 24 mph
32. 42
33. 95
34. 12
35. 40
36. 60
37. 120
38. 4,000 miles
39. 35 ways
40. -11
Target Round Answer Key
1. 29 cookies
2. 49
3. 3
4. 343
5. 2
6. 60 percent
7. 3π
8. 1/9
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