1. St. Luke School Math Tournament
2014

2. What is the sum of all positive integer divisors of 77?
Round 1, Question 1
What is the sum of all positive integer divisors of 77? 

3. Question 1 96

4. In the equation, what is value of x?
Round1, Question 2
In the equation, what is value of x? x=

5. Question 2
  x= 60

6. Round 1, Question 3
Find the value of: Express your answer as a reduced mixed number.

7. Question 3

8. Round 1, Question 4
Sherlock Holmes states, “If a rod of six feet cast a shadow of nine feet, a tree of 64 feet would cast one of…” What length in feet should Sherlock say next? feet

9. Question 4
96 feet

10. Round 1, Question 5
Because of redistricting, Liberty Middle School’s enrollment increased to 598 students. This is an increase of 4% over last year’s enrollment. What was last year’s enrollment?
  students

11. Question 5
575 students

12. Round 1, Question 6
Solve for p:  
  p=

13. Question 6 p=

14. Round 1, Question 7
Fifty ping-pong-balls are numbered 1, 2, 3, …, 49, 50. A ball is chosen at random. What is the probability that the number on the selected ball is a multiple of 5 or 7 or both. Express your answer as a common fraction.

15. Question 7

16. Round 1, Question 8
A container has 10 green disks, 10 white disks and 10 red disks. If the disks are randomly selected from the container without replacement, what is the minimum number of disks that must be drawn to be certain that three disks of the same color have been selected?
disks

17. Question 8
7 disks

18. Round 2, Question 1
The new Starving Games book will have a cover price of $25. The local bookstore is offering two discounts $4.00 off and 20% off. A clever shopper realizes that the prices will be different depending on the order in which she claims her discounts. How much more money will she save by taking one approach over the other? Express your answer in cents.  cents

19. Question 1
80 cents

20. Round 2, Question 2

21. Question 2

22. Round 2, Question 3
How many different three-person committees can be formed from the 10 members of a club? 
committees

23. Question 3
120 committees

24. Round 2, Question 4
ABCD is a square with 4 inch sides, and each of the inside squares is formed by joining the midpoints of the outer square’s sides. What is the area of the shaded region in square inches? square inches

25. Question 4
4 square inches

26. Round 2, Question 5
Triangle ABC has sides of 6 units, 8 units, and 10 units. The width of a rectangle, whose area is equal to the area of the triangle, is 4 units. What is the perimeter of this rectangle, in units? units

27. Question 5
20 units

28. Round 2, Question 6
The product of two consecutive positive even integers is 624. What is the sum of the two integers? 

29. Question 6 50

30. Round 2, Question 7
The pattern is made from toothpicks. If the pattern is continued by adding two toothpicks to the previous stage, how many toothpicks are used to create the 15th stage?

31. Question 7
31 toothpicks

32. Round 2, Question 8
In right triangle ABC, the length of side BC is 2 units, the length of side AC is 4 units and the measure of angle C is 60 degrees. What is the length of side AB, in units? Express your answer in simplest radical form.
  units

33. Question 8
units