St. Luke School Math Tournament 2014

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?   

Question 1 96

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

Question 2   x= 60

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

Question 3  

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

Question 4 96 feet

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

Question 5 575 students

Round 1, Question 6 Solve for p:       p=

Question 6 p=

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.  

Question 7  

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

Question 8 7 disks

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

Question 1 80 cents

Round 2, Question 2  

Question 2  

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

Question 3 120 committees

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

Question 4 4 square inches

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

Question 5 20 units

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

Question 6 50

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?

Question 7 31 toothpicks

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

Question 8 units