4 A pyramid with volume 40 cubic inches has a rectangular base A pyramid with volume 40 cubic inches has a rectangular base. If the length of the base is doubled, the width tripled and the height increased by 50%, what is the volume of the new pyramid, in cubic inches?
8 Cory has 3 apples, 2 oranges and 2 bananas Cory has 3 apples, 2 oranges and 2 bananas. If Cory eats one piece of his fruit per day for a week and the pieces of fruit within each category are indistinguishable, in how many orders can Cory eat the fruit? One such order is AAAOOBB.
18 Each of four students hands in a homework paper Each of four students hands in a homework paper. Later the teacher hands back the graded papers randomly, one to each of the students. In how many ways can the papers be handed back such that every student receives someone else’s paper? The order in which the students receive their papers is irrelevant.
22 A 1 x 1 x 1 wire frame cube is to be made by gluing together pieces of wire. The wire can be bent to form corners of the cube. If exactly 12 units of wire is used to make the frame, what is the fewest number of pieces of wire that can be used to make the frame?
24 A family of five has Momma, Poppa and three children A family of five has Momma, Poppa and three children. Each child generates 2 loads of laundry per week while each parent generates loads per week. How many loads of laundry are generated by this family in 52 weeks?
26 Jane and her brother each spin this spinner once Jane and her brother each spin this spinner once. The spinner has five congruent sectors. If the non-negative difference of their numbers is less than 3, Jane wins. Otherwise, her brother wins. What is the probability that Jane wins? Express your answer as a common fraction.12345
30 In the figure, the visible gray area within the larger circle is equal to three times the area of the white circular region. What is the ratio of the radius of the small circle to the radius of the large circle? Express your answer as a common fraction.
34 The three-digit positive integer N has a ones digit of 3 The three-digit positive integer N has a ones digit of 3. What is the probability that N is divisible by 3? Express your answer as a common fraction.
38 Figure A is made from three unit squares, and will be called “a trio Figure A is made from three unit squares, and will be called “a trio.” Figure B is a 4 by 4 grid of unit squares. Without overlap, what is the maximum number of trios that can be placed on the grid such that each trio covers exactly three of the unit squares in the grid?Figure AFigure B
40 While standing in line to buy concert tickets, Kit moved feet closer to the ticket window over a period of 30 minutes. At this rate, how many minutes will it take her to move the remaining 70 yards to the ticket window?
44 Sue has 122 crates of the same size Sue has 122 crates of the same size. Each crate contains at least 90 apples and at most apples. Crates containing the same number of apples are stacked one on top of another in their own stack. Not all of the stacks have the same number of crates. What is the least possible number of crates in the tallest stack of crates?