1. A train engine has a maximum speed of 120 km/h when no cars are attached. With cars attached, its maximum speed is diminished by a quantity proportional to the square root of the number of cars. With four cars attached its maximum speed is 90 km/h. The largest number of cars that the engine can move is: (A) 127 (B) 63 (C) 33 (D) 31 (E) 16

2. The floor in a room can be covered with n square tiles 2. The floor in a room can be covered with n square tiles. If a smaller tile is used, then 76 extra tiles are required. If the dimensions of the tiles are integers with no common factors and the number n is an integer, the value of n is: (A) 324 (B) 342 (C) 360 (D) 400 (E) 684

3. Big Ben, the clock in Westminster Palace in London, England, takes five seconds to strike six o’clock, from the beginning of the first strike to the end of sixth strike, and each strike takes one quarter of a second. The number of seconds it will take to strike twelve o’clock is: (A) 10 (B) 10.4 (C) 10.7 (D) 11.2 (E) 12  

4. The four wheels of a car rotate independently 4. The four wheels of a car rotate independently. The front and rear wheels are both two meters apart, measured from one side of the car to the other. When the car drives in a certain circular path, its outside wheels are rotating twice as fast as the inside wheels. The length of the circumference of the path, measured in meters, followed by the outside wheels is: (A) 4π (B) 8π (C) 10π (D) 12π (E) 16π

5. Nine identical black marbles are to put into three cups, one red, one green, and one blue, in such a way that each cup contains at least two marbles. The number of ways in which this can be done is: (A) 10 (B) 27 (C) 36 (D) 45 (E) 84

6. A company wants to construct a rectangular box that will hold exactly 150 cubes each of dimension 1 × 1 × 1 centimeter. The minimum possible surface area of the box, measured in square centimeters, is: (A) 120 (B) 160 (C) 170 (D) 190 (E) 230

7. Six mattresses are stacked in a warehouse 7. Six mattresses are stacked in a warehouse. Each mattress was originally 12 cm thick, but thickness is reduced by one third each time an additional mattress is piled on top. The height of the stack, in cm, is closest to: (A) 24 (B) 27 (C) 30 (D) 33 (E) 36

8. Antonino can run around a track in 5 minutes while Bill runs around the same track in 9 minutes. If Antonino and Bill start together, running in the same direction, the number of minutes it will take Antonino to gain one lap on Bill is: (A) 10 (B) 10 ¼ (C) 10 ¾ (D) 11 ¼ (E) 11 ½

9. Five straight lines are drawn on the plane 9. Five straight lines are drawn on the plane. The maximum possible number of intersection points of the five lines is: (A) 5 (B) 6 (C) 10 (D) 15 (E) 20

10. A man 2 meters tall is standing at point A on the ground, a certain distance from a lamppost, and observes his shadow. When the man walks 5 meters farther away from the lamppost, his shadow becomes twice as long. The distance along the ground between point A and the lamppost is: (A) 5 (B) 10 (C) 12 (D) 15 (E) 20

11. If you write all the integers from 1 to 5555, the number of times you write the digit 9 is: (A) 500 (B) 550 (C) 555 (D) 665 (E) 1605

12. If one stamp is randomly selected from a 12 × 12 sheet of stamps, then the probability that the stamp selected is one of the stamps on the border of the sheet is: (A) 1/12 (B) 1/3 (C) 11/36 (D) 25/36 (E) 2/3

13. A ten digit code is represented by 4ABCDEFG8H 13. A ten digit code is represented by 4ABCDEFG8H. If the sum of any three successive digits is 19, the value of the digit D is: (A) 4 (B) 5 (C) 7 (D) 8 (E) 9  

14. Antonino goes to the local fruit stand and spends a total of $20 14. Antonino goes to the local fruit stand and spends a total of $20.01 on peaches and pears. If pears cost 18ȼ and peaches cost 33ȼ, the maximum number of fruits Antonino could have bought is: (A )110 (B)107 (C) 100 (D)92 (E)62  

15. Two overlapping spherical soap bubbles, whose centers are 50 mm apart, have radii of 40 mm and 30 mm. The two spheres intersect in a circle whose diameter, in millimeters, is: (A) 36 (B) 48 (C) 50 (D) 54 (E) 64  

16. Albert has sixteen quarters, one of which is counterfeit and heavier than the other coins. He only has a single balance scale that he can use to identify the counterfeit coin. The minimum number of weighing's that will guarantee that Albert can identify the counterfeit coin is: (A) 1 (B) 2 (C) 3 (D) 4 (E) 5  

17. Dawn goes into a bookstore and buys three items to help her do her crossword puzzles. The most expensive item is a dictionary and the least expensive is an eraser. She also buys a pencil. The total cost of the three items, before tax, is $70.35. After leaving the store she notices that if she multiplies the costs, in dollars, of the three items, the product equals the before tax cost. The cost of the pencil, in dollars, is: (A) 0.15 (B) 0.21 (C) 0.35 (D) 3.00 (E) 5.00  

18. Vancouver is known for its weather 18. Vancouver is known for its weather. Here is a meteorological report for the first 100 days in 2013 in Vancouver: on 90 of the days it was cold, on 80 of the days it was cloudy, on 75 of the days it rained, on 20 of the days it was cold and not cloudy. It was also noted that on days that were not cloudy it never rained, and on days it was cloudy and not cold it always rained. Using this information, the number of the first 100 days in 2013 when it was cold and it rained and it was cloudy was: (A) 35 (B) 45 (C) 55 (D) 65 (E) 75  

19. In a student council election, Samantha received 60% of the votes and Jason received all the rest. Samantha received 55 more votes than Jason. The number of students who voted was: (A) 110 (B) 220 (C) 275 (D) 550 (E) 240  

20. Ahmed has three times as many nickels as dimes and six more pennies than she has dimes. If the total value of the coins is $8.38, the number of dimes Ahmed has is: (A) 32 (B) 33 (C) 38 (D) 39 (E) 46