Steve traveled the first 2 hours of his journey at 40 mph and the last 2 hours of his journey at 80 mph. What is his average speed of travel for the entire journey?
Options:
(A) 53.33 mph
(B) 56.67 mph
(C) 60 mph
(D) 64 mph
(E) 66.67 mph
Answer and stream of consciousness: (C)
Stream of consciousness: Average Speed = Total distance/ Total time = (40 * 2 + 80 * 2)/(2 + 2) = 240/4 = 60

A Martian bat flies at 60 yards per second from its nest to a dry lake. When it arrives there, it immediately continues at 45 yards per second to a nearby cave. If the distance between the lake and the cave is half the distance between the nest and the lake, what is the average speed, in yards per second, of the bat during the whole flight?
Options:
(A) 36
(B) 40
(C) 42
(D) 54
(E) 65
Answer and stream of consciousness: (D)
Stream of consciousness: Distance from nest to lake = d, Speed = 60, Time = d/60
Distance from lake to cave = d/2, Speed = 45, Time = d/90
Average speed = (d + d/2)/(d/60 + d/90) = (3/2)/(1/36) = 54

There are 16 teams in a tournament. If during the first round, each team plays every other team exactly once, how many games will be played in the first round?
Options:
(A) 15
(B) 30
(C) 120
(D) 240
(E) 256
Answer and stream of consciousness: (C)
Stream of consciousness: Number of ways to pick 2 teams from a total of 16 = 16C2 = 16!/14!*2! = 120. Hence

Find the third proportional to 9 and 12?
Options:
(A) 10
(B) 12
(C) 16
(D) 19
(E) 20
Answer and stream of consciousness:
(C)
Stream of consciousness: Formula = Third proportional = (b b)/a
A = 9 and B = 12
(12 12)/ 9 = 144/9 = 16