q: 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
a: 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 The answer is (D).
--
q: A dice is thrown. What is the probability that the number shown in the dice is divisible by 3?
Options:
(A) 5/5
(B) 5/9
(C) 5/1
(D) 1/3
(E) 5/2
a: Stream of consciousness: Total number of outcomes possible when a die is rolled, n(S) = 6 ( 1 or 2 or 3 or 4 or 5 or 6)
E = Event that the number shown in the dice is divisible by 3 = {3, 6}
The probability = 2/6 = 1/3. The answer is (D).
--
q: The speed of a boat in still water is 90kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Options:
(A) 40, 68 kmph
(B) 110, 70 kmph
(C) 90, 60 kmph
(D) 40, 60 kmph
(E) 20, 60 kmph
a:
Stream of consciousness: Speed downstream = 90 + 20 = 110 kmph
Speed upstream = 90 - 20 = 70 kmph The answer is (B).
--