question:If a number is chosen at random from the set {1, 2, 3, 100}, then the probability that the chosen number is a perfect cube is
Options:
(A) 1/25
(B) 1/2
(C) 4/13
(D) 1/10
(E) 3/10
answer:(A)
Stream of consciousness:We have 1, 8, 27 and 64 as perfect cubes from 1 to 100. Thus, the probability of picking a perfect cube is 4/100 = 1/25

question:Find the third proportional to 2 and 10?
Options:
(A) 10
(B) 12
(C) 16
(D) 19
(E) 50
answer:(E)
Stream of consciousness:Formula = Third proportional = (b b)/a
A = 2 and B = 10
(10 10)/ 2 = 100/2 = 50

question:A car traveled from San Diego to San Francisco at an average speed of 54 miles per hour. If the journey back took twice as long, what was the average speed of the trip?
Options:
(A) 24.
(B) 32.
(C) 36.
(D) 42.
(E) 44.
answer:
(C)
Stream of consciousness:Let the time taken be = x
One way distance = 54x
Total distance traveled = 2 * 54x = 108x
Total time taken = x + 2x = 3x
Average speed = 108x/3x = 36