If x is the product of the integers from 1 to 150, inclusive, and 5^y is a factor of x, what is the greatest possible value of y ?
Options:
(A) 30
(B) 34
(C) 36
(D) 37
(E) 39
Answer and stream of consciousness: (D)
Stream of consciousness: It basically asks for the number of 5s in 150!
150/5 + 150/25 + 150/125 = 30 + 6 + 1. Hence 37

Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 3/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
Options:
(A) 3/140
(B) 1/28
(C) 3/56
(D) 3/35
(E) 7/40
Answer and stream of consciousness: (E)
Stream of consciousness: P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*3/8*5/7 + 1/5*5/8*2/7 + 4/5*3/8*2/7 = 7/40.

The speed of a boat in still water is 70kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Options:
(A) 22 kmph
(B) 40 kmph
(C) 78 kmph
(D) 50 kmph
(E) 23 kmph
Answer and stream of consciousness: (D)
Stream of consciousness: Speed downstream = 70 + 20 = 90 kmph
Speed upstream = 70 - 20 = 50 kmph

The number N is 5,H48, where H represents the hundred's digit. If N is divisible by 11, what is the value of H
Options:
(A) 1
(B) 7
(C) 6
(D) 5
(E) 2
Answer and stream of consciousness:
(A)
Stream of consciousness: If the number is divisible by 11, then the alternate digits' sum must be divisible by 11 or difference is 0. Only 1 yields such a number.