A fair coin is tossed repeatedly. If head appears on the first four tosses, then the probability of appearance of tail on the fifth toss is.
Options:
(A) 1/7
(B) 1/2
(C) 3/7
(D) 2/3
(E) 1/3
Answer and stream of consciousness: (B)
Stream of consciousness: Since the coin is a fair coin, every toss is independent of any other toss. Hence, the probability of appearance of tail on the fifth toss is = 1/2


Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
(A) 2134
(B) 2234
(C) 2540
(D) 2560
(E) 5184
Answer and stream of consciousness: (E)
Stream of consciousness: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62


Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?
Options:
(A) 288
(B) 200
(C) 279
(D) 992
(E) 208
Answer and stream of consciousness: (D)
Stream of consciousness: (800*3*3)/100 = 72
920 + 72 = 992


Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
Options:
(A) 7 1/7 sec
(B) 7 7/2 sec
(C) 7 1/8 sec
(D) 7 1/2 sec
(E) 7 3/2 sec
Answer and stream of consciousness:

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
(D)
Stream of consciousness: 70 + 50 = 120 * 5/18 = 100/3 mps
D = 150 + 100 = 250 m
T = 250 * 3/100 = 15/2 = 7 1/2 sec