question: 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
answer: 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: A train 400 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
Options:
(A) 22 kmph
(B) 77 kmph
(C) 54 kmph
(D) 71 kmph
(E) 90 kmph
a: Stream of consciousness: S = 400/16 * 18/5 = 90 kmph The answer is (E).


question: There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one liter every hour in A, it gets filled up like 10, 20, 40, 80, 160 in tank B. (At the end of first hour, B has 10 liters, second hour it has 20, third hour it has 40 and so on). If tank B is 1/32 filled after 21 hours, what is the total duration required to fill it completely?
Options:
(A) 22
(B) 28
(C) 269
(D) 26
(E) 82
answer: Stream of consciousness: The data related to the first tank A is not necessary. As you can see, the capacity that gets filled in the tank B after each hour is doubled. So If the tank is 1/32nd part is full after 21 hours, it is 1/16th part full after 22 hours, 1/8th part full after 23 hours, 1/4th part full after 24 hours, 1/2 full after 25 hours, completely full after 26 hours. The answer is (D).


q: X can finish a work in 15 days. Y can finish the same work in 20 days. Y worked for 12 days and left the job. how many days does X alone need to finish the remaining work?
Options:
(A) 5
(B) 3
(C) 4
(D) 7
(E) 8
a: Stream of consciousness: Work done by X in 1 day = 1/15
Work done by Y in 1 day = 1/20
Work done by Y in 12 days = 12/20 = 3/5
Remaining work = 1 – 3/5 = 2/5
Number of days in which X can finish the remaining work = (1/3) / (1/15) = 5 The answer is (A).


question: What is the probability that Company E's advertisement will be one of the first two be shown during the first commercial break?
Options:
(A)  1/ 225
(B)  1 / 30
(C)  1 /15
(D)  2 / 15
(E)  4 /15
answer: Stream of consciousness: E 1/15 + (14/15) * 1/14 = 2/15 The answer is (D).


question: A bag contains nine black balls, three red balls and four red balls. In how many ways can two balls be drawn from the bag?
Options:
(A) ¹⁶C₂
(B) ⁹C₂
(C) ³C₂
(D) ¹²C₂
(E) ¹⁴C₂
answer:

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
Stream of consciousness: Total number of balls = 9 + 3 + 4
Two balls can be drawn from 16 balls in ¹⁶C₂ ways. The answer is (A).