q: If six persons sit in a row, then the probability that three particular persons are always together is?
Options:
(A) 1/5
(B) 1/4
(C) 1/9
(D) 1/6
(E) 1/1
a: Stream of consciousness: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5 The answer is (C).


question: The average of first 13 even numbers is?
Options:
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
answer: Stream of consciousness: Sum of 13 even numbers = 13 * 14 = 110
Average = 182/13 = 14 The answer is (E).


q: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
(A) 3451
(B) 3467
(C) 3891
(D) 4601
(E) 5184
a: Stream of consciousness: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62 The answer is (E).


question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train?
Options:
(A) 150
(B) 872
(C) 287
(D) 288
(E) 212
answer: Stream of consciousness: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9 = 150 meter The answer is (A).


q: How many Numbers can be formed with digits 2,4,6,8 without repetition?
Options:
(A) 124
(B) 256
(C) 64
(D) 84
(E) 94
a: Stream of consciousness: Number of one digit numbers = 4
Number of two digit numbers = 4 P 2 = 12
Number of Three digit numbers = 4 P 3 = 24
Number of four digit numbers = 4 P 4 = 24
So, total = 24 + 24 + 12 + 4 = 64 The answer is (C).


q: Which one of the following is not a prime number?
Options:
(A) 2
(B) 3
(C) 5
(D) 9
(E) 7
a:

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: 9 is divisible by 3. So, it is not a prime number. The answer is (D).