question: There are 10 students named alphabetically from A to J. What is the Probability that A and D do not sit together if all 10 sit around a circular table?
Options:
(A) 2/9
(B) 2/5
(C) 7/9
(D) 4/5
(E) 8/9
answer: Stream of consciousness: Number of students = 10
Number of ways 10 students can sit around a circular table = (10 - 1)! = 9!
Number of ways A and D sit together (consider A and D as one entity) = (9 - 1)! = 8! * 2
Number of ways A and D do not sit together = 9! - (8! * 2)
Probability = (9! - (8! * 2))/9! = 1 - 2/9 = 7/9 The answer is (C).

q: The number N is 6,2X4, where X represents the ten's digit. If N is divisible by 9, what is the value of X?
Options:
(A) 1
(B) 3
(C) 5
(D) 7
(E) 6
a: Stream of consciousness: Integer is divisible by 9 - Sum of digits is divisible by 9 The answer is (E).

question: A can do a piece of work in 20 days. B in 15 days A and C in 12 days. In how many days can A finish the work if he is assisted by B on one day and C on the next, alternately?
Options:
(A) 7 days
(B) 8 days
(C) 5 days
(D) 4 days
(E) 2 days
answer: Stream of consciousness: A + B = 1/20 + 1/15 = 7/60
A + C = 1/20 + 1/12 = 8/60
7/60 + 8/60 = 15/60 = 1/4
4 days * 2 = 8 days The answer is (B).

q: A man rows his boat 75 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Options:
(A) 5 kmph
(B) 6 kmph
(C) 9 kmph
(D) 8 kmph
(E) 1 kmph
a: Stream of consciousness: Speed downstream = d/t = 75/(2 1/2) = 30 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (30 - 18)/2 = 6 kmph The answer is (B).

question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
(A) 40
(B) 99
(C) 77
(D) 66
(E) 12
answer: Stream of consciousness: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec The answer is (A).

question: An analyst will recommend a combination of 2 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 5 industrial stocks, 4 transportation stocks, and 3 utility stocks, how many different combinations of 6 stocks are possible?
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Options:
(A) 12
(B) 19
(C) 60
(D) 180
(E) 720
answer:
Stream of consciousness: 5C2 * 4C2 * 3C2 = 10*6*3 = 180. The answer is (D).