q: A train running at the speed of 60 km/hr crosses a pole in 3 seconds. Find the length of the train.
Options:
(A) 150 m
(B) 50 m
(C) 75 m
(D) 135 m
(E) 60 m
a: Stream of consciousness: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 3 = 50 meter The answer is (B).

question: The average of first six prime numbers greater than 65 is?
Options:
(A) 55
(B) 77
(C) 56
(D) 67
(E) 98
answer: Stream of consciousness: 67 + 71 + 73 + 79 + 83 + 89 = 462/6 = 77 The answer is (B).

q: A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
Options:
(A) 12 days
(B) 15 days
(C) 18 days
(D) 20 days
(E) 22 days
a: Stream of consciousness: A's two day's work = 2/20 = 1/10
(A + B + C)'s one day's work = 1/20 + 1/30 + 1/60 = 6/60 = 1/10
Work done in 3 days = (1/10 + 1/10) = 1/5
Now, 1/5 work is done in 3 days
Therefore, Whole work will be done in (3 x 5) = 15 days. The answer is (C).

question: A train of 25 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 2.5 km long?
Options:
(A) 4
(B) 3
(C) 5
(D) 7
(E) 9
answer: Stream of consciousness: D = 25 * 60 + 2500 = 4000 m
T = 4000/60 * 18/5 = 240 sec = 4 mins The answer is (A).

q: In how many different ways can be letters of the word SOFTWARE be arranged in such a way that the vowels always come together?
Options:
(A) 13440
(B) 1440
(C) 360
(D) 120
(E) None of these
a: Stream of consciousness: When the vowels are always together, then treat all the vowels as a single letter and then all the letters can be arranged in 6! ways and also all three vowels can be arranged in 3! ways. Hence, required no. of arrangements = 6! 3! = 4320. The answer is (E).

q: If 14m n = p, then which of the following represents the average (arithmetic mean) of m, n, and p, in terms of m?
Options:
(A) 2m 1
(B) 4m
(C) 5m
(D) m/5
(E) 6m/5
a:
Stream of consciousness: 14m - n = p
Add n to both sides:
14m = n + p
Add m to both sides:
15m = n + p + m
Now, divide both sides by 3
5m = (n + p + m)/3 = the average of n, p, and m The answer is (C).