q: Two trains run in opposite directions on a circular track. Train A travels at a rate of 4 miles per hour and Train B runs at a rate of 6 miles per hour. If the track has a radius of 6 miles and the trains both start from Point S at the same time, how long, in hours, after the trains depart will they again meet at Point S?
Options:
(A) 3
(B) 6
(C) 9
(D) 18
(E) 22
a: Stream of consciousness: The trains will travel the perimeter of the circle which is 12 miles. The relative speed of the trains is 2 miles per hour. Time taken to meet = 12/2 = 6 hours The answer is (B).

question: A train running at the speed of 60 km/hr crosses a pole in 12 seconds. Find the length of the train.
Options:
(A) 175 m
(B) 145 m
(C) 140 m
(D) 200 m
(E) 155 m
answer: Stream of consciousness: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 12 = 200 meter The answer is (D).

q: 10 men and 15 women together can complete a work in 3 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?
Options:
(A) 1 2/7 days
(B) 64 2/7 days
(C) 1 7/7 days
(D) 1 8/7 days
(E) 62 2/5 days
a: Stream of consciousness: 1 man's 1 day work = 1/100
(10 men + 15 women)'s 1 day work = 1/3
15 women's 1 day work = (1/3- 10/100) = 7/30
1 woman's 1 day work = 7/450
1 woman alone can complete the work in 64 2/7 days. The answer is (B).

question: A pipe can fill a cistern in 18 minutes whereas the cistern when fill can be emptied by a leak in 20 minutes. When both pipes are opened, find when the cistern will be full?
Options:
(A) 17
(B) 180
(C) 70
(D) 120
(E) 12
answer: Stream of consciousness: 1/18 - 1/20 = 1/180
180 minutes The answer is (B).

q: Five coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
Options:
(A) 2^4
(B) 2^10
(C) 3 * 2^8
(D) 3 * 2^9
(E) 3 * 2^10
a: Stream of consciousness: Fix the third coin as H. The remaining 4 coins have 2^4 outcomes. The answer is (A).

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).