A train running at the speed of 60 km/hr crosses a pole in 6 seconds. Find the length of the train.
Options:
(A) 150 m
(B) 145 m
(C) 100 m
(D) 135 m
(E) 155 m
Answer and stream of consciousness: (C)
Stream of consciousness: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 6 = 100 meter

A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 30 minutes. When both pipes are opened, find when the cistern will be full?
Options:
(A) 17 minutes
(B) 87 minutes
(C) 60 minutes
(D) 27 minutes
(E) 11 minutes
Answer and stream of consciousness: (C)
Stream of consciousness: 1/20 - 1/30 = 1/60
60 minutes

Find the value of y from (12)^3 x 6^4 432 = y?
Options:
(A) 2435
(B) 1243
(C) 1509
(D) 3456
(E) 5184
Answer and stream of consciousness: (E)
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 H.C.F. of two numbers is 12 and their L.C.M. is 600. If one of the numbers is 480, then the other is:
Options:
(A) 11
(B) 10
(C) 8
(D) 15
(E) 12
Answer and stream of consciousness:
(D)
Stream of consciousness: Other number = (12 x 600)/480 = 15.