question: A die is thrown. If G is the event 'the number appearing is a multiple of 3' and H be the event
'the number appearing is even' then find whether G and H are independent ?
Options:
(A) G and H are not independent events.
(B) G and H are independent events.
(C) Only G independent event
(D) Only H independent event
(E) None
answer: Stream of consciousness: We know that the sample space is S = {1, 2, 3, 4, 5, 6}
Now G = { 3, 6}, F = { 2, 4, 6} and E n F = {6}
Then P(G) = 2/6 = 1/3
P(H) = 3/6 = 1/2 and P(G ∩ H) = 1/6
P(G n H) = P(G). P (H)
G and H are independent events. The answer is (B).
--
question: What approximate value should come in place of question mark (?) in the following equation
287.532 + 1894.029 – 657.48 = 843.095 + ?
Options:
(A) 870
(B) 790
(C) 680
(D) 770
(E) 890
answer: Stream of consciousness: ? = 285 + 1895 – 655 – 845 or, ? = 680 The answer is (C).
--
question: A family with 1 mother, 1 father, and 3 children sit in a car with 2 front seats and 3 back seats. If the mother drives with a child in the front, and the father sits in the back center seat with the other two children on either side of him, how many seating arrangements are possible
Options:
(A)  3
(B)  6
(C)  4
(D)  8
(E)  10
answer: Stream of consciousness: Mother has a fixed place and father, so there are 3! ways to arrange the children, hence The answer is (B).
--
question: A train of 24 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 1.4 km long?
Options:
(A) 2 mins 14 sec
(B) 2 mins 34 sec
(C) 2 mins 54 sec
(D) 4 mins 54 sec
(E) 2 mins 44 sec
answer:

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: D = 25 * 60 + 1400 = 2900 m
T = 2900/60 * 18/5 = 174 sec = 2 mins 54 se The answer is (C).
--