question: A can do a piece of work in 12 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?
Options:
(A) 18 days
(B) 11 days
(C) 77 days
(D) 188 days
(E) 66 days
answer: Stream of consciousness: 8/12 + 6/x = 1
X = 18 days The answer is (A).

q: The average of 11 results is 55, if the average of first five results is 49 and that of the last seven is 52. Find the fifth result?
Options:
(A) 4
(B) 5
(C) 7
(D) 8
(E) 9
a: Stream of consciousness: 1 to 11 = 11 * 55 = 605
1 to 5 = 5 * 49 = 245
5 to 11 = 7 * 52 = 364
5th = 245 + 364 605 = 4 The answer is (A).

question: A sum of money doubles itself at a compound interest in 15 years . In how may years it will become 8 times ??
Options:
(A) 30 years
(B) 40 years
(C) 45 years
(D) 50 years
(E) 60 years
answer: Stream of consciousness: If the sum doubles (x2) in 15 years, then it to become 2*2*2 = 8 times as large it should double three times, so three 15 years time period are needed, which is 3*15 = 45 years. The answer is (C).

q: 10 books are placed at random in a shelf. The probability that a pair of books will always be together i
Options:
(A) 1/6
(B) 1/0
(C) 1/5
(D) 1/2
(E) 1/1
a: Stream of consciousness: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5 The answer is (C).

question: 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: 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 answer is (E).

question: Seven different objects must be divided among three persons. In how many ways this can be done if at least one of them gets exactly one object.
Options:
(A) 223
(B) 776
(C) 287
(D) 196
(E) 211
answer:
Stream of consciousness: Division of m+n+p objects into three groups is given by (m+n+p)!m!n!p!(m+n+p)!m!n!p!
But 7 = 1 + 3 + 3 or 1 + 2 + 4 or 1 + 1 + 5
So The number of ways are (7)!1!3!3!12!(7)!1!3!3!12! + (7)!1!2!4!(7)!1!2!4! + (7)!1!1!5!12!(7)!1!1!5!12! = 70 + 105 + 21 = 196 The answer is (D).