q: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is
Options:
(A) 1/9
(B) 1/7
(C) 1/5
(D) 1/6
(E) 1/3
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: Two trains are moving at 75 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
Options:
(A) 6 6/29 sec
(B) 7 1/7 sec
(C) 7 2/2 sec
(D) 8 1/2 sec
(E) 7 1/19 sec
answer: Stream of consciousness: 70 + 75 = 145 * 5/18 = 725/18 mps
D = 150 + 100 = 250 m
T = 250 * 18/725 = 180/29 = 6 6/29 sec The answer is (A).

q: If a man walks to his office at 3/4 of his usual rate, he reaches office 1/3 of an hour later than usual. What is his usual time to reach office.
Options:
(A) 12 hr
(B) 1 hr
(C) 34 hr
(D) 2 hrs
(E) None of these
a: Stream of consciousness: If new speed is ab of original speed, then usual time (ba - 1) = change in time
usual time (43 - 1) = 13
usual time = 13 3 = 1 hr The answer is (B).

question: The average of 9 observations was 9, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?
Options:
(A) 9
(B) 8
(C) 7
(D) 6
(E) 4
answer: Stream of consciousness: 1 to 9 = 9 * 9 = 81
1 to 5 = 5 * 10 = 50
5 to 9 = 5 * 8 = 40
5th = 50 + 40 = 90 81 = 9 The answer is (A).

q: A bank lent $250 to a customer for a one-month loan. At the end of the month, the bank received y dollars more than than the amount that was lent due to interest. The bank also charged a service fee $5. In terms of y, what fraction of the amount that the bank received was the service fee?
Options:
(A) 5/(255+y)
(B) 5y-1
(C) 5y/(250-y)
(D) 5/(250-y)
(E) 5y-250
a: Stream of consciousness: The amount of money the bank received was (250 + 5+ y) dollars. The $5 service fee as a fraction of the amount received was, therefore, 5/(255+y). The answer is (A).

q: what is the next no. 4 12 84
Options:
(A) 632
(B) 732
(C) 832
(D) 850
(E) 902
a:
Stream of consciousness: 3^0 + 3 = 4
3^2 + 3 = 12
3^4 + 3 = 84
3^6 + 3 = 732 The answer is (B).