question: Which of the following is equal to (x-1)!/(x-2)!?
Options:
(A) x-1
(B) 1+(1/x)
(C) 1
(D) x+1
(E) x-1
answer: Stream of consciousness: (x - 1)! = (x - 2)! * (x-1)
(x - 1)!/(x-2)! = x - 1 The answer is (E).

q: A can do a work in 9 days and B can do the same work in 27 days. If they work together, in how many days will they complete the work?
Options:
(A) 6 3/4 days
(B) 7 3/4 days
(C) 5 3/4 days
(D) 6 1/4 days
(E) 6 2/4 days
a: Stream of consciousness: One day's work of A and B = 1/9 + 1/27 = (3+1)/27 = 4/27 So, the time taken to complete the work is 6 3/4 days. The answer is (A).

question: 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
answer: 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 least value of integer N such that N! is divisible by 888 ?
Options:
(A) 13
(B) 88
(C) 31
(D) 37
(E) D) 888
a: Stream of consciousness: 888 = 8*111 = 3*8*37
Hence 888 is a multiple of 37 and we need at least one 37 in N!
Therefore least value of N! is 37!, which will contain all of 3, 8, and 37. The answer is (D).

question: In digging a hole 10 m * 10 m * 100 m the volumes of the sand extracted will be?
Options:
(A) 100 cu.m
(B) 1000 cu.m
(C) 10000 cu.m
(D) 2000 cu.m
(E) 4000 cu.m
answer: Stream of consciousness: 10 * 10 * 100 = 10000 The answer is (C).

question: At 15:00 there were 21 students in the computer lab. At 15:03 and every three minutes after that, 3 students entered the lab. If at 15:10 and every ten minutes after that 8 students left the lab, how many students were in the computer lab at 15:44 ?
Options:
(A) 7
(B) 14
(C) 25
(D) 27
(E) 30
answer:
Stream of consciousness: Initial no of students + 3 * (1 + No of possible 3 minute intervals between 15:03 and 15:44) -
8 *(1 + No of possible 10 minute intervals between 15:10 and 15:44)
20 + 3*14 -8 * 4 = 27 The answer is (D).