question: In how many different ways can the letters of the word "BICYCLE" be rearrangement?
Options:
(A) 5040
(B) 5045
(C) 5140
(D) 5010
(E) 5020
answer: Stream of consciousness: Option 'A'
The total number of arrangements is
7P7 = 7! = 5040 The answer is (A).

q: A pipe can fill a cistern in 18 minutes whereas the cistern when fill can be emptied by a leak in 20 minutes. When both pipes are opened, find when the cistern will be full?
Options:
(A) 17
(B) 180
(C) 70
(D) 120
(E) 12
a: Stream of consciousness: 1/18 - 1/20 = 1/180
180 minutes The answer is (B).

question: 80 white and black tiles will be used to form a 10x10 square pattern. If there must be at least one black tile in every row and at least one white tile in every column, what is the maximum difference between the number of black and white tiles that can be used?
Options:
(A) 75
(B) 80
(C) 85
(D) 90
(E) 60
answer: Stream of consciousness: Answer = E
Please refer diagram below
70 - 10 = 60 The answer is (E).

q: A and B can do a work in 10 days and 15 days respectively. A starts the work and B joins him after 5 days. In how many days can they complete the remaining work?
Options:
(A) 6 days
(B) 2 days
(C) 8 days
(D) 4 days
(E) 3 days
a: Stream of consciousness: Work done by A in 5 days = 5/10 = 1/2
Remaining work = 1/2
Work done by both A and B in one day = 1/10 + 1/15 = 5/30 = 1/6
Remaining work = 1/2 * 6/1 = 3 days. The answer is (E).

question: If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips?
Options:
(A) 3/5
(B) 1/2
(C) 1/5
(D) 1/8
(E) 1/32
answer: Stream of consciousness: On the first three flips, you must get heads. Whats the probability of getting heads ? Its 1/2
So for the first three flips, your probability is (1/2)^3 = 1/8
Now for the last two, you want to get tails only. Whats the prob of getting tails ? Well, its the same as prob of getting a heads, namely, 1/2
For the last two flips, your probability is (1/2)^2 = 1/4
So your overall probability for the event in question is 1/8*1/4 = 1/32 The answer is (E).

question: At what rate percent on simple interest will a sum of money double itself in 40 years?
Options:
(A) 3 1/3%
(B) 2 1/2%
(C) 3 9/3%
(D) 3 2/3%
(E) 3 6/3%
answer:
Stream of consciousness: P = (P*40*R)/100
R = 2 1/2% The answer is (B).