q: 10 people meet and shake hands. The maximum number of handshakes possible if there is to be no "cycle" of handshakes is (A cycle of handshakes is a sequence of k people a1, a2, , ak (k > 2) such that the pairs {a1, a2}, {a2, a3}, , {ak-1, ak}, {ak, a1} shake hands).
Options:
(A) 7
(B) 6
(C) 9
(D) 8
(E) 10
a: Stream of consciousness: The question is not written in proper manner but we can work in 3 methods
1) If these are random handshakes, then total methods = 10*9/2*1 = 45
2) If these are cyclic handshakes, then total methods = 10
3) If these persons are not cyclic but they are arranged in a straight bench, then number of methods = 9 The answer is (C).

question: A and B can do a work in 10 days and 15 days respectively. A starts the work and B joins him after 3 days. In how many days can they complete the remaining work?
Options:
(A) 6 days
(B) 2 days
(C) 8 days
(D) 4 1/5 days
(E) 9 days
answer: Stream of consciousness: Work done by A in 3 days = 3/10
Remaining work = 7/10
Work done by both A and B in one day = 1/10 + 1/15 = 5/30 = 1/6
Remaining work = 7/10 * 6/1 = 21/5 = 4 1/5 days. The answer is (D).

q: If n is the smallest integer such that 432 times n is the square of an integer, what is the value of n?
Options:
(A) 2
(B) 3
(C) 6
(D) 12
(E) 24
a: Stream of consciousness: The prime factorization of a square has to have even powers of all its prime factors. If the original number has a factor, say of 7, then when it's squared, the square will have a factor of 7^2. Another way to say that is: any positive integer all of whose prime factors have even powers must be a perfect square of some other integer. Look at the prime factorization of 432
432 = (2^4)*(3^3)
The factor of 2 already has an even power - that's all set. The factor of 3 currently has an odd power. If n = 3, then 432*n would have an even power of 2 and an even power of 3; therefore, it would be a perfect square. Thus, n = 3 is a choice that makes 432*n a perfect square. The answer is (B).

question: John makes $60 a week from his job. He earns a raise and now makes $120 a week. What is the % increase?
Options:
(A) 16%
(B) 100%
(C) 17%
(D) 17.61%
(E) 17.56%
answer: Stream of consciousness: Increase = (60/60)*100 = (6/6)*100 = 100%. The answer is (B).

q: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train?
Options:
(A) 150
(B) 872
(C) 287
(D) 288
(E) 212
a: Stream of consciousness: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9 = 150 meter The answer is (A).

q: Calculate the largest 3 digit number which is exactly divisible by 89?
Options:
(A) 911
(B) 969
(C) 979
(D) 977
(E) 971
a:
Stream of consciousness: Largest 4 digit number is 999
After doing 999 89 we get remainder 20
Hence largest 3 digit number exactly divisible by 89 = 999 - 20 = 979 The answer is (C).