q: If n is a natural number, then (6n^2 + 6n) is always divisible by
Options:
(A) 6 only
(B) 6 and 12 both
(C) 12 only
(D) 18 only
(E) 12 and 18 both
a: Stream of consciousness: (6n^2 + 6n) = 6n(n + 1), which is divisible by both 6 and 12, since n(n+1) is always even. The answer is (B).

question: An equity analyst needs to select 2 stocks for the upcoming year and rank these securities in terms of their investment potential. If the analyst has narrowed down the list of potential stocks to 5, in how many ways can she choose and rank her top 2 picks?
Options:
(A) 20
(B) 30
(C) 10
(D) 40
(E) 80
answer: Stream of consciousness: Number of ways of choosing 2 stocks = 5C2
Number of ways of ranking the chosen stocks = 2!
Hence total ways of chosing and ranking = 5C2 * 2! = 20 The answer is (A).

q: A can do a piece of work in 3 hours; B and C together can do it in 2 hours, which A and B together can do it in 2 hours. How long will C alone take to do it?
Options:
(A) 2hours
(B) 5hours
(C) 6hours
(D) 4hours
(E) 3hours
a: Stream of consciousness: A's 1 hour work = 1/3;
(B + C)'s 1 hour work = 1/2;
(A + B)'s 1 hour work = 1/2
(A + B + C)'s 1 hour work = (1/3 + 1/2) = 5/6
C's 1 hour work = (5/6 - 1/2) = 1/3
C alone will take 3 hours to do the work. The answer is (E).

question: Find the mean proportional between 81 & 100?
Options:
(A) A) 59
(B) B) 61
(C) C) 63
(D) D) 65
(E) E) 90
answer: Stream of consciousness: Formula = ab
A = 81 and B = 100
81100 = 9 10 = 90 The answer is (E).

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

q: Find the third proportional to 2 and 10?
Options:
(A) 10
(B) 12
(C) 16
(D) 19
(E) 50
a:
Stream of consciousness: Formula = Third proportional = (b b)/a
A = 2 and B = 10
(10 10)/ 2 = 100/2 = 50 The answer is (E).