q: How many positive integers less than 500 can be formed using the numbers 1,2,3,and 5 for digits, each digit being used only once.
Options:
(A) 22
(B) 34
(C) 73
(D) 26
(E) 11
a: Stream of consciousness: Single digit numbers = 4
Double digit numbers = 4 x 3 = 12
Three digit numbers = 3 x 3 x 2 x 1 = 18
Total = 34 The answer is (B).

question: If x, y, and z are positive integers such that x is a factor of y and y is a factor of z, which of the following is NOT necessarily an integer?
Options:
(A) (x + y) /z
(B) (y + z) /x
(C) yz/x
(D) (2y + 3z) /x
(E) (xy + z) /y
answer: Stream of consciousness: As per the question, let x = 2, y = 6, and z = 12. Plugging these into the answer choices, only A does not yield an integer. The answer is (A).

q: Two pipes A and B can fill a cistern in 8 and 12 minutes respectively, and a third pipe C can empty it in 15 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
Options:
(A) 17 1/17 min
(B) 28 1/7 min
(C) 17 1/7 min
(D) 17 1/8 min
(E) 17 5/7 min
a: Stream of consciousness: 1/8 + 1/12 - 1/15 = 17/120
120/17 = 7 1/17 The answer is (A).

question: The average of first six prime numbers greater than 20 is?
Options:
(A) 10
(B) 20
(C) 30
(D) 40
(E) 34
answer: Stream of consciousness: 23 + 29 + 31 + 37 + 41 + 43 = 204/6 = 34 The answer is (E).

q: In what time a sum of money double itself at 7% per annum simple interest?
Options:
(A) 33 1/8%
(B) 33 1/3%
(C) 14 2/7%
(D) 32 1/3%
(E) 23 1/3%
a: Stream of consciousness: P = (P*7*R)/100
R = 14 2/7% The answer is (C).

q: If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 10(B + G) is ?
Options:
(A) Equal to 3
(B) Less than 3
(C) More than 10
(D) Less than 10
(E) none of these
a:
Stream of consciousness: Let number of boys = x
Let number of girls = y
Therefore x/y = B and y/x = G
10(B + G) = 10[(x/y) + (y/x)] = 10[(x2 + y2)/xy] > 10 The answer is (C).