question: Ravi can do a piece of work in 30 days while Prakash can do it in 40 days. In how many days will they finish it together?
Options:
(A) 17 1/7
(B) 17 1/5
(C) 17 1/8
(D) 17 1/1
(E) 17 1/2
answer: Stream of consciousness: 1/30 + 1/40 = 7/120
120/7 = 17 1/7 days The answer is (A).

q: If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 3 (B + G) is ?
Options:
(A) Equal to 3
(B) Less than 3
(C) More than 3
(D) Less than 1/3
(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
3(B + G) = 3[(x/y) + (y/x)] = 3[(x2 + y2)/xy] > 3 The answer is (C).

question: Look at this series: 0.6, 0.3, ____, 0.075, 0.0375, ... What number should fill the blank?
Options:
(A) 0.015
(B) 1.15
(C) 0.15
(D) 0.25
(E) 0.35
answer: Stream of consciousness: This is a simple multiplication series. Each number is multiple by 1/2. The answer is (C).

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: 80 370 ? 1550 2440 3530
Options:
(A) 900
(B) 840
(C) 750
(D) 860
(E) 960
answer: Stream of consciousness: 10^2 - 20 = 80
20^2 - 30 = 370
30^2 - 40 = 860
40^2 - 50 = 1550
50^2 - 60 = 2440
60^2 - 70 = 3530. The answer is (D).

question: A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 40 minutes. When both pipes are opened, find when the cistern will be full?
Options:
(A) 17 minutes
(B) 87 minutes
(C) 40 minutes
(D) 27 minutes
(E) 11 minutes
answer:
Stream of consciousness: 1/20 - 1/40 = 1/40
40 minutes The answer is (C).