question: Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes?
Options:
(A) 5/11
(B) 6/11
(C) 7/11
(D) 8/11
(E) 9/11
answer: Stream of consciousness: Part filled by (A + B + C) in 3 minutes = 3(1/30 + 1/20 + 1/10) = 11/20
Part filled by C in 3 minutes = 3/10
Required ratio = 3/10 * 20/11 = 6/11 The answer is (B).

q: X can finish a work in 20 days. Y can finish the same work in 16 days. Y worked for 12 days and left the job. how many days does X alone need to finish the remaining work?
Options:
(A) 2
(B) 3
(C) 9
(D) 5
(E) 8
a: Stream of consciousness: Work done by X in 1 day = 1/20
Work done by Y in 1 day = 1/16
Work done by Y in 12 days = 12/16 = 3/4
Remaining work = 1 3/4 = 1/4
Number of days in which X can finish the remaining work = (1/4) / (1/20) = 5 The answer is (D).

question: There are four prime numbers written in ascending order of magnitude. The product of the first three is 7429 and of the last three is 12673. Find the fourth number?
A. 17 B. 29 C. 23 D. 31
Options:
(A) 17
(B) 29
(C) 23
(D) 31
(E) 33
answer: Stream of consciousness: (7429/12673) = 17/29 Fourth Number is 29 The answer is (B).

q: During a sale, the price of a pair of shoes is marked down 13% from the regular price. After the sale ends, the price goes back to the original price. What is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes?
Options:
(A) 9%
(B) 10%
(C) 11%
(D) 15%
(E) 90%
a: Stream of consciousness: Assume the price = 100
Price during sale = 87
Price after sale = 100
Percent increase = 13/87*100 = 15% approx. The answer is (D).

question: If x and y are unique prime integers, which of the following must be odd?
Options:
(A) xy^2
(B) 2x+2y
(C) 2x2y
(D) 2x/2y
(E) xy
answer: Stream of consciousness: Any number multiplied by 2 has to be an even number henc The answer is (E).

question: If P(A) = 8/15, P(B) = 4/15, and P(A B) = 16/15 Find P(B|A)
Options:
(A) 1/2
(B) 2/3
(C) 3/2
(D) 2
(E) 4/7
answer:
Stream of consciousness: P(B|A) = P(A B)/P(A)
P(B|A) = (16/15)/(8/15) = 2. The answer is (D).