q: A and B can do a work in 12 days, B and C in 30 days and C and A in 36 days. In how many days will the work be completed, if all three of them work together?
Options:
(A) 180/15
(B) 180/10
(C) 180/13
(D) 180/15
(E) 180/11
a: Stream of consciousness: One day work of A and B = 1/12
One day work of B and C = 1/30
One day work of C and A = 1/36
2(A + B + C) = 1/12 + 1/30 + 1/36
2(A + B + C) = 13/90
(A + B + C) = 13/180
Number of days required = 180/13 days. The answer is (C).

question: The speed of a boat in still water is 30kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Options:
(A) kmph
(B) kmph
(C) kmph
(D) kmph
(E) kmph
answer: Stream of consciousness: Speed downstream = 30+ 20 = 50 kmph
Speed upstream = 30 - 20 = 10 kmph The answer is (B).

q: If a company allocates 10 percent of its budget to advertising, 10 percent to capital improvements, and 72 percent to salaries, what fraction of its budget remains for other allocations?
Options:
(A) 4/5
(B) 2/25
(C) 3/10
(D) 1/5
(E) 1/10
a: Stream of consciousness: 10 + 10 + 72 = 92% 100 - 92 = 8% to all others The answer is (B).

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) 6/18
(B) 6/11
(C) 6/68
(D) 6/19
(E) 6/12
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: A can do a work in 9 days and B can do the same work in 27 days. If they work together, in how many days will they complete the work?
Options:
(A) 6 3/4 days
(B) 7 3/4 days
(C) 5 3/4 days
(D) 6 1/4 days
(E) 6 2/4 days
a: Stream of consciousness: One day's work of A and B = 1/9 + 1/27 = (3+1)/27 = 4/27 So, the time taken to complete the work is 6 3/4 days. The answer is (A).

q: Amy, Bob, Cindy, and Daniel all have the same birthday, but they are all different ages. Today is their birthday. Cindy's age is divisible by Bob's age, and Amy's age is divisible by Cindy's age. If A is Amy's age in years, B is Bob's age, and C is Cindy's age, which of the following CANNOT be Daniel's age?
Options:
(A) AC/B
(B) (A+C) /B
(C) (A+B) /C
(D) AB/C
(E) (A-C) /B
a:
Stream of consciousness: Since today's is Daniel's birthday, his age must be an integer. As per the question, let A = 12, B = 2, and C = 6. Plugging these into the answer choices, only C does not yield an integer. The answer is (C).