question: A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 70 minutes. When both pipes are opened, find when the cistern will be full?
Options:
(A) 17 minutes
(B) 87 minutes
(C) 70 minutes
(D) 28 minutes
(E) 11 minutes
answer: Stream of consciousness: 1/20 - 1/70 = 1/28
28 minutes The answer is (D).


q: Two trains are traveling on parallel tracks in the same direction. The faster train travels at 130 miles per hour, while the slower train travels at 100 miles per hour. At 3 o’clock the faster train is 15 miles behind the slower one. How far apart are the two trains at 5 o'clock?
Options:
(A) 45 miles
(B) 80 miles
(C) 90 miles
(D) 120 miles
(E) 400 miles
a: Stream of consciousness: Answer = A. 45 miles
Relational speed = 130 - 100 = 30 miles per hour
In 2 hours, difference = 30 * 2 = 60 miles
Fast train trailing 15 miles, so effective difference = 60 - 15 = 45 miles The answer is (A).


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


q: Sixteen telegenic contestants with a variety of personality disorders are to be divided into two “tribes” of three members each, tribe A and tribe B, for a competition. How many distinct groupings of two tribes are possible?
Options:
(A) 120
(B) 126
(C) 252
(D) 560
(E) 1260
a: Stream of consciousness: My ans is 16C3 = 560 The answer is (D).


question: The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Options:
(A) 80,70 kmph
(B) 87,40 kmph
(C) 80,40 kmph
(D) 70,40 kmph
(E) 80,44 kmph
answer: Stream of consciousness: Speed downstream = 60 + 20 = 80 kmph
Speed upstream = 60 - 20 = 40 kmph The answer is (C).


question: Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 170 m and 100 m respectively. The time they will take to pass each other completely is?
Options:
(A) 3 sec
(B) 8 sec
(C) 9 sec
(D) 5 sec
(E) 7 sec
answer:

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
Stream of consciousness: 70 + 50 = 120 * 5/18 = 100/3 mps
D = 170 + 100 = 270 m
T = 270 * 3/100 = 8 sec The answer is (B).