q: Four of the following five parts numbered (a), (b), (c), (d) and (e) are exactly equal. The number of the part which is not equal to the other four parts is your answer.
Options:
(A) 2x2 – 3xy + y2
(B) (2x + y) (x – y) 
(C) (x – y) 2 + x(x – y) 
(D) (2x – y) 2 – x(2x – y) 
(E) (2x – y) 2 – 2x2 + xy
a: Stream of consciousness: Other parts are equal to
2x2 + y2 – 3xy. The answer is (B).


question: Find the third proportional to 2 and 10?
Options:
(A) 10
(B) 12
(C) 16
(D) 19
(E) 50
answer: Stream of consciousness: Formula = Third proportional = (b × b)/a
A = 2 and B = 10
(10 × 10)/ 2 = 100/2 = 50 The answer is (E).


q: Four of the following five parts numbered (a), (b), (c), (d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer.
Options:
(A) xy2 – x2y + 2x2y2
(B) xy2(1 – 2x)  + x2y(2y – 1) 
(C) xy2(1 + x)  – x2y(1 – y) 
(D) xy[y(1 + x)  – x(1 – y) ]
(E) xy(y – x + 2xy) 
a: Stream of consciousness: The other parts are equal to xy2 – x2y + 2x2y2. The answer is (B).


question: In what time will a railway train 40 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Options:
(A) 3
(B) 5
(C) 9
(D) 4
(E) 7
answer: Stream of consciousness: T = 40/36 * 18/5 = 4 sec The answer is (D).


q: A does a work in 10 days and B does the same work in 15 days. In how many days they together will do the same work?
Options:
(A) 1
(B) 6
(C) 7
(D) 5
(E) 43
a: Stream of consciousness: A's 1 day work = 1/10; B's 1 day work = 1/15
(A + B)'s 1 day work = (1/10 + 1/15) = 1/6
So, both together will finish the work in 6 days. The answer is (B).


q: Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:
Options:
(A) 9
(B) 7
(C) 6
(D) 5
(E) 4
a:

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: Let B be turned off after x minutes. Then, Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1. x(2/75 + 1/45) + (30 - x). 2/75 = 1 11x/225 + (60 - 2x)/75 = 1 11x + 180 - 6x = 225. x = 9. The answer is (A).