q: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 16. What is the middle number?
Options:
(A) 27
(B) 29
(C) 36
(D) 34
(E) 35
a: Stream of consciousness: The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 14+3 X 16 = 90
So, the middle number is (126 - 90 ) = 36 The answer is (C).


question: A, B and C can do a work in 4 days, 8 days and 12 days respectively. In how many days can all three of them working together, complete the work?
Options:
(A) 2 2/3
(B) 2 2/8
(C) 2 2/0
(D) 2 2/2
(E) 2 2/11
answer: Stream of consciousness: Work done by all three of them in one day = 1/4 + 1/8 + 1/12 = 11/24
The number of days required = 24/11 = 2 2/11 days. The answer is (E).


q: Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?
Options:
(A) 128
(B) 150
(C) 887
(D) 279
(E) 771
a: Stream of consciousness: 1/2 * 20(9 + 6) = 150 cm2 The answer is (B).


question: A and B can do a work in 5 days and 10 days respectively. A starts the work and B joins him after 2 days. In how many days can they complete the remaining work?
Options:
(A) 6
(B) 2
(C) 3
(D) 4
(E) 98
answer: Stream of consciousness: Work done by A in 2 days = 2/5
Remaining work = 3/5
Work done by both A and B in one day = 1/5 + 1/10 = 3/10
Remaining work = 3/5 * 10/3 = 2 day The answer is (B).


q: 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) 35, 25 kmph
(B) 80, 40 kmph
(C) 40, 60 kmph
(D) 50, 55 kmph
(E) 50, 65 kmph
a: Stream of consciousness: Speed downstream = 60 + 20 = 80 kmph
Speed upstream = 60 - 20 = 40 kmph The answer is (B).


q: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
(A) 3456
(B) 4567
(C) 4789
(D) 5678
(E) y=5184
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: Given Exp. = (12)3 x 64 = (12) 3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62 The answer is (E).