question: The average of twelve numbers is 7. The average of first nine numbers is 6 and the average of last two numbers is 10. What is the middle number?
Options:
(A) A) 9
(B) B) 10
(C) C) 12
(D) D) 7
(E) E) 13
answer: Stream of consciousness: The total of twelve numbers = 12X7 = 84
The total of first 9 and last 2 numbers is = 9 X 6+2 X 10 = 74
So, the middle number is (84 - 74 ) = 10 The answer is (B).


q: A can do a piece of work in 20 days. B in 15 days A and C in 12 days. In how many days can A finish the work if he is assisted by B on one day and C on the next, alternately?
Options:
(A) 9 days
(B) 8 days
(C) 5 days
(D) 54 days
(E) 2 days
a: Stream of consciousness: A + B = 1/20 + 1/15 = 7/60
A + C = 1/20 + 1/12 = 8/60
7/60 + 8/60 = 15/60 = 1/4
4 days * 2 = 8 days The answer is (B).


question: Of the families in City X in 1991, 60 percent owned a personal computer. The number of families in City X owning a computer in 1993 was 20 percent greater than it was in 1991, and the total number of families in City X was 9 percent greater in 1993 than it was in 1991. what percent of the families in City X owned a personal computer in 1993?
Options:
(A) 59%
(B) 55%
(C) 63%
(D) 66%
(E) 68%
answer: Stream of consciousness: Say a 100 families existed in 1991 then the number of families owning a computer in 1991 - 60
Number of families owning computer in 1993 = 60 * 120/100 = 72
Number of families in 1993 = 109
The percentage = 72/109 * 100 = 66%. The answer is (D).


q: A wheel rotates 20 times every minute and moves 30 cm during each rotation. How many metres does the wheel move in one hour?
Options:
(A) 360 metre
(B) 12 metre
(C) 320 metre
(D) 1200 metre
(E) 260 metre
a: Stream of consciousness: Number of times wheel moves in 1 hour = 20 * 30 = 1200
:. Distance moves = (1200*30) cms = 36000 cms
In metres = 360 metre The answer is (A).


question: Ravi can do a piece of work in 20 days while Prakash can do it in 40 days. In how many days will they finish it together?
Options:
(A) 5 7/9 days
(B) 6 7/9 days
(C) 5 1/9 days
(D) 5 7/2 days
(E) 4 7/9 days
answer: Stream of consciousness: 1/20 + 1/40 = 3/40
40/7 = 5 7/9 days The answer is (A).


question: A can do a piece of work in 12 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?
Options:
(A) 18
(B) 99
(C) 77
(D) 62
(E) 12
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: 8/12 + 6/x = 1
X = 18 days The answer is (A).