question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
(A) 2560
(B) 3400
(C) 3690
(D) 4500
(E) 5184
answer: 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).


q: P and Q can complete a work in 20 days and 12 days respectively. P alone started the work and Q joined him after 4 days till the completion of the work. How long did the work last?
Options:
(A) 5 days
(B) 9 days
(C) 30 days
(D) 20 days
(E) 10 days
a: Stream of consciousness: Work done by P in 1 day = 1/20
Work done by Q in 1 day = 1/12
Work done by P in 4 days = 4 × (1/20) = 1/5
Remaining work = 1 – 1/5 = 4/5
Work done by P and Q in 1 day = 1/20 + 1/12 = 8/60 = 2/15
Number of days P and Q take to complete the remaining work = (4/5) / (2/15) = 6
Total days = 4 + 6 = 10 The answer is (E).


question: How much 45% of 60 is greater than 35% of 40?
Options:
(A) 18
(B) 13
(C) 15
(D) 17
(E) 71
answer: Stream of consciousness: (45/100) * 60 – (35/100) * 40
27 - 14 = 13 The answer is (B).


q: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
Options:
(A) 26
(B) 27
(C) 29
(D) 32
(E) 36
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 19 = 99
So, the middle number is (126 - 99 ) = 27 The answer is (B).


question: What will come in place of the x in the following Number series? 612, 207, 72, 27, 12, x
Options:
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
answer: Stream of consciousness: 612
612 / 3 + 3 = 207
207 / 3 + 3 = 72
72 / 3 + 3 = 27
27 / 3 + 3 = 12
12 / 3 + 3 = 7 The answer is (B).


question: The length E of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?
Options:
(A) Decreases by 19%
(B) Decreases by 25%
(C) Increases by 6%
(D) Increases by 19%
(E) Increases by 25%
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: Let the length E of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy
Now after the change Length = 85x, and width = 140 y. Area = 11900xy
% Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence The answer is (D).