question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
(A) 2435
(B) 1243
(C) 1509
(D) 3456
(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: Some persons can do a piece of work in 32 days. Two times the number of these people will do half of that work in?
Options:
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
a: Stream of consciousness: 32/ (2 * 2) = 8 days The answer is (E).


question: Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
Options:
(A) 5/9
(B) 5/4
(C) 5/1
(D) 5/6
(E) 5/2
answer: Stream of consciousness: P(at least one graduate) = 1 - P(no graduates)
(6 * 5 * 4)/(10 * 9 * 8) = 5/6 The answer is (D).


q: 5,9,18,31,52,__
Options:
(A) 79
(B) 80
(C) 86
(D) 82
(E) 83
a: Stream of consciousness: (9+5) +4 = 18
(16+9) +6 = 31
(28+16)+8 = 52
(48+28)+10 = 86 The answer is (C).


question: Find the greatest four digit number which leaves respective remainders of 2 and 5 when divided by 15 and 24.
Options:
(A) 9974
(B) 9125
(C) 9565
(D) 9997
(E) None of these
answer: Stream of consciousness: Since the difference between the divisors and the respective remainders is not constant, back substitution is the convenient method. None of the given numbers is satisfying the condition. The answer is (E).


question: A and B can do a work in 12 days, B and C in 30 days and C and A in 36 days. In how many days will the work be completed, if all three of them work together?
Options:
(A) 189/13 days
(B) 188/13 days
(C) 180/13 days
(D) 180/17 days
(E) 280/13 days
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: One day work of A and B = 1/12
One day work of B and C = 1/30
One day work of C and A = 1/36
2(A + B + C) = 1/12 + 1/30 + 1/36
2(A + B + C) = 13/90
(A + B + C) = 13/180
Number of days required = 180/13 days. The answer is (C).