question: If six persons sit in a row, then the probability that three particular persons are always together is ?
Options:
(A) 1/6
(B) 1/2
(C) 1/5
(D) 1/2
(E) 1/1
answer: Stream of consciousness: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5 The answer is (C).
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question: A multiple choice test consists of 4 questions, and each question has 5 answer choices. In how many ways can the test be completed if every question is unanswered?
Options:
(A) 24
(B) 120
(C) 625
(D) 720
(E) 1024
answer: Stream of consciousness: 5 choices for each of the 4 questions, thus total of 5*5*5*5 = 5^4 = 625 ways. The answer is (C).
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question: The area of a side of a box is 120 sq cm. The area of the other side of the box is 72 sq cm. If the area of the upper surface of the box is 60 sq cm then find the volume of the box.
Options:
(A) 259200 cm3
(B) 86400 cm3
(C) 720 cm3
(D) Cannot be determined
(E) None of these
answer: Stream of consciousness: Volume of the box = √120×72×60 = 720 cm3 The answer is (C).
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question: A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?
Options:
(A) 30229
(B) 3000
(C) 278
(D) 274
(E) 287
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: 60*5:36*6:75*3
100: 72: 75
100/247 * 7410 = 3000 The answer is (B).
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