question: All of the bonds on a certain exchange are designated by a 3-letter, a 4-letter, or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different bonds that can be designate with these codes?
Options:
(A) 26(26^3 + 26^4) 
(B) 26(26^3 + 26^5) 
(C) 27(26^3 + 26^5) 
(D) 27(26^3)  + 26^5
(E) 26^3 + 27(26^5) 
answer: Stream of consciousness: 3-letter codes = 26^3;
4-letter codes = 26^4;
5-letter codes = 26^5;
Total = 26^3 + 26^4 + 26^5 = 26^3(1+26) + 26^5 = 26^3*27 + 26^5. The answer is (D).
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question: If six persons sit in a row, then the probability that three particular persons are always together is?
Options:
(A) 1/9
(B) 1/6
(C) 1/5
(D) 1/2
(E) 1/3
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: Express a speed of 720 kmph in meters per second?
Options:
(A) 120 mps
(B) 200 mps
(C) 181 mps
(D) 190 mps
(E) 125 mps
answer: Stream of consciousness: 720 * 5/18 = 200 mps The answer is (B).
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question: A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4 of a day?
Options:
(A) 22
(B) 77
(C) 26
(D) 41
(E) 66
answer:
Stream of consciousness: (1 man + 1 woman)'s 1 day work = (1/3 + 1/4) = 7/12 Work done by 1 man and 1 woman in 1/4 day = (7/12 * 1/4) = 7/48
Remaining work = (1 - 7/48) = 41/48
Work done by 1 boy in 1/4 day = ( 1/12 * 1/4) = 1/48
Number of boys required = 41/48 * 41 = 41. The answer is (D).
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question: All of the bonds on a certain exchange are designated by a 3-letter, a 4-letter, or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different bonds that can be designate with these codes?
Options:
(A) 26(26^3 + 26^4) 
(B) 26(26^3 + 26^5) 
(C) 27(26^3 + 26^5) 
(D) 27(26^3)  + 26^5
(E) 26^3 + 27(26^5) 
answer: Stream of consciousness: 3-letter codes = 26^3;
4-letter codes = 26^4;
5-letter codes = 26^5;
Total = 26^3 + 26^4 + 26^5 = 26^3(1+26) + 26^5 = 26^3*27 + 26^5. The answer is (D).
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question: If six persons sit in a row, then the probability that three particular persons are always together is?
Options:
(A) 1/9
(B) 1/6
(C) 1/5
(D) 1/2
(E) 1/3
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: Express a speed of 720 kmph in meters per second?
Options:
(A) 120 mps
(B) 200 mps
(C) 181 mps
(D) 190 mps
(E) 125 mps
answer: Stream of consciousness: 720 * 5/18 = 200 mps The answer is (B).
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question: A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4 of a day?
Options:
(A) 22
(B) 77
(C) 26
(D) 41
(E) 66
answer:
user
Stream of consciousness: (1 man + 1 woman)'s 1 day work = (1/3 + 1/4) = 7/12 Work done by 1 man and 1 woman in 1/4 day = (7/12 * 1/4) = 7/48
Remaining work = (1 - 7/48) = 41/48
Work done by 1 boy in 1/4 day = ( 1/12 * 1/4) = 1/48
Number of boys required = 41/48 * 41 = 41. The answer is (D).
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assistant
question: All of the bonds on a certain exchange are designated by a 3-letter, a 4-letter, or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different bonds that can be designate with these codes?
Options:
(A) 26(26^3 + 26^4) 
(B) 26(26^3 + 26^5) 
(C) 27(26^3 + 26^5) 
(D) 27(26^3)  + 26^5
(E) 26^3 + 27(26^5) 
answer: Stream of consciousness: 3-letter codes = 26^3;
4-letter codes = 26^4;
5-letter codes = 26^5;
Total = 26^3 + 26^4 + 26^5 = 26^3(1+26) + 26^5 = 26^3*27 + 26^5. The answer is (D).
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question: If six persons sit in a row, then the probability that three particular persons are always together is?
Options:
(A) 1/9
(B) 1/6
(C) 1/5
(D) 1/2
(E) 1/3
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: Express a speed of 720 kmph in meters per second?
Options:
(A) 120 mps
(B) 200 mps
(C) 181 mps
(D) 190 mps
(E) 125 mps
answer: Stream of consciousness: 720 * 5/18 = 200 mps The answer is (B).
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question: A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4 of a day?
Options:
(A) 22
(B) 77
(C) 26
(D) 41
(E) 66
answer:
Stream of consciousness: (1 man + 1 woman)'s 1 day work = (1/3 + 1/4) = 7/12 Work done by 1 man and 1 woman in 1/4 day = (7/12 * 1/4) = 7/48
Remaining work = (1 - 7/48) = 41/48
Work done by 1 boy in 1/4 day = ( 1/12 * 1/4) = 1/48
Number of boys required = 41/48 * 41 = 41. The answer is (D).
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