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QOTD#13 The integer m is a multiple of 154, 250, and 264.
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09 Nov 2016, 15:41
09 Nov 2016, 15:41
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Question Stats:
28% (03:00) correct
71% (02:39) wrong based on 121 sessions
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The integer m is a multiple of 154, 250, and 264. Which of the following do NOT have to be
factors of m?
Indicate all possible values
A. 176
B. 242
C. 275
D. 924
E. 2,500
F. 7,000
factors of m?
Indicate all possible values
A. 176
B. 242
C. 275
D. 924
E. 2,500
F. 7,000
Drill 3
Question: 12
Page: 290
Question: 12
Page: 290
Show: :: OA
A,B,E
Re: QOTD#13 The integer m is a multiple of 154, 250, and 264.
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09 Nov 2016, 15:45
09 Nov 2016, 15:45
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Explanation
To solve this question, turn large numbers into small numbers by working with factors. The prime factors of 154 are 2, 7, and 11; the prime factors of 264 are 2, 2, 2, 3, and 11; and the prime factors of 250 are 2, 5, 5, and 5. The only numbers that must be a factor of m are those made up of factors contained in the other three numbers. You can’t recount factors that overlap in the different numbers, so you know that m is made up of, at least, three 2’s, one 3, three 5’s, one 7, and one 11. Now check the answers. The prime factors of 176 are 2, 2, 2, 2, and 11, which is one 2 too many, so choice (A) is not a factor; since the question asks you to identify which choices are not factors, choice (A) is part of the credited response.
The prime factors of 242 are 2, 11, and 11, which is one 11 too many, so (B) is also not a factor. The prime factors of 275 are 5, 5, and 11, so choice (C) is a factor. The prime factors of 924 are 2, 2, 3, 7, and 11, so choice (D) is a factor. The prime factors of 2,500 are 2, 2, 5, 5, 5, and 5, which is one 5 too many, so choice (E) is not a factor. And, finally, the prime factors of 7,000 are 2, 2, 2, 5, 5, 5, and 7, so choice (F) is a factor. The correct answers are choices (A), (B), and (E).
To solve this question, turn large numbers into small numbers by working with factors. The prime factors of 154 are 2, 7, and 11; the prime factors of 264 are 2, 2, 2, 3, and 11; and the prime factors of 250 are 2, 5, 5, and 5. The only numbers that must be a factor of m are those made up of factors contained in the other three numbers. You can’t recount factors that overlap in the different numbers, so you know that m is made up of, at least, three 2’s, one 3, three 5’s, one 7, and one 11. Now check the answers. The prime factors of 176 are 2, 2, 2, 2, and 11, which is one 2 too many, so choice (A) is not a factor; since the question asks you to identify which choices are not factors, choice (A) is part of the credited response.
The prime factors of 242 are 2, 11, and 11, which is one 11 too many, so (B) is also not a factor. The prime factors of 275 are 5, 5, and 11, so choice (C) is a factor. The prime factors of 924 are 2, 2, 3, 7, and 11, so choice (D) is a factor. The prime factors of 2,500 are 2, 2, 5, 5, 5, and 5, which is one 5 too many, so choice (E) is not a factor. And, finally, the prime factors of 7,000 are 2, 2, 2, 5, 5, 5, and 7, so choice (F) is a factor. The correct answers are choices (A), (B), and (E).
General Discussion
Re: QOTD#13 The integer m is a multiple of 154, 250, and 264.
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15 Oct 2018, 10:56
15 Oct 2018, 10:56
Is it feasible to work this out in 1'45"?
