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If k = 19!/16!, which of the following is the smallest choice that do

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Bunuel
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If k = 19!/16!, which of the following is the smallest choice that do [#permalink] New post   13 Jul 2021, 03:30
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If k = 19!/16!, which of the following is the smallest choice that does not have a prime factor in common with k?

(A) 19
(B) 34
(C) 77
(D) 115
(E) 133
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C
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If k = 19!/16!, which of the following is the smallest choice that do [#permalink] New post   13 Jul 2021, 04:57
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Bunuel wrote:
If k = 19!/16!, which of the following is the smallest choice that does not have a prime factor in common with k?

(A) 19
(B) 34
(C) 77
(D) 115
(E) 133


\(k = \frac{19!}{16!} = \frac{19*18*17*16!}{16!} = 19*18*17 = 2*3^2*17*19\)

(A) 19 OUT
(B) 34 = 2*17 OUT
(C) 77 = 11*7 CORRECT
(D) 115 Bigger than 77 so OUT
(E) 133 Bigger than 77 so OUT

Answer: Option C
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Re: If k = 19!/16!, which of the following is the smallest choice that do [#permalink] New post   13 Jul 2021, 09:40
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Bunuel wrote:
If k = 19!/16!, which of the following is the smallest choice that does not have a prime factor in common with k?

(A) 19
(B) 34
(C) 77
(D) 115
(E) 133


\(k = \frac{19!}{16!} = 19*18*17 = 2*3^2*17*19\).

Choice A has 19 in common, choice B has 2 in common, choice C = 7*11 and k does not have a 7 or 11, so the answer is C.

Ans: C
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Re: If k = 19!/16!, which of the following is the smallest choice that do [#permalink] New post   17 Dec 2022, 00:08
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Re: If k = 19!/16!, which of the following is the smallest choice that do [#permalink]
17 Dec 2022, 00:08
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