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Is k a multiple of 14? (1) k > 13! (2) k = m!, where m is an integer g

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Is k a multiple of 14? (1) k > 13! (2) k = m!, where m is an integer g [#permalink] New post   17 Aug 2016, 12:18
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Is k a multiple of 14?

(1) k > 13!
(2) k = m!, where m is an integer greater than 6.
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B
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Bunuel
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Re: Is k a multiple of 14? (1) k > 13! (2) k = m!, where m is an integer g [#permalink] New post   17 Aug 2016, 12:24
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Is k a multiple of 14?

(1) k > 13! --> there are infinite multiples and non-multiples of 14 greater than any number. Not sufficient.

(2) k = m!, where m is an integer greater than 6 --> k can be 7!, 8!, 9!, 10!, ... In any case it's multiple of both 2 and 7, thus a multiple of 14. Sufficient.

Answer: B.

Hope it's clear.
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Re: Is k a multiple of 14? (1) k > 13! (2) k = m!, where m is an integer g [#permalink] New post   17 Aug 2016, 13:03
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(1) this simply states that K is larger than 13!. There are several numbers larger that is not divisible by 14. E.g 13!+1.

(2)
K=M!
M is an integer larger or equal to 7(as it was stated that IT is larger than 6 and is an integer).
M!=1*2*3*4*5*6*7....*m
We just need 2 and 7 as provided above.
Sufficient. Answer: B

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Donnie84
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Re: Is k a multiple of 14? (1) k > 13! (2) k = m!, where m is an integer g [#permalink] New post   18 Aug 2016, 20:23
St1: k > 13!

We are not told that k is an integer. Numerous possibilities galore.
Not sufficient.

St2: k = m!, where m is an integer greater than 6

Let's take m = 7
7! has 2 and 7 so k will be a multiple of 14.

For all integers m > 7, k will at least have a 2 and a 7 so it will always be a multiple of 14.
Sufficient.

Answer (B).
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Re: Is k a multiple of 14? (1) k > 13! (2) k = m!, where m is an integer g [#permalink] New post   21 Aug 2016, 03:00
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Statement 1 => let K be K!+0.243974979270 => clearly this isn't a multiple of 14
Statement 2 => K must be an integer and k must be at-least 7! because of the ! sign => a 2 and a 7 must be present in K all times.
Suff.
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Re: Is k a multiple of 14? (1) k > 13! (2) k = m!, where m is an integer g [#permalink] New post   19 Oct 2022, 01:16
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Re: Is k a multiple of 14? (1) k > 13! (2) k = m!, where m is an integer g [#permalink]
19 Oct 2022, 01:16
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