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Quantitative :: Data sufficiency:: 04074 (MBA.com practice question)

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Quantitative :: Data sufficiency:: 04074 (MBA.com practice question)  [#permalink]

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New post 25 Jul 2018, 08:46
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I really don't understand this question. Can anyone please help with solution?

Q: Does the integer k have a factor p such that 1 < p < k ?

(1) k > 4!
(2) 13! + 2 ≤ k ≤ 13! + 13

TIA
Archi
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Quantitative :: Data sufficiency:: 04074 (MBA.com practice question)  [#permalink]

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New post 25 Jul 2018, 09:08
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Does the integer k have a factor p such that 1 < p < k ?

The question is indirectly asking whether k is a prime number or not. Think about the definition of prime number. A prime number is not divisible by any integer other than 1 and itself. So, there wont exist a factor p such that 1 < p < k

Statement 1

k > 4!

There are inifinite prime numbers > 4! So we cannot find a unique value for k

Statement 1 is not sufficient

Statement 2

13! + 2 ≤ k ≤ 13! + 13

Now k can have following values

13!+3, 13!+4, 13!+5, 13!+6, .... 13!+12

For each case

if k = 13! + 3 = (1 * 2 * 3 * .... * 12 * 13) + 3 = 3 * (1 * 2 * 4 * ..... * 12 * 13 + 1 )

=> 3 is a factor of k

=> k is not prime

if k = 13! + 4 = (1 * 2 * 3 * 4 * .... * 12 * 13) + 4 = 4 * (1 * 2 * 3 * 5 * ..... * 12 * 13 + 1 )

=> 4 is a factor of k

=> k is not prime

Similarly 5 is a factor of k = 13! + 5, 6 is a factor of k = 13! + 6 and so on

Hence K is not prime

Statement 2 is sufficient

Hence option B
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Re: Quantitative :: Data sufficiency:: 04074 (MBA.com practice question)  [#permalink]

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New post 25 Jul 2018, 10:34
archimaitreya25 wrote:
I really don't understand this question. Can anyone please help with solution?

Q: Does the integer k have a factor p such that 1 < p < k ?

(1) k > 4!
(2) 13! + 2 ≤ k ≤ 13! + 13

TIA
Archi


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Re: Quantitative :: Data sufficiency:: 04074 (MBA.com practice question) &nbs [#permalink] 25 Jul 2018, 10:34
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