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

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Intern
Joined: 27 Apr 2016
Posts: 12
Quantitative :: Data sufficiency:: 04074 (MBA.com practice question)  [#permalink]

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25 Jul 2018, 07:46
00:00

Difficulty:

(N/A)

Question Stats:

67% (00:07) correct 33% (01:31) wrong based on 3 sessions

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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
MBA Section Director
Affiliations: GMATClub
Joined: 22 May 2017
Posts: 1952
Concentration: Nonprofit
GPA: 4
WE: Engineering (Computer Software)
Quantitative :: Data sufficiency:: 04074 (MBA.com practice question)  [#permalink]

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25 Jul 2018, 08:08
1
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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Joined: 02 Sep 2009
Posts: 52386
Re: Quantitative :: Data sufficiency:: 04074 (MBA.com practice question)  [#permalink]

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25 Jul 2018, 09:34
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

This question is discussed here: https://gmatclub.com/forum/quantitative ... 71512.html

Please search before posting and name topics properly.

TOPIC IS LOCKED AND ARCHIVED.
_________________
Re: Quantitative :: Data sufficiency:: 04074 (MBA.com practice question) &nbs [#permalink] 25 Jul 2018, 09:34
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# Quantitative :: Data sufficiency:: 04074 (MBA.com practice question)

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