It is currently 21 Jan 2018, 08:26

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Does the integer k have a factor p such that 1 < p < k

Author Message
Manager
Status: I will not stop until i realise my goal which is my dream too
Joined: 25 Feb 2010
Posts: 221

Kudos [?]: 67 [0], given: 16

Schools: Johnson '15
Does the integer k have a factor p such that 1 < p < k [#permalink]

### Show Tags

25 Jun 2011, 22:23
00:00

Difficulty:

45% (medium)

Question Stats:

73% (00:31) correct 27% (01:35) wrong based on 11 sessions

### HideShow timer Statistics

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

1. k >= 4!
2. 13! + 2 =< k =< 13! + 13

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/does-the-inte ... 26735.html
[Reveal] Spoiler: OA

_________________

Regards,
Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat

Satyameva Jayate - Truth alone triumphs

Kudos [?]: 67 [0], given: 16

Manager
Status: I will not stop until i realise my goal which is my dream too
Joined: 25 Feb 2010
Posts: 221

Kudos [?]: 67 [0], given: 16

Schools: Johnson '15
Re: Does the integer k have a factor p such that 1 < p < k [#permalink]

### Show Tags

25 Jun 2011, 22:24
can somebody please explain me this?
_________________

Regards,
Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat

Satyameva Jayate - Truth alone triumphs

Kudos [?]: 67 [0], given: 16

Manager
Joined: 03 Jun 2010
Posts: 167

Kudos [?]: 73 [0], given: 40

Location: United States (MI)
Concentration: Marketing, General Management
Re: Does the integer k have a factor p such that 1 < p < k [#permalink]

### Show Tags

25 Jun 2011, 23:21
harshavmrg wrote:
can somebody please explain me this?

It's asked whether K is a prime number or no.
from 1) K might equal $$27$$ (and it has such factors as 3 or 9) or it can be $$29$$ (prime number without factors we need)
ins
(2)
write it in this way:
$$2*(1*3*4*...*13+1)<=K<=13*(1*2*3*...*12+1)$$
Now we see you can write any number fro this interval in such form.
Example: $$13!+7=7*(1*2*3*4*5*6*8*...*13+1)$$
we do have a factor that we ask to find.
So, it's (B).

Kudos [?]: 73 [0], given: 40

Math Expert
Joined: 02 Sep 2009
Posts: 43348

Kudos [?]: 139678 [0], given: 12794

Re: Does the integer k have a factor p such that 1 < p < k [#permalink]

### Show Tags

04 Dec 2017, 02:32
Does the integer k have a factor p such that 1<p<k?

Question basically asks whether $$k$$ is a prime number. If it is, then it won't have a factor $$p$$ such that $$1<p<k$$ (definition of a prime number).

(1) $$k>4!$$ --> $$k$$ is more than some number ($$4!=24$$). $$k$$ may or may not be a prime. Not sufficient.

(2) $$13!+2\leq{k}\leq{13!+13}$$ --> $$k$$ can not be a prime. For instance if $$k=13!+8=8*(2*4*5*6*7*9*10*11*12*13+1)$$, then $$k$$ is a multiple of 8, so not a prime. Same for all other numbers in this range. So, $$k=13!+x$$, where $$2\leq{x}\leq{13}$$ will definitely be a multiple of $$x$$ (as we would be able to factor out $$x$$ out of $$13!+x$$, the same way as we did for 8). Sufficient.

Check similar question: http://gmatclub.com/forum/factor-factorials-100670.html

OPEN DISCUSSION OF THIS QUESTION IS HERE: http://gmatclub.com/forum/does-the-inte ... 26735.html

If anything remains unclear please continue discussion there.
_________________

Kudos [?]: 139678 [0], given: 12794

Re: Does the integer k have a factor p such that 1 < p < k   [#permalink] 04 Dec 2017, 02:32
Display posts from previous: Sort by