 It is currently 19 Jun 2019, 22:57 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. Let n = 11!. What is the smallest non-prime positive intege  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Founder  Joined: 18 Apr 2015
Posts: 6920
Followers: 114

Kudos [?]: 1344 , given: 6318

Let n = 11!. What is the smallest non-prime positive intege [#permalink]
Expert's post 00:00

Question Stats: 48% (01:25) correct 52% (02:15) wrong based on 25 sessions

Let n = 11!. What is the smallest non-prime positive integer that is not a factor of n?

[Reveal] Spoiler: OA
26

_________________ Director Joined: 03 Sep 2017
Posts: 520
Followers: 1

Kudos [?]: 356  , given: 66

Re: Let n = 11!. What is the smallest non-prime positive intege [#permalink]
1
KUDOS
To find the smallest non-prime number that is not a factor of k!, we have to take the first prime number greater than k and multiply it by 2 (at least for k greater than 6)
In our case, the smallest prime number greater than 11 is 13, that multiplied by 2 becomes 26.

More generally, the idea is to find the smallest number that cannot be computed as the product of any set of numbers composing 11!. With the rule above, the procedure of checking every number from 12 on is made faster
Intern Joined: 14 Jun 2018
Posts: 36
Followers: 0

Kudos [?]: 7 , given: 100

Re: Let n = 11!. What is the smallest non-prime positive intege [#permalink]
IlCreatore wrote:
To find the smallest non-prime number that is not a factor of k!, we have to take the first prime number greater than k and multiply it by 2 (at least for k greater than 6)
In our case, the smallest prime number greater than 11 is 13, that multiplied by 2 becomes 26.

More generally, the idea is to find the smallest number that cannot be computed as the product of any set of numbers composing 11!. With the rule above, the procedure of checking every number from 12 on is made faster

Could anyone please explain the general rule here for solving this kind of question when k>6? Intern  Joined: 04 May 2017
Posts: 36
Followers: 0

Kudos [?]: 26  , given: 6

Re: Let n = 11!. What is the smallest non-prime positive intege [#permalink]
1
KUDOS
m is non-integer -> m =a*b where a and b are primes in which one of them is not divisible by 11!. We must minimize a,b -> a=2, b=13 -> m=26.
_________________

Do not pray for an easy life, pray for the strength to endure a difficult one - Bruce Lee

Intern Joined: 04 Jun 2018
Posts: 5
Followers: 0

Kudos [?]: 0 , given: 2

Re: Let n = 11!. What is the smallest non-prime positive intege [#permalink]
25 also a non prime and neither hidden in n? Intern Joined: 08 Dec 2018
Posts: 8
Followers: 0

Kudos [?]: 6  , given: 2

Re: Let n = 11!. What is the smallest non-prime positive intege [#permalink]
1
KUDOS
mohanishpatel wrote:
25 also a non prime and neither hidden in n?

25 can be factor from 10 and 5
Intern Joined: 10 Feb 2019
Posts: 7
Followers: 0

Kudos [?]: 1 , given: 0

Re: Let n = 11!. What is the smallest non-prime positive intege [#permalink]
I didn't get it
Intern Joined: 08 Dec 2018
Posts: 8
Followers: 0

Kudos [?]: 6 , given: 2

Re: Let n = 11!. What is the smallest non-prime positive intege [#permalink]
NoorJassem wrote:
I didn't get it

let's take it the long way first so you could see it clearly

11! = 11*10*9*8*7*6*5*4*3*2*1

list of all non-prime number

1-11 are very obvious
12 - 3*4
14 - 7*2
15 - 5*3
16 - 8*2
18 - 9*2
20 - 10*2
21 - 7*3
22 - 11*2
24 - 8*3
25 - 5*5(factor out from 10 = 5*2)
26 - 2*13

since we do not have any factor of 13 in 11! 26 is not a factor of 11! GRE Instructor Joined: 10 Apr 2015
Posts: 1991
Followers: 60

Kudos [?]: 1806  , given: 9

Re: Let n = 11!. What is the smallest non-prime positive intege [#permalink]
1
KUDOS
Expert's post
Carcass wrote:

Let n = 11!. What is the smallest non-prime positive integer that is not a factor of n?

[Reveal] Spoiler: OA
26

GIVEN: x = (11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)

We can clearly see that x is divisible by 11, 10, 9, . . . 3, 2 and 1

So, let's start checking integers that are greater than 11

Is 12 a factor of x?
x = (11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)
= (11)(10)(9)(8)(7)(12)(5)(4)(3)(1)
12 is clearly a factor of x

13 is prime, so we can skip that.

Is 14 a factor of x?
x = (11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)
= (11)(10)(9)(8)(14)(6)(5)(4)(3)(1)
14 is clearly a factor of x

At this point, we can see the pattern.

15 = (5)(3). Since 5 and 3 are both in the product 11!, we know that 15 is a factor of x
16 = (8)(2). Since 8 and 2 are both in the product 11!, we know that 16 is a factor of x
17 is prime - skip
18 = (6)(3)
19 is prime - skip
20 = (4)(5)
21 = (7)(3)
22 = (11)(2)
23 is prime - skip
24 = (3)(8)
25. (5)(5) [aside: one 5 is hiding in the number 10]

26 = (2)(13) HOLD ON! There is no 13 hiding in the product 11!
So, 26 cannot be a factor of 11!

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com  Re: Let n = 11!. What is the smallest non-prime positive intege   [#permalink] 05 Mar 2019, 07:08
Display posts from previous: Sort by

Let n = 11!. What is the smallest non-prime positive intege  Question banks Downloads My Bookmarks Reviews Important topics  Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.