It is currently 18 Jun 2019, 08:54

### 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

# Which of the following is a factor of 18!+1?

Author Message
TAGS:
Director
Joined: 16 May 2014
Posts: 595
GRE 1: Q165 V161
Followers: 97

Kudos [?]: 475 [0], given: 64

Which of the following is a factor of 18!+1? [#permalink]  08 May 2016, 02:51
Expert's post
00:00

Question Stats:

53% (01:06) correct 46% (00:53) wrong based on 30 sessions
Which of the following is a factor of 18!+1?
A. 15
B. 17
C. 19
D. 33
E. 39

Kudos for best explanation! This is a tricky one!
[Reveal] Spoiler: OA
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 09 May 2016
Posts: 161
Location: United States
Followers: 4

Kudos [?]: 140 [5] , given: 0

Re: Which of the following is a factor of 18!+1? [#permalink]  09 May 2016, 15:11
5
KUDOS
Expert's post
soumya1989 wrote:
Which of the following is a factor of 18!+1?
A. 15
B. 17
C. 19
D. 33
E. 39

Kudos for best explanation! This is a tricky one!

In solving this question, we must remember the rule that two consecutive integers will never share the same prime factors. Thus, since 18! and 18! + 1 are two consecutive integers, they do not share the same prime factors.

Also we must remember that n! is divisible by any prime number less than or equal to n, but it’s not divisible by any prime number greater than n. For example, 5! is divisible by 2, 3 and 5, but it’s not divisible by 7, 11, 13, etc. Furthermore, n! is divisible by the product of any two distinct prime numbers less than or equal to n. For example, 5! is divisible by 6 (which 2 x 3), 10 (which is 2 x 5) and 15 (which is 3 x 5).

Therefore, 18! is divisible by 15 (which is 3 x 5), 17, 33 (which is 3 x 11), and 39 (which is 3 x 13). However 18! is not divisible by 19 since 19 > 18. Since 18! and 18! + 1 do not share the same prime factors, 19 must be a prime factor of 18! + 1.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
22 Reviews

5-star rated online GRE quant
self study course

See why Target Test Prep is the top rated GRE quant course on GRE Prep Club. Read Our Reviews

Intern
Joined: 06 Oct 2016
Posts: 7
Followers: 0

Kudos [?]: 1 [0], given: 1

Re: Which of the following is a factor of 18!+1? [#permalink]  18 Dec 2016, 13:55
18! is divisible by 15 (which is 3 x 5), 17, 33 (which is 3 x 11), and 39 (which is 3 x 13). How can you write this, we know that n! is divisible by any prime number less than or equal to n, then 18! is divisible by any prime number less than or equal to n, we found that 18! is divisible by only 2, 3 and 3, i cant understand your explanation! please, can you explain it again? thanks!
GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4810
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 118

Kudos [?]: 1897 [2] , given: 397

Re: Which of the following is a factor of 18!+1? [#permalink]  18 Dec 2016, 14:11
2
KUDOS
Expert's post
The main rule is that two consecutive integers cannot have the same prime factors.

For example 6 can be factorized 2 and 3 but 7 does not have factors 2 and 3.

Factors of 18! cannot be factors of 18!+1.

All the other options apart from C are factors of 18!.

Hence C is the only option possible.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Intern
Joined: 03 Aug 2018
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: Which of the following is a factor of 18!+1? [#permalink]  09 Aug 2018, 06:59
Hi Guys,

I understand perfectly well the explanation. And, although is a little old the post, does the question need to be edited to: "Which of the following is not a factor of 18!+1?
Director
Joined: 09 Nov 2018
Posts: 508
Followers: 0

Kudos [?]: 27 [0], given: 1

Re: Which of the following is a factor of 18!+1? [#permalink]  29 Dec 2018, 14:43
josemu wrote:
Hi Guys,

I understand perfectly well the explanation. And, although is a little old the post, does the question need to be edited to: "Which of the following is not a factor of 18!+1?

In this case probably no.
Re: Which of the following is a factor of 18!+1?   [#permalink] 29 Dec 2018, 14:43
Display posts from previous: Sort by