GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 31 May 2020, 00:29

### 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

# Factorials, divisibility & composite doubt

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 18 Mar 2019
Posts: 13
Factorials, divisibility & composite doubt  [#permalink]

### Show Tags

16 Jul 2019, 23:18
Hi. I have a bit of a vague question if anybody can help fill in the blanks.

1) Is 5!+2 a composite? Why?
2) How is 5!+3 divisible by 3?
3) is 6!+3 a composite?

I do understand it when I open up 5! But if someone could help me with the logic of figuring this out, I'd be very grateful.

Posted from my mobile device
SVP
Joined: 20 Jul 2017
Posts: 1506
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: Factorials, divisibility & composite doubt  [#permalink]

### Show Tags

17 Jul 2019, 04:44
2
Dhwani12 wrote:
Hi. I have a bit of a vague question if anybody can help fill in the blanks.

1) Is 5!+2 a composite? Why?
2) How is 5!+3 divisible by 3?
3) is 6!+3 a composite?

I do understand it when I open up 5! But if someone could help me with the logic of figuring this out, I'd be very grateful.

Posted from my mobile device

5! = 1x2x3x4x5
So, if you agree that 5! Can be written as 2k, for some positive integer k
Or
3m, for some positive integer m
And
6! Can be written as 3n, for some positive integer n

1) Is 5!+2 a composite? Why?
—> 2k + 2 = 2(k + 1)
—> factors are 1, 2, k+1 & 2(k+1)
So, composite

2) How is 5!+3 divisible by 3?
—> 3m + 3 = 3(m+1)
—> factors are 1, 3, m+1 & 3(m+1)
So, composite

3) is 6!+3 a composite?
—> 3n + 3 = 3(n+1)
—> factors are 1, 3, n+1 & 3(n+1)
So, composite
GMAT Tutor
Joined: 16 Sep 2014
Posts: 489
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Factorials, divisibility & composite doubt  [#permalink]

### Show Tags

10 Aug 2019, 05:33
5! is a multiple of 2, 3, 4, and 5. This means 5! + 3 is a multiple of 3 plus 3, therefore it is a multiple of 3.
5!+2 is even because 5! and 2 are even, and even + even = even. This means 5!+2 is divisible by at least 3 factors: 5!+2, 1, 2. Thus it is composite.
6!+3 is a multiple of 3 + 3, so it is divisible by at least 3 factors: 6!+3, 3, and 1. Thus it is also composite.
_________________
Source: We are an NYC based, in-person and online GMAT tutoring and prep company. We are the only GMAT provider in the world to guarantee specific GMAT scores with our flat-fee tutoring packages, or to publish student score increase rates. Our typical new-to-GMAT student score increase rate is 3-9 points per tutoring hour, the fastest in the world. Feel free to reach out!
Factorials, divisibility & composite doubt   [#permalink] 10 Aug 2019, 05:33

# Factorials, divisibility & composite doubt

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne