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

 It is currently 24 May 2020, 23:44 ### 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.  # N! is ending with x zeroes. (N + 3)! is ending with (x + 2) zeroes. Ho

Author Message
TAGS:

### Hide Tags

DS Forum Moderator V
Joined: 19 Oct 2018
Posts: 1826
Location: India
N! is ending with x zeroes. (N + 3)! is ending with (x + 2) zeroes. Ho  [#permalink]

### Show Tags

5 00:00

Difficulty:   55% (hard)

Question Stats: 68% (02:32) correct 32% (03:24) wrong based on 22 sessions

### HideShow timer Statistics

N! is ending with x zeroes. (N + 3)! is ending with (x + 2) zeroes. How many such N's will exist, given N is positive integer less than 50?

A. 5
B. 6
C. 7
D. 8
E. 9
SVP  V
Joined: 20 Jul 2017
Posts: 1506
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: N! is ending with x zeroes. (N + 3)! is ending with (x + 2) zeroes. Ho  [#permalink]

### Show Tags

1
nick1816 wrote:
N! is ending with x zeroes. (N + 3)! is ending with (x + 2) zeroes. How many such N's will exist, given N is positive integer less than 50?

A. 5
B. 6
C. 7
D. 8
E. 9

We have to understand that to increase 2 number of 0's, (n+3) should have either '25' or '50' {25x4 = 100, 50x4 = 200) and 'n' SHOULD NOT have any of '25' and '50'. Only then there would be an addition of 2 0's

So, possible values of n are 22, 23, 24, 47, 48 and 49.

IMO B.
ISB School Moderator P
Joined: 08 Dec 2013
Posts: 776
Location: India
Concentration: Nonprofit, Sustainability
Schools: ISB
GMAT 1: 630 Q47 V30 WE: Operations (Non-Profit and Government)
Re: N! is ending with x zeroes. (N + 3)! is ending with (x + 2) zeroes. Ho  [#permalink]

### Show Tags

3
nick1816 wrote:
N! is ending with x zeroes. (N + 3)! is ending with (x + 2) zeroes. How many such N's will exist, given N is positive integer less than 50?

A. 5
B. 6
C. 7
D. 8
E. 9

I've used two concepts-

1. In any n! the number of zeroes is primarily contributed by 5s in the product. (we have more 2s in comparison to 5)
2. Box Function- to calculate the number of zeroes in a factorial. Trailing Zeroes: https://gmatclub.com/forum/how-many-tra ... l#p2190991

Interesting facts- Number of 5s gets bumped at 25, 50 etc.

Possible combinations: (N, N+3); N<50
22, 25
23, 26
24, 27

47, 50
48, 51
49, 52

So, 6 Ns are possible. B
CEO  V
Joined: 03 Jun 2019
Posts: 2889
Location: India
GMAT 1: 690 Q50 V34 WE: Engineering (Transportation)
N! is ending with x zeroes. (N + 3)! is ending with (x + 2) zeroes. Ho  [#permalink]

### Show Tags

1
nick1816 wrote:
N! is ending with x zeroes. (N + 3)! is ending with (x + 2) zeroes. How many such N's will exist, given N is positive integer less than 50?

A. 5
B. 6
C. 7
D. 8
E. 9

N+3 = 5^2k = 25k form
N+3 = {25,50}
N = {22,23,24,47,48,49}

IMO B
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com N! is ending with x zeroes. (N + 3)! is ending with (x + 2) zeroes. Ho   [#permalink] 28 Mar 2020, 04:16

# N! is ending with x zeroes. (N + 3)! is ending with (x + 2) zeroes. Ho  