It is currently 23 Oct 2017, 10:34

### 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

# least value of N (m09q33)

Author Message
VP
Joined: 18 May 2008
Posts: 1258

Kudos [?]: 530 [3], given: 0

least value of N (m09q33) [#permalink]

### Show Tags

18 Mar 2009, 03:41
3
KUDOS
7
This post was
BOOKMARKED
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

What is the least $$N$$ such that $$N!$$ is divisible by 1000?

(A) 8
(B) 10
(C) 15
(D) 20
(E) 25

[Reveal] Spoiler: OA
C

Source: GMAT Club Tests - hardest GMAT questions

Kudos [?]: 530 [3], given: 0

Manager
Joined: 22 Feb 2009
Posts: 136

Kudos [?]: 149 [2], given: 10

Schools: Kellogg (R1 Dinged),Cornell (R2), Emory(Interview Scheduled), IESE (R1 Interviewed), ISB (Interviewed), LBS (R2), Vanderbilt (R3 Interviewed)
Re: least value of N [#permalink]

### Show Tags

18 Mar 2009, 04:21
2
KUDOS
Ans C
1000= 5^3 * 2^3

Least Number that has 5^3 * 2^3 is 15!

Kudos [?]: 149 [2], given: 10

Senior Manager
Joined: 16 Apr 2006
Posts: 270

Kudos [?]: 240 [0], given: 2

Re: least value of N (m09q33) [#permalink]

### Show Tags

03 Sep 2010, 04:41
C.
15! has 10*(4*5)*(8*15) = atleast 3 0's at the end
_________________

Trying hard to achieve something unachievable now....

Kudos [?]: 240 [0], given: 2

Director
Joined: 21 Dec 2009
Posts: 582

Kudos [?]: 835 [7], given: 20

Concentration: Entrepreneurship, Finance
Re: least value of N (m09q33) [#permalink]

### Show Tags

03 Sep 2010, 05:28
7
KUDOS
1000 = 2^3 x 5^3
so, we are looking for a number N such that N! contains at least 2^3 x 5^3 as factors.
A. 8! = 2^3.7.6.5.4! .... only 2^3.5 wrong
B. 10! = (2*5).9.8.7.6.5.4!...only 2^3.5^2 wrong, we need an additional 5.
C. 15! = (3*5).(2*7).13.(2*6).11.(2*5).9.8! 2^3.5^3 is available in 15!...corect
D. 20! we looking for the least- 20! is not necessary
E. 25! same as option D
_________________

KUDOS me if you feel my contribution has helped you.

Kudos [?]: 835 [7], given: 20

Math Expert
Joined: 02 Sep 2009
Posts: 41913

Kudos [?]: 129475 [3], given: 12201

Re: least value of N (m09q33) [#permalink]

### Show Tags

03 Sep 2010, 05:44
3
KUDOS
Expert's post
1
This post was
BOOKMARKED
ritula wrote:
What is the least $$N$$ such that $$N!$$ is divisible by 1000?

(A) 8
(B) 10
(C) 15
(D) 20
(E) 25

[Reveal] Spoiler: OA
C

Source: GMAT Club Tests - hardest GMAT questions

$$n!$$ to be divisible by 1,000 it must have 3 trailing zeros. So $$n$$ must have 3 factors of 5 in it, so the answer is 15 as 15/5=3.

For more on trailing zeros see: everything-about-factorials-on-the-gmat-85592.html

Hope it helps.
_________________

Kudos [?]: 129475 [3], given: 12201

Manager
Joined: 27 Jul 2010
Posts: 190

Kudos [?]: 46 [0], given: 15

Location: Prague
Schools: University of Economics Prague
Re: least value of N (m09q33) [#permalink]

### Show Tags

03 Sep 2010, 05:52
Since 1000 = 2^3 x 5^3 we need 3 times 5 to do that job. 5*10*15 makes this. simple. C
_________________

You want somethin', go get it. Period!

Kudos [?]: 46 [0], given: 15

Manager
Joined: 20 Oct 2009
Posts: 104

Kudos [?]: 49 [0], given: 0

Re: least value of N (m09q33) [#permalink]

### Show Tags

04 Sep 2010, 08:16
1000= 2^3 * 5^3

So you need at least a number that will repeat the 5 three times for you.....C

ritula wrote:
What is the least $$N$$ such that $$N!$$ is divisible by 1000?

(A) 8
(B) 10
(C) 15
(D) 20
(E) 25

[Reveal] Spoiler: OA
C

Source: GMAT Club Tests - hardest GMAT questions

_________________

Dream the impossible and do the incredible.

Live. Love. Laugh.

Kudos [?]: 49 [0], given: 0

Intern
Joined: 07 Jun 2009
Posts: 24

Kudos [?]: 10 [1], given: 4

Re: least value of N (m09q33) [#permalink]

### Show Tags

05 Sep 2010, 09:33
1
KUDOS
For such questions, always work through the answers choice from lowest to highest i.e. A to E. The moment you get an answers that matches, stop and mark that as the answer and move on.

1000 = 2^3 x 5^3
N! has to contain 2^3 x 5^3 as factors.
A) 8! --> only 2^3 * 5^1 --> wrong
B) 10! --> only 2^3 * 5^2 --> wrong
C) 15! = --> 2^3 * 5^3 --> BINGO
_________________

If you like my post, consider giving me a kudos. THANKS!

Kudos [?]: 10 [1], given: 4

Intern
Joined: 02 Sep 2010
Posts: 7

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

Re: least value of N (m09q33) [#permalink]

### Show Tags

09 Sep 2010, 11:06
For the N! to be divisible by 1,000, it needs 3 5's and 3 2's in it (5^3 and 2^3). We can just look at 5's since 2's will be more abundant. There are some good posts on divisibility by factors of 10 that work out this more clearly.

As we go up from 1!, we would get a 5 in each of: 5, 10, and 15. If you want to check there are three 2's by the time you get to 4! so we're covered. 15! will be the first that is divisible by 1,000.

It might be tempting to look at 10! since you get above 100 so quickly, but 10! if 3,628,800, which /1,000 is not an integer (done in excel, not needed on the test or if you understand the concepts.

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

Manager
Joined: 27 Jul 2010
Posts: 86

Kudos [?]: 22 [0], given: 6

Re: least value of N (m09q33) [#permalink]

### Show Tags

08 Sep 2011, 04:55
since 1000 = 2*2*2*5*5*5
N! should include three 5s => 5, 10 & 15

Kudos [?]: 22 [0], given: 6

Senior Manager
Joined: 01 Nov 2010
Posts: 284

Kudos [?]: 85 [0], given: 44

Location: India
Concentration: Technology, Marketing
GMAT Date: 08-27-2012
GPA: 3.8
WE: Marketing (Manufacturing)
Re: least value of N (m09q33) [#permalink]

### Show Tags

08 Sep 2011, 05:04
easy..
ans is C.
1000=5*5*5*2*2*2
2 wont create any problem , we need to look for 5.
min no in which we will get three 5 is 15 (5,10,15).

15!=1*2*3*4*5*6*7*8*9*10*11*12*13*14*15
_________________

kudos me if you like my post.

Attitude determine everything.
all the best and God bless you.

Kudos [?]: 85 [0], given: 44

Manager
Joined: 08 Sep 2011
Posts: 68

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

Concentration: Finance, Strategy
Re: least value of N (m09q33) [#permalink]

### Show Tags

08 Sep 2011, 11:09
C.1000= 5^3 * 2^3 so you need 3 5's in your answer, which C gives you. or that's at least my thought process

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

Manager
Joined: 04 Jun 2011
Posts: 182

Kudos [?]: 56 [0], given: 21

Re: least value of N (m09q33) [#permalink]

### Show Tags

08 Sep 2011, 12:37
Bunuel rocks!! i used his method to get this answer in 10 sec.

Kudos [?]: 56 [0], given: 21

Manager
Joined: 11 Feb 2011
Posts: 70

Kudos [?]: 2 [0], given: 0

Re: least value of N (m09q33) [#permalink]

### Show Tags

08 Sep 2011, 15:56
easy one C is the answer

Kudos [?]: 2 [0], given: 0

Manager
Affiliations: NABE
Joined: 25 Apr 2010
Posts: 66

Kudos [?]: 18 [0], given: 8

Location: United States
Concentration: Strategy
GPA: 3.1
WE: Marketing (Energy and Utilities)
Re: least value of N (m09q33) [#permalink]

### Show Tags

25 Oct 2011, 22:00
sarathy wrote:
For such questions, always work through the answers choice from lowest to highest i.e. A to E. The moment you get an answers that matches, stop and mark that as the answer and move on.

I would add that for "least" questions this should be done. The opposite should be done for "greatest".

Kudos [?]: 18 [0], given: 8

Director
Status: Final Countdown
Joined: 17 Mar 2010
Posts: 535

Kudos [?]: 354 [0], given: 75

Location: India
GPA: 3.82
WE: Account Management (Retail Banking)
Re: least value of N (m09q33) [#permalink]

### Show Tags

10 Sep 2012, 09:09
What is the least $$N$$ such that $$N!$$ is divisible by 1000?

we need "three zeros" in the factorial multiplication as 1000 has it in.

(A) 8
it will have only one zero - 2 & 5 will multiply and get one zero- incorrect

(B) 10
it will give two zeros- 2&5 will give one zero ; 10 will have one - incorrect

(C) 15
it will give 3 zeros - 2&5;10;12&15 -correct

(D) 20
more than 3 zeros

(E) 25
more than 3 zeros
_________________

" Make more efforts "
Press Kudos if you liked my post

Kudos [?]: 354 [0], given: 75

Current Student
Status: Go Bruins! UCLA Anderson bound
Joined: 31 Aug 2012
Posts: 168

Kudos [?]: 56 [0], given: 102

GMAT 1: 740 Q48 V44
GPA: 3.35
Re: least value of N (m09q33) [#permalink]

### Show Tags

10 Sep 2012, 12:06
Bunuel that is awesome. Great time saver. Thank you kindly.
_________________

If you can't be first, be ahead of who's second.

Kudos [?]: 56 [0], given: 102

BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2212

Kudos [?]: 845 [0], given: 595

Re: least value of N (m09q33) [#permalink]

### Show Tags

10 Nov 2016, 12:16
Here for n! to be divisible by 1000 it must have at-least 3 fives as the number of 2's will always be ample.
To have 3 fives n must be 15.
Hence C
_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 845 [0], given: 595

Re: least value of N (m09q33)   [#permalink] 10 Nov 2016, 12:16
Display posts from previous: Sort by

# least value of N (m09q33)

Moderator: Bunuel

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.