GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 15 Dec 2018, 01:15

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Free GMAT Strategy Webinar

     December 15, 2018

     December 15, 2018

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
  • $450 Tuition Credit & Official CAT Packs FREE

     December 15, 2018

     December 15, 2018

     10:00 PM PST

     11:00 PM PST

    Get the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)

If 200!/10^n is an integer, what is the largest possible value of n?

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51215
If 200!/10^n is an integer, what is the largest possible value of n?  [#permalink]

Show Tags

New post 28 Apr 2016, 02:36
2
8
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

58% (00:58) correct 42% (01:40) wrong based on 269 sessions

HideShow timer Statistics

Manager
Manager
avatar
B
Joined: 01 Jul 2010
Posts: 62
Location: India
GMAT 1: 660 Q43 V38
GPA: 3.4
GMAT ToolKit User
If 200!/10^n is an integer, what is the largest possible value of n?  [#permalink]

Show Tags

New post 28 Apr 2016, 04:44
1
1
We have to basically count the number of 5s withing 200
200/5 =40
200/5^2=8
200/5^3=1

We know for sure that there will be atleast 49 even numbers(multiples of 2)within 200

So there are 49 10s in 200!

The ans is E
Board of Directors
User avatar
P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4277
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member CAT Tests
If 200!/10^n is an integer, what is the largest possible value of n?  [#permalink]

Show Tags

New post 28 Apr 2016, 09:29
2
2
Bunuel wrote:
If 200!/10^n is an integer, what is the largest possible value of n?

A. 40
B. 42
C. 44
D. 48
E. 49


The question actually asks the highest power of 10 which divides 200! ( For a number to be an integer - Without any remainder all the trailing zeroe's must be divided by the denominator)

10 = 2 x 5


200 factorial will have 49 as -

200/5 = 40
40/5 = 8
8/5 =1

So answer will be (E) 49
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Current Student
avatar
B
Joined: 12 Jan 2016
Posts: 70
Location: United States
Concentration: Operations, General Management
GMAT 1: 690 Q49 V35
GPA: 3.5
WE: Supply Chain Management (Consumer Electronics)
Re: If 200!/10^n is an integer, what is the largest possible value of n?  [#permalink]

Show Tags

New post 04 May 2016, 16:15
1
3
The question is essentially asking "what is the number of trailing zeros in 200!".

Number of trailing zeros in n! is calculated as n/5 + n /\(5^{2}\) + n/\(5^{3}\)+...+n/\(5^{k}\) where \(n\leq{5^k}\)

So, number of trailing zeros in 200! = 200/5 + 200/25 + 200/125 = 40 + 8 + 1 = 49.
Director
Director
User avatar
B
Joined: 04 Jun 2016
Posts: 571
GMAT 1: 750 Q49 V43
Re: If 200!/10^n is an integer, what is the largest possible value of n?  [#permalink]

Show Tags

New post 25 Jul 2016, 05:16
Bunuel wrote:
If 200!/10^n is an integer, what is the largest possible value of n?

A. 40
B. 42
C. 44
D. 48
E. 49


\(10^n\) can be written as \((2*5)^n\) = \(2^n*5^n\)

SO we have to figure out how many 2 and 5 are in 200! and then we can remove the common number of 2 and 5 (thus removing 10) from the expression

2 is present 197 times in 200!
5 is present 49 times in 200!

Since 2*5 = 10 , so taking 49 as common we can remove \((2*5)^{49}\) or \(10^{49}\) from 200!
Answer is E
_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2627
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User Premium Member
Re: If 200!/10^n is an integer, what is the largest possible value of n?  [#permalink]

Show Tags

New post 28 Jul 2016, 10:44
Abhishek009 wrote:
Bunuel wrote:
If 200!/10^n is an integer, what is the largest possible value of n?

A. 40
B. 42
C. 44
D. 48
E. 49


The question actually asks the highest power of 10 which divides 200! ( For a number to be an integer - Without any remainder all the trailing zeroe's must be divided by the denominator)

10 = 2 x 5


200 factorial will have 49 as -

200/5 = 40
40/5 = 8
8/5 =1

So answer will be (E) 49


I didnt understand what you mean here.
Here is what i did =>
Number of two's are adequate , we need the number of 5's
5,5,5,5,5^2,5,5,5,5,5^2,5,5,5,5,5^2,5,5,5,5,5^2,5,5,5,5,5^3,5,5,5,5,5^2,5,5,5,5,5^2,5,5,5,5,5^2 => 49
Smash that E
_________________


MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

Director
Director
User avatar
B
Joined: 04 Jun 2016
Posts: 571
GMAT 1: 750 Q49 V43
If 200!/10^n is an integer, what is the largest possible value of n?  [#permalink]

Show Tags

New post 28 Jul 2016, 10:53
stonecold wrote:

I didnt understand what you mean here.
Here is what i did =>
Number of two's are adequate , we need the number of 5's
5,5,5,5,5^2,5,5,5,5,5^2,5,5,5,5,5^2,5,5,5,5,5^2,5,5,5,5,5^3,5,5,5,5,5^2,5,5,5,5,5^2,5,5,5,5,5^2 => 49
Smash that E


Seems like unnecessary counting and chances of skipping and missing a digit are high.
Also time factor is crucial.
Why don't you apply an easier formula to get the exact numbers of 5's in less than three or four steps ?
Frankly not to be harsh .. you method is rudimentary and inundated with numerous opportunities for silly careless mistakes, not to mention the eons it will take for such a counting.
Imagine if the question was \(\frac{3195!}{10^n}\)
_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

Current Student
User avatar
Joined: 18 Oct 2014
Posts: 846
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
GMAT ToolKit User
Re: If 200!/10^n is an integer, what is the largest possible value of n?  [#permalink]

Show Tags

New post 28 Jul 2016, 11:00
1
Bunuel wrote:
If 200!/10^n is an integer, what is the largest possible value of n?

A. 40
B. 42
C. 44
D. 48
E. 49


For 200!/10^n to be an integer. 200! must be a multiple of 10^n or (2*5)^n

Since 5 appears less than 2 does in 200!, 5 is the deciding factor in value of n

200/5= 40
200/5^2= 9

5 appears 40+9= 49 times, which is the maximum value of n

E is the answer
_________________

I welcome critical analysis of my post!! That will help me reach 700+

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9164
Premium Member
Re: If 200!/10^n is an integer, what is the largest possible value of n?  [#permalink]

Show Tags

New post 03 Sep 2018, 01:21
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: If 200!/10^n is an integer, what is the largest possible value of n? &nbs [#permalink] 03 Sep 2018, 01:21
Display posts from previous: Sort by

If 200!/10^n is an integer, what is the largest possible value of n?

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


cron
Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.