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

It is currently 16 Oct 2019, 23:02

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

How many zeroes are there at the end of the number N, if N = 100! + 20

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

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
B
Joined: 01 Nov 2015
Posts: 18
Reviews Badge
How many zeroes are there at the end of the number N, if N = 100! + 20  [#permalink]

Show Tags

New post 08 Jun 2016, 10:50
7
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

60% (01:24) correct 40% (01:40) wrong based on 228 sessions

HideShow timer Statistics

How many zeroes are there at the end of the number N, if N = 100! + 200! ?

A) 73
B) 49
C) 20
D) 48
E) 24
Marshall & McDonough Moderator
User avatar
D
Joined: 13 Apr 2015
Posts: 1684
Location: India
GMAT ToolKit User
Re: How many zeroes are there at the end of the number N, if N = 100! + 20  [#permalink]

Show Tags

New post 08 Jun 2016, 11:11
1
There are 24 trailing zeros in 100! and 49 trailing zeros in 200!

Addition of 100! and 200! will result in only 24 trailing zeros.

Answer: E
SVP
SVP
avatar
B
Joined: 06 Nov 2014
Posts: 1873
Re: How many zeroes are there at the end of the number N, if N = 100! + 20  [#permalink]

Show Tags

New post 09 Jun 2016, 03:50
aayushagrawal wrote:
How many zeroes are there at the end of the number N, if N = 100! + 200! ?

A) 73
B) 49
C) 20
D) 48
E) 24


The number of zeroes at the end of 100! will be less than the number of zeroes at the end of 200!
Hence it would be sufficient to calculate the number of zeroes at the end of 100!

Number of zeroes = [100/5] + [100/25] + [100/125] = 20 + 4 + 0 = 24

Correct Option: E
Senior Manager
Senior Manager
avatar
B
Joined: 13 Oct 2016
Posts: 359
GPA: 3.98
Re: How many zeroes are there at the end of the number N, if N = 100! + 20  [#permalink]

Show Tags

New post 16 Dec 2016, 04:14
1
aayushagrawal wrote:
How many zeroes are there at the end of the number N, if N = 100! + 200! ?

A) 73
B) 49
C) 20
D) 48
E) 24


\(100! + 200! = 100! (1 + 101*102*103* … *200)\)

Expression in the parenthesis will have \(1\) as its units digit. Hence we need to know only the number of trailing zeros at the end of \(100! = 24\)
Board of Directors
User avatar
D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4782
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User
Re: How many zeroes are there at the end of the number N, if N = 100! + 20  [#permalink]

Show Tags

New post 16 Dec 2016, 07:59
2
aayushagrawal wrote:
How many zeroes are there at the end of the number N, if N = 100! + 200! ?

A) 73
B) 49
C) 20
D) 48
E) 24


No of zeroes in the 100! + 200! will be the numebr of zeroes in 100!..

100! has 24 zeroes ..

100/5 = 20
20/5 = 4

So, the correct answer will be (E) 24

_________________
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 )
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3074
Re: How many zeroes are there at the end of the number N, if N = 100! + 20  [#permalink]

Show Tags

New post 31 Dec 2017, 11:00
1
1
aayushagrawal wrote:
How many zeroes are there at the end of the number N, if N = 100! + 200! ?

A) 73
B) 49
C) 20
D) 48
E) 24



While adding two numbers, the numbers of zeros will depend on the number with lesser number of zeros.

For example, 200 + 2000 will have only 2 trailing zeros and the number of zeros is limited by 200 which has 2 only zeros. [200 + 2000 = 2200]

So, instead of wasting time in finding the number of zeros of 200!, we can simply find the number of zeros in 100! and mark the answer.

The number of zeros in \(100! = \frac{100}{5} + \frac{20}{5} = 20 + 4 = 24\)

Hence the correct answer is Option E.


Regards,
Saquib
e-GMAT
Quant Expert
_________________
Manager
Manager
avatar
B
Joined: 08 Jul 2018
Posts: 73
Location: United States
Reviews Badge
Re: How many zeroes are there at the end of the number N, if N = 100! + 20  [#permalink]

Show Tags

New post 11 Jul 2018, 00:49
EgmatQuantExpert wrote:
aayushagrawal wrote:
How many zeroes are there at the end of the number N, if N = 100! + 200! ?

A) 73
B) 49
C) 20
D) 48
E) 24



While adding two numbers, the numbers of zeros will depend on the number with lesser number of zeros.

For example, 200 + 2000 will have only 2 trailing zeros and the number of zeros is limited by 200 which has 2 only zeros. [200 + 2000 = 2200]

So, instead of wasting time in finding the number of zeros of 200!, we can simply find the number of zeros in 100! and mark the answer.

The number of zeros in \(100! = \frac{100}{5} + \frac{20}{5} = 20 + 4 = 24\)

Hence the correct answer is Option E.


Regards,
Saquib
e-GMAT
Quant Expert



I don't understand this part here

The number of zeros in \(100! = \frac{100}{5} + \frac{20}{5} = 20 + 4 = 24\)

Can someone please explain?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58391
Re: How many zeroes are there at the end of the number N, if N = 100! + 20  [#permalink]

Show Tags

New post 11 Jul 2018, 00:54
1
jackjones wrote:
EgmatQuantExpert wrote:
aayushagrawal wrote:
How many zeroes are there at the end of the number N, if N = 100! + 200! ?

A) 73
B) 49
C) 20
D) 48
E) 24



While adding two numbers, the numbers of zeros will depend on the number with lesser number of zeros.

For example, 200 + 2000 will have only 2 trailing zeros and the number of zeros is limited by 200 which has 2 only zeros. [200 + 2000 = 2200]

So, instead of wasting time in finding the number of zeros of 200!, we can simply find the number of zeros in 100! and mark the answer.

The number of zeros in \(100! = \frac{100}{5} + \frac{20}{5} = 20 + 4 = 24\)

Hence the correct answer is Option E.


Regards,
Saquib
e-GMAT
Quant Expert



I don't understand this part here

The number of zeros in \(100! = \frac{100}{5} + \frac{20}{5} = 20 + 4 = 24\)

Can someone please explain?



Theory on Trailing Zeros: http://gmatclub.com/forum/everything-ab ... 85592.html

For more check Trailing Zeros Questions and Power of a number in a factorial questions in our Special Questions Directory.


Hope this helps.
_________________
Intern
Intern
avatar
B
Joined: 11 Oct 2018
Posts: 21
Location: Germany
Re: How many zeroes are there at the end of the number N, if N = 100! + 20  [#permalink]

Show Tags

New post 19 Jan 2019, 16:45
vitaliyGMAT wrote:
aayushagrawal wrote:
How many zeroes are there at the end of the number N, if N = 100! + 200! ?

A) 73
B) 49
C) 20
D) 48
E) 24


\(100! + 200! = 100! (1 + 101*102*103* … *200)\)

Expression in the parenthesis will have \(1\) as its units digit. Hence we need to know only the number of trailing zeros at the end of \(100! = 24\)


If the expression in the parentheses would end with 1 as units digit, then how can the whole expression have any trailing zeros?

Example:

\(100! < 200!\)

So small number + big number (with 1 as units digit):

\(200 + 200001=200201 -> no trailing zeros.\)

Can you please explain? vitaliyGMAT
GMAT Club Bot
Re: How many zeroes are there at the end of the number N, if N = 100! + 20   [#permalink] 19 Jan 2019, 16:45
Display posts from previous: Sort by

How many zeroes are there at the end of the number N, if N = 100! + 20

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





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