NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 10:51 It is currently 26 Apr 2024, 10:51
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

What is the largest value of non negative integer N for which 10N is a

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
G
ashikaverma13
Manager
Manager
Joined: 19 Aug 2016
Posts: 129
Own Kudos [?]: 293 [59]
Given Kudos: 59
Location: India
Schools: ISB '20 (WD) Schulich Sept 18 Intake (A) Rotman '20 (S)
GMAT 1: 640 Q47 V31
GPA: 3.82
Send PM
Reviews Badge
What is the largest value of non negative integer N for which 10N is a [#permalink] New post   Updated on: 17 Jan 2017, 23:30
5
Kudos
54
Bookmarks
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

73% (01:08) correct 27% (01:23) wrong based on 851 sessions
Hide Show timer Statistics
What is the largest value of non negative integer N for which \(10^N\) is a factor of 50!?

A. 5
B. 6
C. 12
D. 15
E. 20
ShowHide Answer
Official Answer
C

Originally posted by ashikaverma13 on 17 Jan 2017, 12:38.
Last edited by abhimahna on 17 Jan 2017, 23:30, edited 1 time in total.
Edited the question.
Most Helpful Reply
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11181
Own Kudos [?]: 31957 [8]
Given Kudos: 291
Send PM
Reviews Badge
Re: What is the largest value of non negative integer N for which 10N is a [#permalink] New post   19 Jan 2017, 05:36
3
Kudos
5
Bookmarks
Expert Reply
ashikaverma13 wrote:
ashikaverma13 wrote:
What is the largest value of non negative integer N for which 10N is a factor of 50!?

A. 5
B. 6
C. 12
D. 15
E. 20




Thanks for your response!

Could you elaborate a bit more on the reasoning?

why do we have to find the no of 5s and how exactly did it come to 12?


Hi,
The reasoning for these type of Qs is...

What does ! Or factorial mean ..
It means product of all positive integers till that number..
So 50! Means 1*2*3*4*5....*49*50
Now when we multiply 2 and 5 we get a 10..
So 2s will be more than 5s and that is why number of 10s will be equal to number of 5s...

Now how do we find number of 5s in 50!..
When you divide by 5 you get all multiples of 5 till 50..
50/5=10..
These 10 numbers are 5,10,15,20,25,30,35,.40,45,50..
When we divide by 25 we get numbers which had 5^2 in it..
50/25 =2..
And these are 25 Aand 50..
So you have 12 5s or 10s..
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18764
Own Kudos [?]: 22060 [5]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: What is the largest value of non negative integer N for which 10N is a [#permalink] New post   16 Feb 2018, 10:39
5
Bookmarks
Expert Reply
ashikaverma13 wrote:
What is the largest value of non negative integer N for which \(10^N\) is a factor of 50!?

A. 5
B. 6
C. 12
D. 15
E. 20


To determine the largest number of N, we need to determine how many times 10 divides 50!. Since 10 breaks into primes of 5 and 2, and since there are there are fewer 5s in 50! than 2s, we can find the number of 5s and thus be able to determine the number of 5-and-2 pairs.

To determine the number of 5s within 50!, we can use the following shortcut in which we divide 50 by 5, then divide the quotient of 50/5 by 5 and continue this process until we no longer get a nonzero quotient.

50/5 = 10

10/5 = 2

Since 2/5 does not produce a nonzero quotient, we can stop.

The final step is to add up our quotients; that sum represents the number of factors of 5 within 50!.

Thus, there are 10 + 2 = 12 factors of 5 and hence 12 factors of 10 within 50!

Answer: C
General Discussion
User avatar
G
ccooley
Manhattan Prep Instructor
Joined: 04 Dec 2015
Posts: 935
Own Kudos [?]: 1541 [0]
Given Kudos: 115
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Send PM
Re: What is the largest value of non negative integer N for which 10N is a [#permalink] New post   17 Jan 2017, 14:43
Expert Reply
Should the question read \(10^N\) rather than 10N? That's what you'd need in order for the answers to make sense (otherwise, 10N would be a factor for all of these answer choices.)
User avatar
L
rohit8865
Director
Director
Joined: 05 Mar 2015
Posts: 852
Own Kudos [?]: 861 [2]
Given Kudos: 45
Send PM
Reviews Badge
Re: What is the largest value of non negative integer N for which 10N is a [#permalink] New post   17 Jan 2017, 19:20
2
Kudos
ashikaverma13 wrote:
What is the largest value of non negative integer N for which 10N is a factor of 50!?

A. 5
B. 6
C. 12
D. 15
E. 20


Considering the highlighted part to be 10^n

50! has as many 10's as it have 5's
calculating 5's
50!/5=10
50!/25=2
sum=12

Ans C
User avatar
G
ashikaverma13
Manager
Manager
Joined: 19 Aug 2016
Posts: 129
Own Kudos [?]: 293 [0]
Given Kudos: 59
Location: India
Schools: ISB '20 (WD) Schulich Sept 18 Intake (A) Rotman '20 (S)
GMAT 1: 640 Q47 V31
GPA: 3.82
Send PM
Reviews Badge
Re: What is the largest value of non negative integer N for which 10N is a [#permalink] New post   19 Jan 2017, 05:24
rohit8865 wrote:
ashikaverma13 wrote:
What is the largest value of non negative integer N for which 10N is a factor of 50!?

A. 5
B. 6
C. 12
D. 15
E. 20


Considering the highlighted part to be 10^n

50! has as many 10's as it have 5's
calculating 5's
50!/5=10
50!/25=2
sum=12

Ans C



Thanks for your response!

Could you elaborate a bit more on the reasoning?

why do we have to find the no of 5s and how exactly did it come to 12?
User avatar
B
MvArrow
Manager
Manager
Joined: 06 Sep 2016
Posts: 107
Own Kudos [?]: 56 [0]
Given Kudos: 100
Location: Italy
Schools: EDHEC (A$)
GMAT 1: 650 Q43 V37
GPA: 3.2
WE:General Management (Human Resources)
Send PM
Re: What is the largest value of non negative integer N for which 10N is a [#permalink] New post   22 Jan 2018, 07:33
Is there a faster way than counting all the 5s and the 2s?
avatar
B
khan0210
Intern
Intern
Joined: 20 Jan 2017
Posts: 34
Own Kudos [?]: 37 [3]
Given Kudos: 107
Location: United Arab Emirates
Schools: Owen '22
Send PM
Re: What is the largest value of non negative integer N for which 10N is a [#permalink] New post   24 Jan 2018, 14:10
1
Kudos
2
Bookmarks
So I think the following method is helpful and short too. Finding non-prime factors in factorials (based on a different thread I read).

50/(5^1)+50/(5^2)
=>10+2
Therefore, there are 12 5's in 50.
We know every alternate number is a multiple of 2.

Given the maximim number of 2's and 5's to create a ten can be 12 of each (10^N = 2^12 * 5^12)
The answer is C - 12.

Extra:
Say we calculate the number of 2's in 50 regardless
50/(2^1)+50/(2^2)+50/(2^3)+50/(2^4)
=>25+12+8+3+1
Therefor there are 49 2's in 50.
avatar
B
Sajjad1093
Intern
Intern
Joined: 11 Mar 2017
Posts: 9
Own Kudos [?]: 0 [0]
Given Kudos: 11
Send PM
Re: What is the largest value of non negative integer N for which 10N is a [#permalink] New post   13 Feb 2018, 10:45
chetan2u wrote:
ashikaverma13 wrote:
ashikaverma13 wrote:
What is the largest value of non negative integer N for which 10N is a factor of 50!?

A. 5
B. 6
C. 12
D. 15
E. 20




Thanks for your response!

Could you elaborate a bit more on the reasoning?

why do we have to find the no of 5s and how exactly did it come to 12?


Hi,
The reasoning for these type of Qs is...

What does ! Or factorial mean ..
It means product of all positive integers till that number..
So 50! Means 1*2*3*4*5....*49*50
Now when we multiply 2 and 5 we get a 10..
So 2s will be more than 5s and that is why number of 10s will be equal to number of 5s...

Now how do we find number of 5s in 50!..
When you divide by 5 you get all multiples of 5 till 50..
50/5=10..
These 10 numbers are 5,10,15,20,25,30,35,.40,45,50..
When we divide by 25 we get numbers which had 5^2 in it..
50/25 =2..
And these are 25 Aand 50..
So you have 12 5s or 10s..


Hi Chetan,

Can you please explain from here onwards "So 2s will be more than 5s and that is why number of 10s will be equal to number of 5s..."

1) why are 2s more than 5s?
2) why do we need to calculate how many 5s are there?

Thanks
avatar
B
NiravUmaretiya
Intern
Intern
Joined: 03 Feb 2020
Posts: 11
Own Kudos [?]: 4 [0]
Given Kudos: 22
Send PM
Re: What is the largest value of non negative integer N for which 10N is a [#permalink] New post   29 Feb 2020, 22:48
You need to identify how many 10s are there in 50!
For this first ask, what is 10 made of?
---> it's made of 5*2 ... ... ...(5*2=10)

So we understand that to create a 10 you will need one 5 and one 2.

Now ask, in 50! how many 5s are there and how many 2s are there?
(side note: once you identify the number of 5s, you don't actually need to find the number of 2s; because the number of 2s> the number of 5s in 50!)

So there are ten 5s in 50! because there are ten multiples of 5 till 50. And, there is one additional 5 in 25 (5*5=25) and one additional in 50 (5*5*2=50)

Thus there is a total of twelve 5s in 50!

So with twelve 5s, we can make twelve 10s in 50!
Thus ans. is C
User avatar
B
vivek1810971
Intern
Intern
Joined: 28 Mar 2021
Posts: 37
Own Kudos [?]: 7 [0]
Given Kudos: 452
Location: India
Schools: ESADE'26 ISB '25 Oxford Said'25 Tepper '26 HEC Montreal'25 IMD Jan'24 intake Mendoza '26 Ivey '25 NUS '26 Owen '26 Rotman '26 Schulich Rotterdam'25 Ross '26 McCombs '26 Broad'26 (D)
GMAT 1: 640 Q47 V31
GMAT 2: 680 Q47 V37 (Online)
GMAT 3: 690 Q47 V37 (Online)
GPA: 2.95
Send PM
What is the largest value of non negative integer N for which 10N is a [#permalink] New post   26 Feb 2023, 00:55
This is basically a question of finding the number of trailing zeroes in a given factorial.

Using the following formula,
Attachment:
Screenshot 2023-02-26 132151.png
Screenshot 2023-02-26 132151.png [ 19.22 KiB | Viewed 3546 times ]
The formula is from the GMAT CLUB MATH GUIDE.

(50/5) + (50/25) = 10 + 2 = 12 trailing zeroes.

Therefore, in 10^N, N = 12.

You're welcome.
User avatar
B
pdfff
Intern
Intern
Joined: 10 Mar 2023
Posts: 9
Own Kudos [?]: 0 [0]
Given Kudos: 5
Send PM
Re: What is the largest value of non negative integer N for which 10N is a [#permalink] New post   02 Sep 2023, 07:30
ashikaverma13 wrote:
What is the largest value of non negative integer N for which \(10^N\) is a factor of 50!?

A. 5
B. 6
C. 12
D. 15
E. 20

avigutman sir I cannot understand how the answer is 12
I chose 5 as an answer as there are 5 factors of 10 = 2^n * 5^n inside 50! i.e. 10,20,30,40,50
User avatar
S
Paras96
Director
Director
Joined: 11 Sep 2022
Posts: 501
Own Kudos [?]: 152 [0]
Given Kudos: 2
Location: India
Paras: Bhawsar
GMAT 1: 590 Q47 V24
GMAT 2: 580 Q49 V21
GMAT 3: 700 Q49 V35
GPA: 3.2
WE:Project Management (Other)
Send PM
Re: What is the largest value of non negative integer N for which 10N is a [#permalink] New post   02 Sep 2023, 09:16
Successively dividing 50 by 5

=>50/5=>10/5=>2

Hence largest N = 10+2 = 12

Answer C

NOTE :- 10 = 5*2, we could have checked for 2 as well but for all 10 we need 5 also so the largest power of 5 will dominate here
User avatar
D
avigutman
Tutor
Joined: 17 Jul 2019
Posts: 1304
Own Kudos [?]: 2287 [0]
Given Kudos: 66
Location: Canada
Schools: NYU Stern (WA)
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Send PM
Re: What is the largest value of non negative integer N for which 10N is a [#permalink] New post   02 Sep 2023, 12:49
Expert Reply
pdfff wrote:
ashikaverma13 wrote:
What is the largest value of non negative integer N for which \(10^N\) is a factor of 50!?

A. 5
B. 6
C. 12
D. 15
E. 20

avigutman sir I cannot understand how the answer is 12
I chose 5 as an answer as there are 5 factors of 10 = 2^n * 5^n inside 50! i.e. 10,20,30,40,50

pdfff You're missing numbers that contribute just a '2' or just a '5'.
An analogy about pairs of shoes might help. Imagine that factors of 2 are right shoes, and factors of 5 are left shoes, and we want to know how many pairs of shoes we can get out of all those numbers. So, for example, 9 has no shoes, but 12 has two right shoes and 15 has one left shoe and 20 has two right shoes and one left shoe.
There are obviously going to be more right shoes in the end, so our limiting factor (pun intended) is the left shoes (right shoes without matching left shoes are useless to us).
So, if I can figure out how many left shoes there are, I'm done.
GMAT Club Bot
gmatclubot
Re: What is the largest value of non negative integer N for which 10N is a [#permalink]
02 Sep 2023, 12:49
Moderators:
Bunuel
Math Expert
92947 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions