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

 It is currently 19 Oct 2019, 18:16 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.  What is the value of N?

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

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58445
What is the value of N?  [#permalink]

Show Tags

4
16 00:00

Difficulty:   95% (hard)

Question Stats: 36% (02:14) correct 64% (01:48) wrong based on 363 sessions

HideShow timer Statistics

What is the value of N?

(1) N! ends with 28 zeroes

(2) (N+2)! ends with 31 zeroes and (N-1)! ends with 28 zeroes

Kudos for a correct solution.

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 58445
Re: What is the value of N?  [#permalink]

Show Tags

4
4
Bunuel wrote:
What is the value of N?

(1) N! ends with 28 zeroes

(2) (N+2)! ends with 31 zeroes and (N-1)! ends with 28 zeroes

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION

In any N!, the number of trailing zeroes = number of factors of 2 and 5. For example, for 6! (which is 720), the ending 0 is created by taking the numbers 2 and 5 in (6)(5)(4)(3)(2)(1) and multiplying them together. It's also important to realize that since every second number is divisible by 2 but every fifth number is a multiple of 5, the number of occurrences of 5 is less than 2, hence the limiting factor is 5.

Sine we know we're working with giant numbers, we can start getting an idea of what we're looking at by seeing how many zeroes 100! ends with

Every multiple of 5 between that 1 and 100 provides one factor of 5, and at 25, 50, 75, and 100, you get an extra 5 (for example, 75 = 3 * 5 * 5, so 75 provides two factors of 5). So the number of factors in 100! is 24 as a starting point for us.

Now since N! ends with 28 zeroes, we need to four more 5’s in 100!, so N should be 120. But one thing is to be noticed here is 120!, 121!, 122!, 123! and 124! also have 28 zeroes as from 120! to 124! there is no more extra 5 factor.

Hence Statement 1 is not sufficient.

As per Statement 2 the (N+2)! has 31 zeroes.

So let’s check which numbers can have 30 zeroes. We know from the above that 120!-124! should have 28 zeroes.

But when it comes to 125!, we have 5^3 factor so 125!-129! have 31 zeroes.

So N+2 can be any number between 125 to 129, but the statement also says N-1 has 28 zeroes that means N-1 can be any number from 120! to 124!.

So N can be 125 or 124 or 123 so again Statement 2 is not sufficient.

Let’s combine Statements 1 and 2: in this case, N could be 124 or it could be 123, so E is the correct answer.
_________________
Math Expert V
Joined: 02 Aug 2009
Posts: 7984
Re: What is the value of N?  [#permalink]

Show Tags

2
2
Bunuel wrote:
What is the value of N?

(1) N! ends with 28 zeroes

(2) (N+2)! ends with 31 zeroes and (N-1)! ends with 28 zeroes

Kudos for a correct solution.

ans E..

firstly the value of zeroes depends on power of 5 as power of 2 will always be greater than power of 5...
as we see (N+2)! increases the zeroes by 3 digits...it means between N and N+2, there is 5^3 multiple..125,250... here 125 fits in ..

1) statement one gives us values 120 to 124....as 119 will give 27 zeroes and 125 will give 31 zeroes.. insufficient..
2) statement two gives us values 123 to 127 as N+2 < 130... insufficient..

combined two values still remain... 123 and 124.. insufficient
_________________
General Discussion
Manager  Joined: 04 Oct 2013
Posts: 160
GMAT 1: 590 Q40 V30 GMAT 2: 730 Q49 V40 WE: Project Management (Entertainment and Sports)
Re: What is the value of N?  [#permalink]

Show Tags

1
Bunuel wrote:
What is the value of N?

(1) N! ends with 28 zeroes

(2) (N+2)! ends with 31 zeroes and (N-1)! ends with 28 zeroes

Kudos for a correct solution.

stastement 1: If N=124 --> total number of zeroes=124/5+124/25=28. If N=123 --> total number of zeroes=123/5+123/25=28.

statement 2: works with both 123 and 124.

1+2) works with both 123 and 124.

_________________
learn the rules of the game, then play better than anyone else.
Director  G
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 563
Location: India
GMAT 1: 780 Q51 V46 Re: What is the value of N?  [#permalink]

Show Tags

1
Hi all,
Again a value DS question.
1). Statement 1 is insufficient.
To find the number of zeros all we need is find number of five’s.
For N values 120,121,122,123,124… the number of zeros(Number of five's) is 28
So insufficient
2). Statement 2 is insufficient.
N values again can be 123,124,125…
Together also insufficient,
Because N can be 123 or 124.
So answer is E
_________________
- CrackVerbal Prep Team

Register for the Free GMAT Kickstarter Course : http://bit.ly/2DDHKHq

Register for our Personal Tutoring Course : https://www.crackverbal.com/gmat/personal-tutoring/

Join the free 4 part GMAT video training series : http://bit.ly/2DGm8tR
Math Expert V
Joined: 02 Aug 2009
Posts: 7984
Re: What is the value of N?  [#permalink]

Show Tags

CrackVerbalGMAT wrote:
Hi all,
Again a value DS question.
1). Statement 1 is insufficient.
To find the number of zeros all we need is find number of five’s.
For N values 120,121,122,123,124… the number of zeros(Number of five's) is 28
So insufficient
2). Statement 2 is insufficient.
N values again can be 123,124,125…
Together also insufficient,
Because N can be 123 or 124.
So answer is E

hi N cannot be 125....
because it is given N! has 28 zeroes in end..
_________________
Manager  Joined: 14 Jul 2014
Posts: 88
Re: What is the value of N?  [#permalink]

Show Tags

I dont understand why has everyone picked 124, 125 as the starting point for N

Not clear - Can somebody pls explain
Math Expert V
Joined: 02 Sep 2009
Posts: 58445
Re: What is the value of N?  [#permalink]

Show Tags

Bunuel wrote:
Bunuel wrote:
What is the value of N?

(1) N! ends with 28 zeroes

(2) (N+2)! ends with 31 zeroes and (N-1)! ends with 28 zeroes

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION

In any N!, the number of trailing zeroes = number of factors of 2 and 5. For example, for 6! (which is 720), the ending 0 is created by taking the numbers 2 and 5 in (6)(5)(4)(3)(2)(1) and multiplying them together. It's also important to realize that since every second number is divisible by 2 but every fifth number is a multiple of 5, the number of occurrences of 5 is less than 2, hence the limiting factor is 5.

Sine we know we're working with giant numbers, we can start getting an idea of what we're looking at by seeing how many zeroes 100! ends with

Every multiple of 5 between that 1 and 100 provides one factor of 5, and at 25, 50, 75, and 100, you get an extra 5 (for example, 75 = 3 * 5 * 5, so 75 provides two factors of 5). So the number of factors in 100! is 24 as a starting point for us.

Now since N! ends with 28 zeroes, we need to four more 5’s in 100!, so N should be 120. But one thing is to be noticed here is 120!, 121!, 122!, 123! and 124! also have 28 zeroes as from 120! to 124! there is no more extra 5 factor.

Hence Statement 1 is not sufficient.

As per Statement 2 the (N+2)! has 31 zeroes.

So let’s check which numbers can have 30 zeroes. We know from the above that 120!-124! should have 28 zeroes.

But when it comes to 125!, we have 5^3 factor so 125!-129! have 31 zeroes.

So N+2 can be any number between 125 to 129, but the statement also says N-1 has 28 zeroes that means N-1 can be any number from 120! to 124!.

So N can be 125 or 124 or 123 so again Statement 2 is not sufficient.

Let’s combine Statements 1 and 2: in this case, N could be 124 or it could be 123, so E is the correct answer.

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

Hope this helps.
_________________
Math Expert V
Joined: 02 Aug 2009
Posts: 7984
What is the value of N?  [#permalink]

Show Tags

buddyisraelgmat wrote:
I dont understand why has everyone picked 124, 125 as the starting point for N

Not clear - Can somebody pls explain

hi

firstly the value of zeroes depends on power of 5 as power of 2 will always be greater than power of 5...
as we see (N+2)! increases the zeroes by 3 digits...it means between N and N+2, there is 5^3 multiple..125,250... here 125 fits in ..
because no of zeroes=125/5+125/5^2+125/5^3=25+5+1=31...
_________________
Intern  Joined: 26 Nov 2014
Posts: 7
Re: What is the value of N?  [#permalink]

Show Tags

Bunuel wrote:
Bunuel wrote:
What is the value of N?

(1) N! ends with 28 zeroes

(2) (N+2)! ends with 31 zeroes and (N-1)! ends with 28 zeroes

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION

In any N!, the number of trailing zeroes = number of factors of 2 and 5. For example, for 6! (which is 720), the ending 0 is created by taking the numbers 2 and 5 in (6)(5)(4)(3)(2)(1) and multiplying them together. It's also important to realize that since every second number is divisible by 2 but every fifth number is a multiple of 5, the number of occurrences of 5 is less than 2, hence the limiting factor is 5.

Sine we know we're working with giant numbers, we can start getting an idea of what we're looking at by seeing how many zeroes 100! ends with

Every multiple of 5 between that 1 and 100 provides one factor of 5, and at 25, 50, 75, and 100, you get an extra 5 (for example, 75 = 3 * 5 * 5, so 75 provides two factors of 5). So the number of factors in 100! is 24 as a starting point for us.

Now since N! ends with 28 zeroes, we need to four more 5’s in 100!, so N should be 120. But one thing is to be noticed here is 120!, 121!, 122!, 123! and 124! also have 28 zeroes as from 120! to 124! there is no more extra 5 factor.

Hence Statement 1 is not sufficient.

As per Statement 2 the (N+2)! has 31 zeroes.

So let’s check which numbers can have 30 zeroes. We know from the above that 120!-124! should have 28 zeroes.

But when it comes to 125!, we have 5^3 factor so 125!-129! have 31 zeroes.

So N+2 can be any number between 125 to 129, but the statement also says N-1 has 28 zeroes that means N-1 can be any number from 120! to 124!.

So N can be 125 or 124 or 123 so again Statement 2 is not sufficient.

Let’s combine Statements 1 and 2: in this case, N could be 124 or it could be 123, so E is the correct answer.

I got a little doubt

Zeros in 120! to 124! is 29

Correct me i assumed it like: dividing 120! with 5,25&75 i will get 24+4+1 number of 5's i.e 29

while taking 100!= 24 and then counting 5's in 105,110,115,120 will take to 28 . whats missing here?
Math Expert V
Joined: 02 Aug 2009
Posts: 7984
What is the value of N?  [#permalink]

Show Tags

1
ikishan wrote:

I got a little doubt

Zeros in 120! to 124! is 29

Correct me i assumed it like: dividing 120! with 5,25&75 i will get 24+4+1 number of 5's i.e 29

while taking 100!= 24 and then counting 5's in 105,110,115,120 will take to 28 . whats missing here?

hi,
to find power of 5 or zeroes in any factorial, we have to divide the number with increasing power of 5.... 5^1,5^2,5^3 and so on....
you have correctly divided by 5,25 but 75 is wrong as next number would be 5^3=125..
and you cannot divide 120 by 125...
so answer is 24+4=28 and not 29...
hope it is clear...
_________________
Intern  Joined: 26 Nov 2014
Posts: 7
Re: What is the value of N?  [#permalink]

Show Tags

chetan2u wrote:
ikishan wrote:

I got a little doubt

Zeros in 120! to 124! is 29

Correct me i assumed it like: dividing 120! with 5,25&75 i will get 24+4+1 number of 5's i.e 29

while taking 100!= 24 and then counting 5's in 105,110,115,120 will take to 28 . whats missing here?

hi,
to find power of 5 or zeroes in any factorial, we have to divide the number with increasing power of 5.... 5^1,5^2,5^3 and so on....
you have correctly divided by 5,25 but 75 is wrong as next number would be 5^3=125..
and you cannot divide 120 by 125...
so answer is 24+4=28 and not 29...

hope it is clear...

Thanks man, that filled clarity.
Non-Human User Joined: 09 Sep 2013
Posts: 13275
Re: What is the value of N?  [#permalink]

Show Tags

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.
_________________ Re: What is the value of N?   [#permalink] 10 Jan 2019, 02:32
Display posts from previous: Sort by

What is the value of N?

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

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