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

It is currently 13 Nov 2019, 16:00

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

Find the number of trailing zeros in the expansion of

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

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
Joined: 08 Oct 2010
Posts: 179
Location: Uzbekistan
Schools: Johnson, Fuqua, Simon, Mendoza
WE 3: 10
Find the number of trailing zeros in the expansion of  [#permalink]

Show Tags

New post Updated on: 06 Jul 2013, 03:04
20
200
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

57% (02:47) correct 43% (02:33) wrong based on 1544 sessions

HideShow timer Statistics

Find the number of trailing zeros in the expansion of (20!*21!*22! ……… *33!)^3!.

A. 468
B. 469
C. 470
D. 467
E. 471

Can someone help me how to solve this question? I think, there must be more than one solution method.

Do questions of such a level of difficulty appear on the actual GMAT?

Originally posted by feruz77 on 25 Jan 2011, 06:48.
Last edited by Bunuel on 06 Jul 2013, 03:04, edited 1 time in total.
Edited the answer choices.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59020
Find the number of trailing zeros in the expansion of  [#permalink]

Show Tags

New post 25 Jan 2011, 08:01
50
56
feruz77 wrote:
Find the number of trailing zeros in the expansion of (20!*21!*22! ……… *33!)^3!.

a) 10^468
b) 10^469
c) 10^470
d) 10^467
e) 10^471

Can someone help me how to solve this question? I think, there must be more than one solution method.

Do questions of such a level of difficulty appear on the actual GMAT?


# of trailing zeros in 20!, 21!, 22!, 23!, and 24! will be 4 (20/5=4. For 21!, 22!, 23! and 24!, instead of 20 you'll have 21, 22, ... but the result will be the same) --> total of 4*5=20 trailing zeros for these 5 terms. (Note here that this won't always be correct: for example 20 and 50 have one trailing zero each but 20*50=1,000 has three trailing zeros not two. That's because extra 2 in 20 and extra 5 in 50 "produced" one more trailing zero. In our case though, we won't have any extra 5-s in any factorial, as all are already used for existing trailing zeros);

# of trailing zeros in 25!, 26!, 27!, 28!, and 29! will be 5+1=6 (25/5+25/5^2=6) --> total of 6*5=30 trailing zeros for these 5 terms;

# of trailing zeros in 30!, 31!, 32!, and 33! will be 6+1=7 (30/5+30/5^2=7) --> total of 7*4=28 trailing zeros for these 5 terms;

So, \((20!*21!*22!*...*33!)^{3!}=(10^{20}*10^{30}*10^{28}*something)^{3!}=(10^{78}*something)^6=10^{468}*something^6\).

Total of 468 trailing zeros.

Answer: A.

OR: as we have (something)^6 then the # of trailing zeros must be multiple of 6 only answer choice A satisfies this.

Theory on this topic: http://gmatclub.com/forum/everything-ab ... 85592.html
_________________
Most Helpful Community Reply
SVP
SVP
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2479
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Reviews Badge
Re: trailing zeros question (complicated one)  [#permalink]

Show Tags

New post 29 Jan 2011, 02:04
54
13
feruz77 wrote:
Find the number of trailing zeros in the expansion of (20!*21!*22! ……… *33!)^3!.

a) 10^468
b) 10^469
c) 10^470
d) 10^467
e) 10^471

Can someone help me how to solve this question? I think, there must be more than one solution method.

Do questions of such a level of difficulty appear on the actual GMAT?


Excellent explanation by Bunuel.
Let me give you one quick way to solve such questions.

3! = 6 => the answer must be of the form \(10^{6n}\)
Only A and C have even powers. Hence B C E are out

Out of A and C only A's power is divisible by 3, hence C is out.

Hence A is the answer.
_________________
Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html
General Discussion
Manager
Manager
avatar
Joined: 08 Oct 2010
Posts: 179
Location: Uzbekistan
Schools: Johnson, Fuqua, Simon, Mendoza
WE 3: 10
Re: trailing zeros question (complicated one)  [#permalink]

Show Tags

New post Updated on: 19 Feb 2011, 08:34
1
Thank You Bunuel.

I have one more remark:
This series is not a series of numbers, it is a factorial and in this respect your approach makes sense because in a factorial, as a ganeral rule, a number of trailing zeros will depend on the highest power of 5.

Thank You one more time.

Originally posted by feruz77 on 29 Jan 2011, 01:57.
Last edited by feruz77 on 19 Feb 2011, 08:34, edited 1 time in total.
Senior Manager
Senior Manager
User avatar
Joined: 08 Nov 2010
Posts: 269
WE 1: Business Development
GMAT ToolKit User
Re: trailing zeros question (complicated one)  [#permalink]

Show Tags

New post 18 Feb 2011, 23:06
Bunuel - i understand the rule of trailing zeroes, but how did u deduct from that
that if its ^6 - it have be a multiply of 6?

thanks.
_________________
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59020
Re: trailing zeros question (complicated one)  [#permalink]

Show Tags

New post 19 Feb 2011, 03:15
7
144144 wrote:
Bunuel - i understand the rule of trailing zeroes, but how did u deduct from that
that if its ^6 - it have be a multiply of 6?

thanks.


For example:
100 has 2 trailing zeros, 100^6=(10^2)^6=10^12 will have 2*6 trailing zeros.

Now, we have (something)^6: if # of trailing zeros of that something is x then # of trailing zeros of (something)^6 will be 6x, so multiple of 6.
_________________
Senior Manager
Senior Manager
User avatar
Joined: 08 Nov 2010
Posts: 269
WE 1: Business Development
GMAT ToolKit User
Re: trailing zeros question (complicated one)  [#permalink]

Show Tags

New post 19 Feb 2011, 03:21
oh... thanks. +1
do u ever sleep btw? ;)
_________________
Manager
Manager
avatar
Joined: 09 Jan 2010
Posts: 68
Re: trailing zeros question (complicated one)  [#permalink]

Show Tags

New post 01 Apr 2011, 08:40
1
gurpreetsingh wrote:
feruz77 wrote:
Find the number of trailing zeros in the expansion of (20!*21!*22! ……… *33!)^3!.

a) 10^468
b) 10^469
c) 10^470
d) 10^467
e) 10^471

Can someone help me how to solve this question? I think, there must be more than one solution method.

Do questions of such a level of difficulty appear on the actual GMAT?


Excellent explanation by Bunuel.
Let me give you one quick way to solve such questions.

3! = 6 => the answer must be of the form \(10^{6n}\)
Only A and C have even powers. Hence B C E are out

Out of A and C only A's power is divisible by 3, hence C is out.

Hence A is the answer.




Hi gurpreet
can u pls tell me , out of A,C ,why did u check whether the ans is div by 3

I know their is smthng silly i am missing ,....but pls tell me what is that.....
SVP
SVP
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2479
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Reviews Badge
Re: trailing zeros question (complicated one)  [#permalink]

Show Tags

New post 03 Apr 2011, 07:48
2
read my solution again.

he given impression is raised to the power 3! which is 6.

=> the answer should be of the form - something raised to the power 6n.

out of all the given powers,which are raised on 10, only A and C are eligible to be divisible by 6 as all others are odd numbers.

Now out of A and C, 470 is not divisible by 6n, hence it can not be the answer.

let me know if you are still not able to make it.
_________________
Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html
Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 399
Concentration: Marketing, Finance
GPA: 3.23
GMAT ToolKit User
Re: Find the number of trailing zeros in the expansion of  [#permalink]

Show Tags

New post 21 Dec 2012, 01:47
2
1
I love trailing zeroes.

20! has 4 factors of 5 = 5^4
21! to 24! also have 4 factors of 5 each = 5^16
25! has 6 factors of 5 = 5^6
26! to 29! also have 6 factors of 5 each = 5^24
30! has 7 factors of 5 = 5^7
31! to 33! has 7 factors of 5 = 5^21

There are 5^78 then raised to 3!=6 so we have 5^468. Obviously we have more than 468 factors of 2 so the count of 5 is our limiting factor.

Answer: A
_________________
Impossible is nothing to God.
Intern
Intern
avatar
Joined: 23 Dec 2012
Posts: 2
Re: Find the number of trailing zeros in the expansion of  [#permalink]

Show Tags

New post Updated on: 03 Jan 2013, 19:57
2
I cannot seem to understand how A is the correct answer. I do understand that should be 468 trailing zeros. But 10^468 is not correct. For example 6! has 1 trailing zero (and not 10^1=10, trailing zeros). I guess the answer choices should only be 468,...,471 (without the 10^), Isn't it? Maybe I am missing something.

Originally posted by joe123 on 03 Jan 2013, 17:39.
Last edited by joe123 on 03 Jan 2013, 19:57, edited 1 time in total.
Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 399
Concentration: Marketing, Finance
GPA: 3.23
GMAT ToolKit User
Re: Find the number of trailing zeros in the expansion of  [#permalink]

Show Tags

New post 03 Jan 2013, 18:49
joe123 wrote:
I cannot seem to understand how A is the correct answer. I do understand that should be 468 trailing zeros. But 10^468 is not correct. For example 6! has 1 trailing zero (and not 10^1=10, trailing zeros). I guess the answer choices should only be 468,...,471, Isn't it? Maybe I am missing something.


20! = 20*19*18*17*...*4*3*2*1

We know that from the above has 5^4.
We know that from the above it has 10 even numbers and some of them like 8 = 2^3. Thus, there are at least 10 factors of 2 or 2^17 to be exact.

To get the trailing zero, you have to capture a pair of 5 and 2. Choose the limiting factor.
Thus, we have 5^4*2^17=(5^4)(2^4)(2^13) giving 10^4...

Continue to do this in the other factorials.

21!,22!,23!,24! will have a total of 10^16
25! will have 10^6 since 25 has two factors of 5.

Do it until 33! and we will have 78 factors of 10.

But we have to raise by 3! = 6. 78*6= 468
_________________
Impossible is nothing to God.
Senior Manager
Senior Manager
avatar
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 421
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Re: Find the number of trailing zeros in the expansion of  [#permalink]

Show Tags

New post 09 Jan 2013, 01:42
do we get such questions on gmat?
_________________
hope is a good thing, maybe the best of things. And no good thing ever dies.

Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : http://gmatclub.com/forum/end-of-my-gmat-journey-149328.html#p1197992
Intern
Intern
User avatar
Status: Single
Joined: 04 Oct 2010
Posts: 1
Schools: Harvard, Stanford, ISB, Kellog, Wharton
Re: Find the number of trailing zeros in the expansion of  [#permalink]

Show Tags

New post 09 Jan 2013, 02:23
joe123 wrote:
I cannot seem to understand how A is the correct answer. I do understand that should be 468 trailing zeros. But 10^468 is not correct. For example 6! has 1 trailing zero (and not 10^1=10, trailing zeros). I guess the answer choices should only be 468,...,471 (without the 10^), Isn't it? Maybe I am missing something.


Lets say
20! = 10^x
21! = 10^y
22! = 10^z

Then

(20!*21!*22! ……… *33!)^3! = (10^x * 10^y * 10^z....10^n)^3!
= (10)^(3!(x*y*z*...n)
= (10)^6(xyz...n)

In given options, 6 is the multiple of 468 only.
So Ans :arrow: (A)
_________________
Cheers,
Maddy

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59020
Re: Find the number of trailing zeros in the expansion of  [#permalink]

Show Tags

New post 09 Jan 2013, 03:00
Manager
Manager
User avatar
Joined: 12 Jan 2013
Posts: 56
Location: United States (NY)
GMAT 1: 780 Q51 V47
GPA: 3.89
Re: Find the number of trailing zeros in the expansion of  [#permalink]

Show Tags

New post 14 Jan 2013, 00:27
joe123 wrote:
I cannot seem to understand how A is the correct answer. I do understand that should be 468 trailing zeros. But 10^468 is not correct. For example 6! has 1 trailing zero (and not 10^1=10, trailing zeros). I guess the answer choices should only be 468,...,471 (without the 10^), Isn't it? Maybe I am missing something.


You are correct. The answer is 468, not \(10^{468}\). The problem statement is wrong.
_________________
Sergey Orshanskiy, Ph.D.
I tutor in NYC: http://www.wyzant.com/Tutors/NY/New-York/7948121/#ref=1RKFOZ
Intern
Intern
avatar
Joined: 18 Nov 2011
Posts: 32
Concentration: Strategy, Marketing
GMAT Date: 06-18-2013
GPA: 3.98
Re: Find the number of trailing zeros in the expansion of  [#permalink]

Show Tags

New post 07 Feb 2013, 01:28
joe123 wrote:
I cannot seem to understand how A is the correct answer. I do understand that should be 468 trailing zeros. But 10^468 is not correct. For example 6! has 1 trailing zero (and not 10^1=10, trailing zeros). I guess the answer choices should only be 468,...,471 (without the 10^), Isn't it? Maybe I am missing something.



That threw me for a loop as well. I was going crazy trying to figure out how there would be so many damn zeros.

The answers should be 468 - 471 or the problem should written differently.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59020
Re: Find the number of trailing zeros in the expansion of  [#permalink]

Show Tags

New post 08 Jul 2013, 01:08
Intern
Intern
avatar
B
Joined: 01 Feb 2013
Posts: 36
Location: India
Concentration: Technology, Leadership
GMAT 1: 750 Q50 V41
GPA: 3.49
WE: Engineering (Computer Software)
Reviews Badge
Re: Find the number of trailing zeros in the expansion of  [#permalink]

Show Tags

New post 25 Sep 2013, 09:09
Superb question. Captured the essence of GMAT in a single shot.
As soon as I saw the ^ 3! I made a note (some number) x6 on my scrap paper.
Started going through the choices for anything dividing by 6 and voila!
468 was the first choice and was divisible. Saw that the rest are consecutive so marked it directly.
+1 Cheers for the poster
Manager
Manager
avatar
Joined: 07 May 2013
Posts: 87
Re: Find the number of trailing zeros in the expansion of  [#permalink]

Show Tags

New post 12 Oct 2013, 04:08
Buneul, here's my doubt:
# of trailing zeros in 25!, 26!, 27!, 28!, and 29! will be 5+1=6 (25/5+25/5^2=6) --> total of 6*5=30 trailing zeros for these 5 terms;

# of trailing zeros in 30!, 31!, 32!, and 33! will be 6+1=7 (30/5+30/5^2=7) --> total of 7*4=28 trailing zeros for these 5 terms;
for calculating trailing zeros up til 24! you did just 20/5=4.
but above those numbers i.e., from 25! on wards you did (25/5+25/5^2=6) and (30/5+30/5^2=7)
Suppose I want # of trailing zeros in 310!
using your concept 310/5+310/5^2=62+12=74 trailing zeroes
BUT using the factorial calculator below I am getting 76 trailing zeroes
http://www.nitrxgen.net/factorialcalc.php
please suggest a fool proof method for calculating trailing zeroes of any +ve integer.
GMAT Club Bot
Re: Find the number of trailing zeros in the expansion of   [#permalink] 12 Oct 2013, 04:08

Go to page    1   2   3    Next  [ 43 posts ] 

Display posts from previous: Sort by

Find the number of trailing zeros in the expansion of

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





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