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

 It is currently 14 Nov 2018, 03:56

### 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

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### \$450 Tuition Credit & Official CAT Packs FREE

November 15, 2018

November 15, 2018

10:00 PM MST

11:00 PM MST

EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth \$100 with the 3 Month Pack (\$299)
• ### Free GMAT Strategy Webinar

November 17, 2018

November 17, 2018

07:00 AM PST

09:00 AM PST

Nov. 17, 7 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.

# IF N=5^5*..., then how many zeroes exist between decimal and first non

Author Message
TAGS:

### Hide Tags

Intern
Joined: 28 Mar 2015
Posts: 3
IF N=5^5*..., then how many zeroes exist between decimal and first non  [#permalink]

### Show Tags

02 Apr 2015, 08:25
2
25
00:00

Difficulty:

95% (hard)

Question Stats:

51% (02:36) correct 49% (02:20) wrong based on 293 sessions

### HideShow timer Statistics

IF N=5^5*10^10*15^15*20^20*25^25*30^30*35^35*40^40*45^45*50^50 , then how many zeroes exist between decimal and first non zero digit of N ?

150
200
250
300
350
Retired Moderator
Joined: 06 Jul 2014
Posts: 1241
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
Re: IF N=5^5*..., then how many zeroes exist between decimal and first non  [#permalink]

### Show Tags

02 Apr 2015, 08:33
8
9
CrazyIvan wrote:
IF N=5^5*10^10*15^15*20^20*25^25*30^30*35^35*40^40*45^45*50^50 , then how many zeroes exist between decimal and first non zero digit of N ?

150
200
250
300
350

For calculating 0 at the end we should calculate quantity of "2" and "5" in the final number.

in all numbers which end at 5 we don't have any "2" but have a lot of "5".
So in final number we will have more "5" than "2" and we need to calculate quantity of "2" in each number
10 - one "2" in 10 exponent = 10
20 - two "2" in 20 exponent = 40
30 - one "2" in 30 exponent = 30
40 - three "2" in 40 exponent = 120
50 - one "2" in 50 exponent = 50

10 + 40 + 30 + 120 + 50 = 250
_________________
##### General Discussion
Founder
Joined: 04 Dec 2002
Posts: 16923
Location: United States (WA)
GMAT 1: 750 Q49 V42
Re: IF N=5^5*..., then how many zeroes exist between decimal and first non  [#permalink]

### Show Tags

02 Apr 2015, 08:36
Slight Subject modification for readability. Thank you.
_________________

Founder of GMAT Club

Just starting out with GMAT? Start here...
OG2019 Directory is here! - New!
Verbal OG2019 Directory is here! - New!
Quant OG2019 Directory is here! - New!

Co-author of the GMAT Club tests

Director
Joined: 07 Aug 2011
Posts: 539
GMAT 1: 630 Q49 V27
Re: IF N=5^5*..., then how many zeroes exist between decimal and first non  [#permalink]

### Show Tags

02 Apr 2015, 11:27
CrazyIvan wrote:
IF N=5^5*10^10*15^15*20^20*25^25*30^30*35^35*40^40*45^45*50^50 , then how many zeroes exist between decimal and first non zero digit of N ?

150
200
250
300
350

I have no different method than what has been provided by Harley1980.
thats the most obvious and efficient way IMO.

does anyone have urls for such questions?
Dont even know which category these questions fall into.
chetan2u any idea?
_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the to appreciate my post !!

Retired Moderator
Joined: 06 Jul 2014
Posts: 1241
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
Re: IF N=5^5*..., then how many zeroes exist between decimal and first non  [#permalink]

### Show Tags

02 Apr 2015, 11:32
1
Lucky2783 wrote:
CrazyIvan wrote:
IF N=5^5*10^10*15^15*20^20*25^25*30^30*35^35*40^40*45^45*50^50 , then how many zeroes exist between decimal and first non zero digit of N ?

150
200
250
300
350

I have no different method than what has been provided by Harley1980.
thats the most obvious and efficient way IMO.

does anyone have urls for such questions?
Dont even know which category these questions fall into.
chetan2u any idea?

I think this is Number properties
Here is some examples:
how-many-zeros-does-100-end-with-100599.html
how-many-zeros-are-the-end-of-142479.html
_________________
Current Student
Joined: 03 Aug 2011
Posts: 285
Concentration: Strategy, Finance
GMAT 1: 640 Q44 V34
GMAT 2: 700 Q42 V44
GMAT 3: 680 Q44 V39
GMAT 4: 740 Q49 V41
GPA: 3.7
WE: Project Management (Energy and Utilities)
Re: IF N=5^5*..., then how many zeroes exist between decimal and first non  [#permalink]

### Show Tags

04 Aug 2015, 06:15
Awesome question!

Can this somehow be solved by applying @Bunuel's approach in dividing by 5 and it's exponents (25, 125, etc.)?

Thank you!
_________________

Thank you very much for reading this post till the end! Kudos?

Director
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 610
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Re: IF N=5^5*..., then how many zeroes exist between decimal and first non  [#permalink]

### Show Tags

05 Aug 2015, 20:08
Thank you
CrazyIvan wrote:
IF N=5^5*10^10*15^15*20^20*25^25*30^30*35^35*40^40*45^45*50^50 , then how many zeroes exist between decimal and first non zero digit of N ?

150
200
250
300
350

_________________

Ankit

Check my Tutoring Site -> Brush My Quant

GMAT Quant Tutor
How to start GMAT preparations?
How to Improve Quant Score?
Gmatclub Topic Tags
Check out my GMAT debrief

How to Solve :
Statistics || Reflection of a line || Remainder Problems || Inequalities

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8527
Location: Pune, India
Re: IF N=5^5*..., then how many zeroes exist between decimal and first non  [#permalink]

### Show Tags

05 Aug 2015, 21:28
1
1
bgpower wrote:
Awesome question!

Can this somehow be solved by applying @Bunuel's approach in dividing by 5 and it's exponents (25, 125, etc.)?

Thank you!

No. If N were

N = 5*10*15*20*25*... and so on, then you could have put all the 5s together and you would have been left with 1*2*3*4*5*6*7...
Here, to find the number of 5s, you could have used Bunuel's approach of dividing by 5 and then 25 etc. Note that that approach works for factorials only.

OR if N were

N = 5^5 * 10^5 * 15^5 * 20^5 * 25^5 ... and so on, then you could have also used that method by raising the whole thing to a common power of 5 and then proceeding as done above.
_________________

Karishma
Veritas Prep GMAT Instructor

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Intern
Joined: 07 Aug 2014
Posts: 8
Re: IF N=5^5*..., then how many zeroes exist between decimal and first non  [#permalink]

### Show Tags

31 Oct 2015, 23:11
How does the approach ,shown by Harley1980, take into account the n! counting method of n/5 + n/5^2 + n/5^3......n/5^k ?

I cant see how this counting method can be used in this question ?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8527
Location: Pune, India
Re: IF N=5^5*..., then how many zeroes exist between decimal and first non  [#permalink]

### Show Tags

02 Nov 2015, 20:37
EricImasogie wrote:
How does the approach ,shown by Harley1980, take into account the n! counting method of n/5 + n/5^2 + n/5^3......n/5^k ?

I cant see how this counting method can be used in this question ?

It doesn't since we cannot use that method here. Every term has a different exponent so you have to account for the exponents too. In that method, the exponent is always 1.
10! = 1*2*3*4*5*6*7*8*9*10

N=5^5*10^10*15^15*20^20*25^25*30^30*35^35*40^40*45^45*50^50
There are 2s only in alternate terms
10^10 * 20^20 * 30^30 * 40^40 * 50^50

So you just consider independent terms and that's all.
_________________

Karishma
Veritas Prep GMAT Instructor

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Non-Human User
Joined: 09 Sep 2013
Posts: 8767
Re: IF N=5^5*..., then how many zeroes exist between decimal and first non  [#permalink]

### Show Tags

27 Jul 2018, 18:34
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: IF N=5^5*..., then how many zeroes exist between decimal and first non &nbs [#permalink] 27 Jul 2018, 18:34
Display posts from previous: Sort by