It is currently 11 Dec 2017, 18:07

### 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 June
Open Detailed Calendar

# ps

Author Message
Senior Manager
Joined: 18 Sep 2009
Posts: 350

Kudos [?]: 612 [1], given: 2

### Show Tags

27 Mar 2011, 20:26
1
KUDOS
2
This post was
BOOKMARKED
If N is the product of all multiples of 10 between 199 and 301, what is the greatest integer m for which [N][/1o]m is an integer?here m is 10 to the number of times m(likex.x)
10
11
13
14
15
[Reveal] Spoiler:
E

Kudos [?]: 612 [1], given: 2

Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 868

Kudos [?]: 404 [0], given: 123

### Show Tags

27 Mar 2011, 21:15
Let me write all the multiples of 10 and see how many zeroes we get.

200 ---> two zeroes
210 ---> one zeroes
220 ---> one zeroes
230 ---> one zeroes
240 ---> one zeroes
250 ---> three zeroes. 250 = 5*5 *10. Every 5 delivers one zero.
260 ---> one zeroes
270 ---> one zeroes
280 ---> one zeroes
290 ---> one zeroes
300 ---> two zeroes

Adding we get 2+1+1+1+1+3+1+1+1+1+2 = 15

TomB wrote:
If N is the product of all multiples of 10 between 199 and 301, what is the greatest integer m for which [N][/1o]m is an integer?here m is 10 to the number of times m(likex.x)
10
11
13
14
15
[Reveal] Spoiler:
E

Kudos [?]: 404 [0], given: 123

Senior Manager
Joined: 09 Feb 2011
Posts: 272

Kudos [?]: 220 [0], given: 13

Concentration: General Management, Social Entrepreneurship
Schools: HBS '14 (A)
GMAT 1: 770 Q50 V47

### Show Tags

28 Mar 2011, 00:18
Basically we have to start by counting how many zeroes does this product have.
Each multiple of 10 will by efault give one zero --> How many multiples of 10 between 199 and 301? (300-200)/10 + 1= 11
So 11 zeroes counted

Now what are the other ways of 0 coming in this product? Any combination of 5 and 2 will yield another 0. This should be over and above the zero that we have counted in default zeroes - e.g. 210 = (2*5 *3 *7) We have already counted this 2 and this 5
Which means the number we are counting will atleast have 2 5's or will be a multiple of 25 along with being a multiple of 10. These are:
200 = 10 * 5*4---> 1 more zero
250 = 10 * 5 * 5
300 = 10 *5 *2 *3 --> 1 more zero
We have counted 13 zeros.
The 2 5's of 250 will pick 2 2's from other number of the product. e.g. (220 = 10*11*2) and give two more zeroes
Hence 15 zeroes.

Kudos [?]: 220 [0], given: 13

Re: ps   [#permalink] 28 Mar 2011, 00:18
Display posts from previous: Sort by

# ps

Moderator: Bunuel

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.