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.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: least value of N (m09q33) [#permalink]
03 Sep 2010, 04:28

7

This post received KUDOS

1000 = 2^3 x 5^3 so, we are looking for a number N such that N! contains at least 2^3 x 5^3 as factors. A. 8! = 2^3.7.6.5.4! .... only 2^3.5 wrong B. 10! = (2*5).9.8.7.6.5.4!...only 2^3.5^2 wrong, we need an additional 5. C. 15! = (3*5).(2*7).13.(2*6).11.(2*5).9.8! 2^3.5^3 is available in 15!...corect D. 20! we looking for the least- 20! is not necessary E. 25! same as option D _________________

KUDOS me if you feel my contribution has helped you.

Re: least value of N (m09q33) [#permalink]
05 Sep 2010, 08:33

1

This post received KUDOS

For such questions, always work through the answers choice from lowest to highest i.e. A to E. The moment you get an answers that matches, stop and mark that as the answer and move on.

1000 = 2^3 x 5^3 N! has to contain 2^3 x 5^3 as factors. A) 8! --> only 2^3 * 5^1 --> wrong B) 10! --> only 2^3 * 5^2 --> wrong C) 15! = --> 2^3 * 5^3 --> BINGO _________________

If you like my post, consider giving me a kudos. THANKS!

Re: least value of N (m09q33) [#permalink]
09 Sep 2010, 10:06

For the N! to be divisible by 1,000, it needs 3 5's and 3 2's in it (5^3 and 2^3). We can just look at 5's since 2's will be more abundant. There are some good posts on divisibility by factors of 10 that work out this more clearly.

As we go up from 1!, we would get a 5 in each of: 5, 10, and 15. If you want to check there are three 2's by the time you get to 4! so we're covered. 15! will be the first that is divisible by 1,000.

It might be tempting to look at 10! since you get above 100 so quickly, but 10! if 3,628,800, which /1,000 is not an integer (done in excel, not needed on the test or if you understand the concepts.

Re: least value of N (m09q33) [#permalink]
25 Oct 2011, 21:00

sarathy wrote:

For such questions, always work through the answers choice from lowest to highest i.e. A to E. The moment you get an answers that matches, stop and mark that as the answer and move on.

I would add that for "least" questions this should be done. The opposite should be done for "greatest".