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

It is currently 21 Aug 2019, 19:56

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

For any positive integer n, n>1, the "length" of n is the

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

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 29 Sep 2011
Posts: 16
For any positive integer n, n>1, the "length" of n is the  [#permalink]

Show Tags

New post 21 Jan 2012, 07:25
1
31
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

67% (01:30) correct 33% (01:50) wrong based on 811 sessions

HideShow timer Statistics

For any positive integer n, n>1, the "length" of n is the number of positive primes (not necessary distinct) whose product is n. For ex, the length of 50 is 3, since 50=2x5x5. What is the greatest possible length of a positive integer less than 1000.

A. 10
B. 9
C. 8
D. 7
E. 6

Thanks!
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 57197
Re: Length of an integer  [#permalink]

Show Tags

New post 21 Jan 2012, 07:32
4
10
Splendidgirl666 wrote:
Hi,

is there a short cut for this question:

For any positive integer n, n>1, the "length" of n is the number of positive primes (not necessary distinct) whose product is n. For ex, the length of 50 is 3, since 50=2x5x5. What is the greatest possible length of a positive integer less than 1000.

1. 10
2. 9
3. 8
4. 7
5. 6

Thanks!


Basically the length of an integer is the sum of the powers of its prime factors. For example the length of 24 is 4 because 24=2^3*3^1 --> 3+1=4.

Now, to maximize the length of an integer less then 1,000 we should minimize its prime base(s). Minimum prime base is 2: so 2^x<1,000 --> x<10 --> maximum length is 9 for 2^9=512. Note that 2^9 is not the only integer whose length is 9, for example 2^8*3=768<100 also has the length of 8+1=9.

Answer: B.

Check similar questions to practice:
for-any-integer-k-1-the-term-length-of-an-integer-108124.html
for-any-positive-integer-n-the-length-of-n-is-defined-as-126740.html

Hope it helps.
_________________
General Discussion
Manager
Manager
avatar
Joined: 16 Feb 2012
Posts: 162
Concentration: Finance, Economics
GMAT ToolKit User
Re: For any positive integer n, n>1, the "length" of n is the  [#permalink]

Show Tags

New post 10 Feb 2013, 08:39
1
1
To maximize the length you should use the smallest prime number, 2.
2x2x2x2x2x2x2x2x2 = 2^9 = 512; 2^10 = 1024 which is > 1000, so you have to use 2^9.
The answer is B.
_________________
Kudos if you like the post!

Failing to plan is planning to fail.
Manager
Manager
avatar
Joined: 24 Apr 2013
Posts: 52
Location: United States
Re: For any positive integer n, n>1, the "length" of n is the  [#permalink]

Show Tags

New post 21 Oct 2013, 02:37
its really helpful to remember here that 2^10 = 1024 , so the second smallest integer less than 1024 would be 2^9
_________________
Struggling: make or break attempt
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1785
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
For any positive integer n, n>1, the "length" of n is the  [#permalink]

Show Tags

New post 20 Nov 2014, 01:10
1
To have "Maximum length", base should be least.....

\(2^{10} = 1024\)

less than 1000 is \(2^9\)

Answer = B = 9
_________________
Kindly press "+1 Kudos" to appreciate :)
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 7420
Location: United States (CA)
Re: For any positive integer n, n>1, the "length" of n is the  [#permalink]

Show Tags

New post 16 Jul 2017, 17:28
Splendidgirl666 wrote:
For any positive integer n, n>1, the "length" of n is the number of positive primes (not necessary distinct) whose product is n. For ex, the length of 50 is 3, since 50=2x5x5. What is the greatest possible length of a positive integer less than 1000.

A. 10
B. 9
C. 8
D. 7
E. 6


In order to maximize the “length,” we need to minimize the values of the prime factors of n. Since 2 is the smallest prime, let’s see how many factors of 2 we can use to get a product less than 1000. Since 2^9 = 512, we see that the largest possible length of a positive integer less than 1000 is 9.

Answer: B
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 12063
Re: For any positive integer n, n>1, the "length" of n is the  [#permalink]

Show Tags

New post 13 Aug 2018, 21:47
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.
_________________
GMAT Club Bot
Re: For any positive integer n, n>1, the "length" of n is the   [#permalink] 13 Aug 2018, 21:47
Display posts from previous: Sort by

For any positive integer n, n>1, the "length" of n is the

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





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