Find all School-related info fast with the new School-Specific MBA Forum

It is currently 22 Aug 2014, 04:23

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 29 Sep 2011
Posts: 16
Followers: 1

Kudos [?]: 4 [0], given: 0

For any positive integer n, n>1, the "length" of n is the [#permalink] New post 21 Jan 2012, 06:25
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

70% (01:00) correct 30% (01:24) wrong based on 126 sessions
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!
[Reveal] Spoiler: OA
Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19047
Followers: 3367

Kudos [?]: 24497 [2] , given: 2680

Re: Length of an integer [#permalink] New post 21 Jan 2012, 06:32
2
This post received
KUDOS
Expert's post
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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
avatar
Joined: 16 Feb 2012
Posts: 259
Concentration: Finance, Economics
Followers: 4

Kudos [?]: 53 [0], given: 106

GMAT ToolKit User
Re: For any positive integer n, n>1, the "length" of n is the [#permalink] New post 10 Feb 2013, 07:39
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: 75
Location: United States
Followers: 0

Kudos [?]: 6 [0], given: 23

Re: For any positive integer n, n>1, the "length" of n is the [#permalink] New post 21 Oct 2013, 01:37
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

Re: For any positive integer n, n>1, the "length" of n is the   [#permalink] 21 Oct 2013, 01:37
    Similar topics Author Replies Last post
Similar
Topics:
2 For any positive integer n, the length of n is defined as jimjohn 3 26 Dec 2007, 19:16
For any positive integer n, the length of n is defined as r019h 1 23 Oct 2007, 08:43
for any positive integer n, the length of n is defined as young_gun 1 08 Oct 2007, 16:48
1 Experts publish their posts in the topic For any positive integer n, n>1, the "length" of n is the Sumithra Sen 3 18 Aug 2007, 11:24
For any positive integer n , n > 1, the terp26 2 08 Mar 2007, 20:09
Display posts from previous: Sort by

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

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.