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

It is currently 23 Jul 2014, 07:04

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

In N is a positive integer less than 200, and 14N/60 is an

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 23 Jun 2009
Posts: 47
Followers: 0

Kudos [?]: 2 [0], given: 6

In N is a positive integer less than 200, and 14N/60 is an [#permalink] New post 27 Jul 2009, 00:15
00:00
A
B
C
D
E

Difficulty:

  25% (low)

Question Stats:

76% (01:55) correct 24% (00:49) wrong based on 146 sessions
In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors?

A. 2
B. 3
C. 5
D. 6
E. 8

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-n-is-a-positive-integer-less-than-200-and-14n-60-is-an-100763.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Nov 2012, 00:24, edited 2 times in total.
Renamed the topic and edited the question.
Kaplan GMAT Prep Discount CodesKnewton GMAT Discount CodesManhattan GMAT Discount Codes
Director
Director
avatar
Joined: 05 Jun 2009
Posts: 852
WE 1: 7years (Financial Services - Consultant, BA)
Followers: 8

Kudos [?]: 173 [0], given: 106

GMAT Tests User
Re: HOW MANY different positive prime factors? [#permalink] New post 27 Jul 2009, 00:32
X = 14n/60 is an integer

X= 14n/60 = 7n/30

n has to be a multiple of 30 in this case for X to be integer.

possible values for n < 200
= 30*(1 to 6)

==> possible prime factors - 2,3 and 5

_________________

Consider kudos for the good post ... :beer
My debrief : journey-670-to-720-q50-v36-long-85083.html

Manager
Manager
User avatar
Joined: 03 Jul 2009
Posts: 107
Location: Brazil
Followers: 2

Kudos [?]: 47 [0], given: 13

GMAT Tests User
Re: HOW MANY different positive prime factors? [#permalink] New post 27 Jul 2009, 16:23
I like to put the numbers in prime factors so it is easier and faster to visualize.

14*n/60

If we write the factors of 14 --> 2, 7, and the factors of 60 --> 2, 2, 3, 5, we have

(2*7*n)/(2^2*3*5)
Simplifying
7*n/(2*3*5)

The only way the equation above has an integer value is if n has AT LEAST the factors 2, 3 and 5, so we can simplify again and we have the number 7.

The number could be 2*3*5, or 2*3*5*2, or 2*3*5*.....

However to be less than 200 we can not add any prime number.
2*3*5 = 120
If we added the next prime factor 7, we would have 2*3*5*7 = 840

Thus, answer B

Again, The explanation might looks long. But try to do this question following this procedure and you will see it is faster.

Good studies

PS.: If you liked the explanation, consider a kudo! ;) I am almost accessing the GMATClub tests!!! :)
Manager
Manager
avatar
Joined: 22 Mar 2008
Posts: 56
Followers: 1

Kudos [?]: 8 [0], given: 1

Re: HOW MANY different positive prime factors? [#permalink] New post 29 Jul 2009, 09:56
14n/60 = 7n/30
since this is an integer n has to be a multiple of 30.
now, the prime factors of 30 = 2, 3, 5
hence n must have atleast these 3 prime factors.

so B.
Manager
Manager
avatar
Status: K... M. G...
Joined: 22 Oct 2012
Posts: 51
Concentration: General Management, Leadership
GMAT Date: 08-27-2013
GPA: 3.8
Followers: 0

Kudos [?]: 5 [0], given: 118

Re: HOW MANY different positive prime factors? [#permalink] New post 03 Nov 2012, 00:17
coelholds wrote:
I like to put the numbers in prime factors so it is easier and faster to visualize.

14*n/60

If we write the factors of 14 --> 2, 7, and the factors of 60 --> 2, 2, 3, 5, we have

(2*7*n)/(2^2*3*5)
Simplifying
7*n/(2*3*5)

The only way the equation above has an integer value is if n has AT LEAST the factors 2, 3 and 5, so we can simplify again and we have the number 7.

The number could be 2*3*5, or 2*3*5*2, or 2*3*5*.....

However to be less than 200 we can not add any prime number.
2*3*5 = 120
If we added the next prime factor 7, we would have 2*3*5*7 = 840


Thus, answer B

Again, The explanation might looks long. But try to do this question following this procedure and you will see it is faster.

Good studies

PS.: If you liked the explanation, consider a kudo! ;) I am almost accessing the GMATClub tests!!! :)



2*3*5=30 & its not 120.... or I have missed something here.. Kindly explain
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18693
Followers: 3235

Kudos [?]: 22255 [0], given: 2602

Re: HOW MANY different positive prime factors? [#permalink] New post 03 Nov 2012, 00:25
Expert's post
breakit wrote:
coelholds wrote:
I like to put the numbers in prime factors so it is easier and faster to visualize.

14*n/60

If we write the factors of 14 --> 2, 7, and the factors of 60 --> 2, 2, 3, 5, we have

(2*7*n)/(2^2*3*5)
Simplifying
7*n/(2*3*5)

The only way the equation above has an integer value is if n has AT LEAST the factors 2, 3 and 5, so we can simplify again and we have the number 7.

The number could be 2*3*5, or 2*3*5*2, or 2*3*5*.....

However to be less than 200 we can not add any prime number.
2*3*5 = 120
If we added the next prime factor 7, we would have 2*3*5*7 = 840


Thus, answer B

Again, The explanation might looks long. But try to do this question following this procedure and you will see it is faster.

Good studies

PS.: If you liked the explanation, consider a kudo! ;) I am almost accessing the GMATClub tests!!! :)



2*3*5=30 & its not 120.... or I have missed something here.. Kindly explain


Clearly it's a typo.

In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors?

A. 2
B. 3
C. 5
D. 6
E. 8

Given: 0<n=integer<200 and \frac{14n}{60}=integer.

\frac{14n}{60}=\frac{7n}{30}=integer --> \frac{7n}{30} to be an integer n must be a multiple of 30=2*3*5, so n definitely has these three different positive prime factors. Also, n can not have more than 3 as if it has for example 4 different prime factors then least value of n would be 2*3*5*7=210>200.

So n has exactly 3 different positive prime factors: 2, 3, and 5.

Answer: B.

Hope it helps.

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-n-is-a-positive-integer-less-than-200-and-14n-60-is-an-100763.html

_________________

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

Re: HOW MANY different positive prime factors?   [#permalink] 03 Nov 2012, 00:25
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic In N is a positive integer less than 200, and 14N/60 is an DSGB 7 09 Sep 2010, 15:39
If n is a positive integer less than 200 and 14n/60 is an geomatrace 6 04 Sep 2007, 22:26
If n is a postive integer less than 200 and 14n/60 is an Sumithra Sen 5 15 Aug 2007, 18:58
n is a positive integer less than 200 and 14n/ 60 is an Sam Kana 9 22 Oct 2006, 17:57
If n is a positive integer less than 200 and 14n/60 is an likar 2 16 Jul 2006, 06:07
Display posts from previous: Sort by

In N is a positive integer less than 200, and 14N/60 is an

  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®.