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

It is currently 14 Oct 2019, 15:56

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

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

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

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 06 Sep 2010
Posts: 16
Schools: HBS
WE 1: Management Consulting- 2 years
WE 2: Private Equity- 2 years
If N is a positive integer less than 200, and 14N/60 is an  [#permalink]

Show Tags

New post Updated on: 17 Sep 2018, 23:26
2
1
20
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

82% (01:32) correct 18% (01:52) wrong based on 679 sessions

HideShow timer Statistics

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

Originally posted by DSGB on 09 Sep 2010, 16:39.
Last edited by bb on 17 Sep 2018, 23:26, edited 2 times in total.
Renamed the topic and edited the question.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58320
Re: If N is a positive integer less than 200, and 14N/60 is an  [#permalink]

Show Tags

New post 09 Sep 2010, 16:50
10
4
jjewkes wrote:
I am not sure how to solve this one:

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.
_________________
General Discussion
Intern
Intern
User avatar
Joined: 24 Aug 2010
Posts: 9
Re: If N is a positive integer less than 200, and 14N/60 is an  [#permalink]

Show Tags

New post 16 Sep 2010, 16:40
"n" has to be multiple of 60 if 14n/60 has to be an integer. The multiples of 60 < 200 are 60,120,180.

The prime factors of 60 are 2,3,5 . It would be the same with 120 and 180.
The number of prime factors are 3. Hence B.

Pls correct me if my explanation is wrong.
Retired Moderator
User avatar
Joined: 02 Sep 2010
Posts: 728
Location: London
GMAT ToolKit User Reviews Badge
Re: If N is a positive integer less than 200, and 14N/60 is an  [#permalink]

Show Tags

New post 16 Sep 2010, 16:45
1
dharani1234 wrote:
"n" has to be multiple of 60 if 14n/60 has to be an integer. The multiples of 60 < 200 are 60,120,180.

The prime factors of 60 are 2,3,5 . It would be the same with 120 and 180.
The number of prime factors are 3. Hence B.

Pls correct me if my explanation is wrong.


For 14n/60 to be an integer, n only needs to be a multiple of 30.
But the same logic holds even in that case.
As a multiple of 30, it already has 2,3,5 as factors
For 7 to be a factor (next smallest prime), n would need to be 210 which is not possible
Hence the answer is 3.
_________________
Intern
Intern
User avatar
Joined: 24 Aug 2010
Posts: 9
Re: If N is a positive integer less than 200, and 14N/60 is an  [#permalink]

Show Tags

New post 16 Sep 2010, 16:48
shrouded1 wrote:
dharani1234 wrote:
"n" has to be multiple of 60 if 14n/60 has to be an integer. The multiples of 60 < 200 are 60,120,180.

The prime factors of 60 are 2,3,5 . It would be the same with 120 and 180.
The number of prime factors are 3. Hence B.

Pls correct me if my explanation is wrong.


For 14n/60 to be an integer, n only needs to be a multiple of 30.
But the same logic holds even in that case.
As a multiple of 30, it already has 2,3,5 as factors
For 7 to be a factor (next smallest prime), n would need to be 210 which is not possible
Hence the answer is 3.


Yeah I think my answer would have been wrong if the question was n<220 ... in which case I would have considered 30 :P
Magoosh GMAT Instructor
User avatar
Joined: 28 Nov 2011
Posts: 300
Re: If N is a positive integer less than 200, and 14N/60 is an  [#permalink]

Show Tags

New post 19 Dec 2011, 17:43
5
The lowest prime number, 2, is also the only even prime number. 2, 3, 5, 7, 11…

Every number is made up of at least one prime factor, except for the number 1.

Every number that is not a prime can be broken into prime factors.

Of course this is very basic, but it is important to keep in mind when factoring larger numbers. For instance if we take the number 60 we can see that it is comprised of the factors 4 x 3 x 5. Notice that 3 and 5 are both primes, however 4 is not. A number that is not a prime can always be broken down into more than one prime number, whether those number or numbers are distinct. Therefore 4 can be broken down to 2 and 2.

When taking apart larger numbers sometimes a factoring tree can be helpful. (The U.S. emphasizes this skill and thus it comes naturally for those schooled in the U.S. ). With a large number sometimes the easiest way to approach it is by dividing by 2 if it is even, and if odd, knowing the divisibility rules for 3, 5, etc.

Let’s take a random number, say 136. We can start dividing by 2 as follows: 136/2 = 68, 68/2 = 34, 34/2 = 17. Now we have the prime factors. Three ‘2s’ and a ’17.’ Sometimes a question, such as the question in the thread, will ask for distinct or different primes. In the case of 136, the distinct primes will be 2 and 17.

This of course is really high-level and unless you are at the 200-300 GMAT level you would never such a question. Nonetheless, these fundamentals apply even to difficult prime factorization problems.

So back to the question at hand:

14n/60, can be reduced to 7n/30. Because 7n/30 has to be an integer, n has to be a multiple of 30. The prime factors of 30 are 2, 3, and 5.

The next important part to the question is “different positive factors.” So if we multiply the prime factors 2, 3, 5 times 30, we do not change the number of different prime factors. But as soon as we multiply n times the next highest prime factor, 7, we go over 200: n = 30x7 = 210. Therefore n contains only three prime factors: 2, 3, and 5.

Hope that helped!
_________________
Christopher Lele
Magoosh Test Prep

Image

Image
Manager
Manager
avatar
Joined: 12 Oct 2011
Posts: 155
Re: If N is a positive integer less than 200, and 14N/60 is an  [#permalink]

Show Tags

New post 05 Jan 2012, 04:40
7n/30 tells us that n is a factor of 30, which has 2, 3, and 5 as its prime factors. Each of them is distinct. Moreover, all multiples of 30 less than 200 can be derived by multiplying these prime factors alone. Thus, number of different prime factors is 3.
Answer: B
_________________
Consider KUDOS if you feel the effort's worth it
Manager
Manager
avatar
Joined: 08 Aug 2011
Posts: 92
GPA: 3.5
Re: If N is a positive integer less than 200, and 14N/60 is an  [#permalink]

Show Tags

New post 05 Jan 2012, 06:19
60 can be factorized into 2,2,3 and 5.
14 already has one 2 so n must have 2,3 and 5 to yield an integer and which are 3 distinct prime numbers hence B.
Manager
Manager
User avatar
Joined: 29 Jul 2011
Posts: 76
Location: United States
Re: If N is a positive integer less than 200, and 14N/60 is an  [#permalink]

Show Tags

New post 05 Jan 2012, 15:23
1
14n/60, lets factorize this as 2x7xn / 2x2x3x5 -> 7xn / 2x3x5. Therefore, n has 2, 3, 5 for this to be an integer. That is n needs to be a factor of 30.

3 prime factors, B.
_________________
I am the master of my fate. I am the captain of my soul.
Please consider giving +1 Kudos if deserved!

DS - If negative answer only, still sufficient. No need to find exact solution.
PS - Always look at the answers first
CR - Read the question stem first, hunt for conclusion
SC - Meaning first, Grammar second
RC - Mentally connect paragraphs as you proceed. Short = 2min, Long = 3-4 min
Manager
Manager
avatar
Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 121
Location: India
Concentration: Finance, International Business
WE: Information Technology (Investment Banking)
Re: If N is a positive integer less than 200, and 14N/60 is an  [#permalink]

Show Tags

New post 05 Jan 2012, 21:04
Impenetrable wrote:
Hi guys,
I never really had to deal with prime factors (they don't really matter in the German school system) and that's why I often struggle with questions.

In n is a positive integer smaller than 200 and (14n)/60 is an integer, then n has how many different positive prime factors?

2
3
5
6
8


Can you please explain your answer and maybe give me some tipps for those kind of questions?

Thanks!

Here first we further break down the no 14n/60 to 7n/30

now 30 = 2*3*5

so to get an integer the numerator must be a multiple of 2*3*5
so the smallest number which satisfies this condition is 30
thus we have 3 prime numbers here for n i.e 2,3,5

so ans is B
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9699
Location: Pune, India
Re: If N is a positive integer less than 200, and 14N/60 is an  [#permalink]

Show Tags

New post 06 Jan 2012, 04:49
Impenetrable wrote:
Hi guys,
I never really had to deal with prime factors (they don't really matter in the German school system) and that's why I often struggle with questions.

In n is a positive integer smaller than 200 and (14n)/60 is an integer, then n has how many different positive prime factors?

2
3
5
6
8


Can you please explain your answer and maybe give me some tipps for those kind of questions?

Thanks!


Some time back, I had written a couple of posts on prime factors discussing their usage on GMAT. You might find them useful.

http://www.veritasprep.com/blog/2010/12 ... ly-number/
http://www.veritasprep.com/blog/2010/12 ... t-squares/
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Intern
Intern
avatar
Joined: 25 Jun 2015
Posts: 8
Location: Portugal
GMAT 1: 370 Q37 V37
GPA: 2.92
GMAT ToolKit User
Re: If N is a positive integer less than 200, and 14N/60 is an  [#permalink]

Show Tags

New post 17 Aug 2016, 04:12
I multiplied 60 x 14 and did prime factorisation, counted the prime #´s from 200 below and was 3, 5 and 7 = 3 prime #´s. Can it be solved that way or I was lucky?
Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2572
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User
Re: If N is a positive integer less than 200, and 14N/60 is an  [#permalink]

Show Tags

New post 23 Aug 2016, 10:16
Board of Directors
User avatar
D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4765
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User
Re: If N is a positive integer less than 200, and 14N/60 is an  [#permalink]

Show Tags

New post Updated on: 22 Oct 2016, 02:15
1
Impenetrable wrote:
In n is a positive integer smaller than 200 and (14n)/60 is an integer, then n has how many different positive prime factors?

2
3
5
6
8


\(\frac{14n}{60}\) = \(\frac{2*7*n}{2^2*3*5}\) = \(\frac{7*n}{2*3*5}\)

Since the numerator and denominator has nothing in common so, n must be a multiple of 2*3*5 for the numerator to be divisible by 60

Thus the number of Prime factors of n will be 3

_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Originally posted by Abhishek009 on 21 Oct 2016, 11:21.
Last edited by Abhishek009 on 22 Oct 2016, 02:15, edited 1 time in total.
TYPO edited : a multiple of
Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2572
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User
Re: If N is a positive integer less than 200, and 14N/60 is an  [#permalink]

Show Tags

New post 22 Oct 2016, 01:45
Abhishek009 wrote:
Impenetrable wrote:
In n is a positive integer smaller than 200 and (14n)/60 is an integer, then n has how many different positive prime factors?

2
3
5
6
8


\(\frac{14n}{60}\) = \(\frac{2*7*n}{2^2*3*5}\) = \(\frac{7*n}{2*3*5}\)

Since the numerator and denominator has nothing in common so, n must be 2*3*5 for the numerator to be divisible by 60
Thus the number of Prime factors of n will be 3


=> Hey..! Looks like there is an error here Abhishek009.You shouldn't write that n must be 2*3*5. Instead N can be 2*3*5 or 2*3*5*2 or 2*3*5*3 or 2*3*5*4 or 2*3*5*5 . In all the cases N will have 3 prime factors.
The smallest value for n to have more than 3 prime factors will be 210 which is not allowed in the bound specified for n

_________________
Board of Directors
User avatar
D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4765
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User
Re: If N is a positive integer less than 200, and 14N/60 is an  [#permalink]

Show Tags

New post 22 Oct 2016, 02:14
stonecold wrote:
Abhishek009 wrote:
Impenetrable wrote:
In n is a positive integer smaller than 200 and (14n)/60 is an integer, then n has how many different positive prime factors?

2
3
5
6
8


\(\frac{14n}{60}\) = \(\frac{2*7*n}{2^2*3*5}\) = \(\frac{7*n}{2*3*5}\)

Since the numerator and denominator has nothing in common so, n must be a multiple of 2*3*5 for the numerator to be divisible by 60
Thus the number of Prime factors of n will be 3


=> Hey..! Looks like there is an error here Abhishek009.You shouldn't write that n must be 2*3*5. Instead N can be 2*3*5 or 2*3*5*2 or 2*3*5*3 or 2*3*5*4 or 2*3*5*5 . In all the cases N will have 3 prime factors.
The smallest value for n to have more than 3 prime factors will be 210 which is not allowed in the bound specified for n


It was a TYPO in the highlighted part, else it will change our answer as you have correctly pointed out... :oops:
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8043
Location: United States (CA)
Re: If N is a positive integer less than 200, and 14N/60 is an  [#permalink]

Show Tags

New post 23 Oct 2016, 16:37
DSGB wrote:
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


We are given that N is a positive integer less than 200, and 14N/60 is an integer, and we need to determine the number of different positive prime factors of N. Let’s begin by simplifying 14N/60.

14N/60 = 7N/30

In order for 7N/30 to be an integer, N must be divisible by 30. In other words, N must be a multiple of 30. The multiples of 30 less than 200 are: 30, 60, 90, 120, 150 and 180. First let’s investigate 30, the smallest positive number that is a multiple of 30.

Since 30 = 2 x 3 x 5, N has 3 different positive prime factors.

However, even if we break 60, 90, 120, 150, or 180 into prime factors, we will see that each of those numbers has 3 different prime factors (2, 3, and 5).

Thus, we can conclude that N has 3 different positive prime factors

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.

GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4000
Location: Canada
Re: If N is a positive integer less than 200, and 14N/60 is an  [#permalink]

Show Tags

New post 01 Jan 2018, 09:03
Top Contributor
DSGB wrote:
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


Let's choose a nice value of N that satisfies the given information.

GIVEN: 14N/60 is an integer
Prime factorize the numerator and denominator to get: (7)(2)(N)/(2)(2)(3)(5) is an integer
Simplify: (7)(N)/(2)(3)(5) is an integer
Notice that, when N = 30 (aka the product of 2, 3, and 5), then (7)(N)/(2)(3)(5) = (7)(2)(3)(5)/(2)(3)(5) = 7, which IS an integer
So, N = 30 satisfies the given information.

N has how many different positive prime factors?
30 = (2)(3)(5)
So, N has 3 different positive prime factors (2, 3 and 5)

Answer: B

RELATED VIDEO FROM OUR COURSE

_________________
Test confidently with gmatprepnow.com
Image
Intern
Intern
User avatar
S
Joined: 05 Oct 2017
Posts: 45
Location: Bangladesh
Concentration: Accounting, Social Entrepreneurship
Re: If N is a positive integer less than 200, and 14N/60 is an  [#permalink]

Show Tags

New post 29 Oct 2018, 13:15
DSGB wrote:
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



I believe the question is asking for the number of distinct positive prime factors

14n/60 can be simplified to 7n/30. If 7n/30 is a positive integer, then 30 must be a factor of n, as it is not a factor of 7.

The possibilities for n (given that n < 200) are 30, 60, 90, 120, 150, 180

If you test these numbers you will quickly see that they all have the same 3 distinct prime factors: 3, 2 and 5.

Hope that helps...

Posted from my mobile device
_________________
.... You are already NAKED. There is NO reason not to FOLLOW your heart.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13144
Re: If n is a positive integer less than 200 and 14n/60 is an  [#permalink]

Show Tags

New post 08 Oct 2019, 05:52
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: If n is a positive integer less than 200 and 14n/60 is an   [#permalink] 08 Oct 2019, 05:52
Display posts from previous: Sort by

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

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





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