It is currently 13 Dec 2017, 05:24

# Decision(s) Day!:

CHAT Rooms | Ross R1 | Kellogg R1 | Darden R1 | Tepper R1

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 06 Sep 2010
Posts: 17

Kudos [?]: 94 [1], given: 6

Schools: HBS
WE 1: Management Consulting- 2 years
WE 2: Private Equity- 2 years
In N is a positive integer less than 200, and 14N/60 is an [#permalink]

### Show Tags

09 Sep 2010, 15:39
1
KUDOS
8
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

80% (01:03) correct 20% (01:12) wrong based on 368 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
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Nov 2012, 00:20, edited 1 time in total.
Renamed the topic and edited the question.

Kudos [?]: 94 [1], given: 6

Math Expert
Joined: 02 Sep 2009
Posts: 42579

Kudos [?]: 135467 [4], given: 12695

Re: Challening PS Question- factors and multiples, need help! [#permalink]

### Show Tags

09 Sep 2010, 15:50
4
KUDOS
Expert's post
3
This post was
BOOKMARKED
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.

Hope it helps.
_________________

Kudos [?]: 135467 [4], given: 12695

Intern
Joined: 24 Aug 2010
Posts: 9

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

### Show Tags

16 Sep 2010, 15:40
"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.

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

Retired Moderator
Joined: 02 Sep 2010
Posts: 792

Kudos [?]: 1230 [1], given: 25

Location: London

### Show Tags

16 Sep 2010, 15:45
1
KUDOS
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
_________________

Kudos [?]: 1230 [1], given: 25

Intern
Joined: 24 Aug 2010
Posts: 9

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

### Show Tags

16 Sep 2010, 15:48
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

Yeah I think my answer would have been wrong if the question was n<220 ... in which case I would have considered 30

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

Magoosh GMAT Instructor
Joined: 28 Nov 2011
Posts: 303

Kudos [?]: 1280 [3], given: 2

### Show Tags

19 Dec 2011, 16:43
3
KUDOS
Expert's post
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

Kudos [?]: 1280 [3], given: 2

Senior Manager
Joined: 12 Oct 2011
Posts: 254

Kudos [?]: 67 [0], given: 110

### Show Tags

05 Jan 2012, 03:40
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.
_________________

Consider KUDOS if you feel the effort's worth it

Kudos [?]: 67 [0], given: 110

Manager
Joined: 08 Aug 2011
Posts: 189

Kudos [?]: 18 [0], given: 51

GPA: 3.5

### Show Tags

05 Jan 2012, 05:19
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.

Kudos [?]: 18 [0], given: 51

Manager
Joined: 29 Jul 2011
Posts: 104

Kudos [?]: 73 [0], given: 6

Location: United States

### Show Tags

05 Jan 2012, 14:23
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

Kudos [?]: 73 [0], given: 6

Manager
Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 171

Kudos [?]: 106 [0], given: 1

Location: India
WE: Information Technology (Investment Banking)

### Show Tags

05 Jan 2012, 20:04
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

Kudos [?]: 106 [0], given: 1

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7792

Kudos [?]: 18111 [0], given: 236

Location: Pune, India

### Show Tags

06 Jan 2012, 03:49
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
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 18111 [0], given: 236

Intern
Joined: 25 Jun 2015
Posts: 9

Kudos [?]: [0], given: 269

Location: Portugal
GMAT 1: 370 Q37 V37
GPA: 2.92
Re: In N is a positive integer less than 200, and 14N/60 is an [#permalink]

### Show Tags

17 Aug 2016, 03:12
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?

Kudos [?]: [0], given: 269

Retired Moderator
Joined: 12 Aug 2015
Posts: 2209

Kudos [?]: 901 [0], given: 607

GRE 1: 323 Q169 V154
Re: In N is a positive integer less than 200, and 14N/60 is an [#permalink]

### Show Tags

23 Aug 2016, 09:16
Here 14n/60 is an integer
Hence n=30p for some p
n<200=>n can be 30,60,90,120,150,180
All have three prime factors
Smash that B
_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 901 [0], given: 607

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3106

Kudos [?]: 1144 [0], given: 327

Location: India
GPA: 3.5
In N is a positive integer less than 200, and 14N/60 is an [#permalink]

### Show Tags

21 Oct 2016, 10:21
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 )

Last edited by Abhishek009 on 22 Oct 2016, 01:15, edited 1 time in total.
TYPO edited : a multiple of

Kudos [?]: 1144 [0], given: 327

Retired Moderator
Joined: 12 Aug 2015
Posts: 2209

Kudos [?]: 901 [0], given: 607

GRE 1: 323 Q169 V154
In N is a positive integer less than 200, and 14N/60 is an [#permalink]

### Show Tags

22 Oct 2016, 00:45
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

_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 901 [0], given: 607

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3106

Kudos [?]: 1144 [0], given: 327

Location: India
GPA: 3.5
Re: In N is a positive integer less than 200, and 14N/60 is an [#permalink]

### Show Tags

22 Oct 2016, 01:14
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...
_________________

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 )

Kudos [?]: 1144 [0], given: 327

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1931

Kudos [?]: 1015 [0], given: 3

Location: United States (CA)
Re: In N is a positive integer less than 200, and 14N/60 is an [#permalink]

### Show Tags

23 Oct 2016, 15:37
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

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 1015 [0], given: 3

Non-Human User
Joined: 09 Sep 2013
Posts: 14878

Kudos [?]: 287 [0], given: 0

Re: In N is a positive integer less than 200, and 14N/60 is an [#permalink]

### Show Tags

26 Nov 2017, 01:38
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.
_________________

Kudos [?]: 287 [0], given: 0

Re: In N is a positive integer less than 200, and 14N/60 is an   [#permalink] 26 Nov 2017, 01:38
Display posts from previous: Sort by