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

It is currently 16 Oct 2019, 17:38

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

How many prime factors does N have?

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

Hide Tags

Find Similar Topics 
Intern
Intern
User avatar
S
Joined: 03 Oct 2018
Posts: 14
GMAT ToolKit User
How many prime factors does N have?  [#permalink]

Show Tags

New post Updated on: 29 Oct 2018, 21:47
10
2
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

38% (01:28) correct 63% (01:42) wrong based on 119 sessions

HideShow timer Statistics

How many prime factors does N have?

(1) The least prime factor of N is greater than √N.

(2) N has 2 positive factors.

Originally posted by piyush26 on 29 Oct 2018, 11:21.
Last edited by Bunuel on 29 Oct 2018, 21:47, edited 1 time in total.
Renamed the topic.
GMATH Teacher
User avatar
P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: How many prime factors does N have?  [#permalink]

Show Tags

New post 29 Oct 2018, 15:19
2
piyush26 wrote:
How many prime factors does the positive integer N have?

(1) The least prime factor of N is greater than √N.

(2) N has exactly 2 positive factors.

Very nice conceptual problem, piyush26 (kudos) !

\(?\,\, = \,\,\,\,\# \,\,{\text{prime}}\,{\text{factors}}\,\,{\text{of}}\,\,N\,\,\,\,\,\,\left( {N \geqslant 1\,\,\operatorname{int} } \right)\)


\(\left( 1 \right)\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,N\,\,{\text{prime}}\,\,\,\,\, \Rightarrow \,\,\,\,? = 1\,\,\,\left( {N\,\,{\text{itself}}} \right)\)


\(\left( * \right)\,\,\left\{ \begin{gathered}
N = 1\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{no}}\,\,{\text{prime}}\,\,{\text{factors}} \hfill \\
N \geqslant 4\,\,{\text{not}}\,\,{\text{prime}}\,\,\,\,\, \Rightarrow \,\,\,\,\,\,2 \leqslant p\,\,{\text{prime}}\,\,{\text{factor}}\,\,{\text{of}}\,\,N\,\, \leqslant \sqrt N \,\,{\text{exists}} \hfill \\
\end{gathered} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{contradicts}}\,\,\left( 1 \right)\)


\(\left( 2 \right)\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {**} \right)} \,\,\,\,N\,\,{\text{prime}}\,\,\,\,\, \Rightarrow \,\,\,\,? = 1\,\,\,\left( {N\,\,{\text{itself}}} \right)\)

\(\left( {**} \right)\,\,\left\{ \begin{gathered}
N = 1\,\,\,\,\, \Rightarrow \,\,\,{\text{only}}\,\,1\,\,{\text{positive}}\,\,{\text{factor}}\,\,\left( {N\,\,{\text{itself}} } \right) \hfill \\
N \geqslant 4\,\,{\text{not}}\,\,{\text{prime}}\,\,\,\,\, \Rightarrow \,\,\,{\text{more}}\,\,{\text{than}}\,\,{\text{the}}\,\,{\text{trivial}}\,\,{\text{two}}\,\,\left( {1\,\,{\text{and}}\,\,N} \right)\,\,{\text{positive}}\,\,{\text{factors}} \hfill \\
\end{gathered} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{contradicts}}\,\,\left( 2 \right)\,\,\,\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Retired Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1256
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: How many prime factors does N have?  [#permalink]

Show Tags

New post 29 Oct 2018, 18:11
Hii
Statement 1: least prime factor of N is greater than √N, hence no there is no factor of N except 1 and the number N inself. It is a prime number. So no of prime factors =1. Sufficient.

Statement 2:
Since N has 2 prime factors, it is a prime number and hence the no of prime factors is 1. Sufficient.

Answer D

Don't forget to tag me in case of any doubt.

piyush26 wrote:
How many prime factors does N have?

(1) The least prime factor of N is greater than √N.

(2) N has 2 positive factors.


Posted from my mobile device
_________________
Intern
Intern
avatar
B
Joined: 19 Aug 2018
Posts: 31
Re: How many prime factors does N have?  [#permalink]

Show Tags

New post 29 Oct 2018, 19:48
Why statement 1 is sufficient? is because of 2?
Retired Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1256
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: How many prime factors does N have?  [#permalink]

Show Tags

New post 29 Oct 2018, 20:00
1
we need to check for factors only upto \(\sqrt{n}\) because the factors repeat after this. See attached file
Attachment:
2018_10_30 08_26 Office Lens.jpg
2018_10_30 08_26 Office Lens.jpg [ 98.8 KiB | Viewed 796 times ]

jorgetomas9 wrote:
Why statement 1 is sufficient? is because of 2?

_________________
Retired Moderator
User avatar
V
Joined: 28 Mar 2017
Posts: 1195
Location: India
GMAT 1: 730 Q49 V41
GPA: 4
Re: How many prime factors does N have?  [#permalink]

Show Tags

New post 30 Oct 2018, 10:27
piyush26 wrote:
How many prime factors does N have?

(1) The least prime factor of N is greater than √N.

(2) N has 2 positive factors.


Stmt 2 is obviously sufficient

let's look at stmt 1:

In GMAT world we don't have sq rt of -ve numbers ... thus we will consider only whole numbers.

0 and 1 are out of commission because they don't have prime factors.

2 --> least prime factor pf 2 is 2 which is greater than sq rt of 2 i.e. 1.41
3 and other prime numbers --> same as 2
4 --> least prime factor = sq rt of 4 = 2 .... this doesn't satisfy our condition ... thus we can't consider 4

For all even numbers > 4, least prime factor = 2 will be lesser than sq rt of that number thus we can't consider those numbers

9 --> least prime factor = sq rt of 9 = 3 .... this doesn't satisfy our condition ... thus we can't consider 9

Next odd non prime number = 15 --> least prime number = 3 which is lesser than sq rt of 15 .... thus we can't consider odd non prime numbers ....

This leaves us with ONLY PRIME NUMBERS.

This is sufficient to answer our question.

Thus answer = D

I hope that helps!
_________________
Intern
Intern
avatar
Joined: 10 May 2018
Posts: 34
Re: How many prime factors does N have?  [#permalink]

Show Tags

New post 30 Oct 2018, 13:11
piyush26 wrote:
How many prime factors does N have?

(1) The least prime factor of N is greater than √N.

(2) N has 2 positive factors.


Either statement suggests that N is prime.

D
Intern
Intern
avatar
B
Joined: 08 Jul 2017
Posts: 43
GMAT 1: 740 Q51 V38
Reviews Badge
Re: How many prime factors does N have?  [#permalink]

Show Tags

New post 01 Nov 2018, 22:25
How many prime factors does N have?

(1) The least prime factor of N is greater than √N.

(2) N has 2 positive factors.

1. Imagine, this is possible only when the greatest prime factor is the prime number itself. Hence, N is a prime number and has only 1 prime factor- N itself.

2. This is possible only for a prime number. Only a prime number has 2 factors. Any prime number has one prime factor (the number itself). Hence, the answer is 1. Sufficient.

D.
Retired Moderator
User avatar
V
Joined: 28 Mar 2017
Posts: 1195
Location: India
GMAT 1: 730 Q49 V41
GPA: 4
Re: How many prime factors does N have?  [#permalink]

Show Tags

New post 02 Nov 2018, 04:12
Aamirso wrote:
piyush26 wrote:
How many prime factors does N have?

(1) The least prime factor of N is greater than √N.

(2) N has 2 positive factors.


Either statement suggests that N is prime.

D


Hi,

Please try to post meaningful posts. The option D in DS questions means that both the statements are individually sufficient to answer the question.

Best.

Posted from my mobile device
_________________
GMAT Club Bot
Re: How many prime factors does N have?   [#permalink] 02 Nov 2018, 04:12
Display posts from previous: Sort by

How many prime factors does N have?

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





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