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

It is currently 19 May 2019, 02:03
Register
GMAT Club Tests
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
CLICK HERE TO HIDE/SHOW EVENTS

M and N are two positive integers and each of them has 20 factors. If

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
  Sort by Date Sort by Kudos  
Search for:
 
Print view
First unread post
Author Message
TAGS:

Hide Tags

 
Intern
Intern
User avatar
B
Joined: 25 Apr 2018
Posts: 10
Location: India
Concentration: Strategy, Finance
Schools: ISB '20, SMU '21
GMAT 1: 600 Q40 V33
Reviews Badge CAT Tests
M and N are two positive integers and each of them has 20 factors. If  [#permalink]

Show Tags

New post 21 Apr 2019, 07:37
1
4
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

44% (02:07) correct 56% (01:52) wrong based on 32 sessions

HideShow timer Statistics

M and N are two positive integers and each of them has 20 factors. If r is the total number of prime factors of M and s is the total number of prime factors of N,then what is the maximum value of r-s?

a)0
b)1
c)2
d)6
e)26
Spoiler: OA

_________________
Gmat aspirant
Target score 750 !
Signature Read More
Most Helpful Community Reply
Senior Manager
Senior Manager
User avatar
D
Joined: 15 Jan 2018
Posts: 277
Location: India
Concentration: General Management, Finance
Schools: HBS '22, Stanford '22, Wharton '22, Kellogg '22, Booth '22, Sloan '22, Haas '22, Yale '22
GMAT 1: 720 Q50 V37
WE: Information Technology (Computer Software)
Premium Member Reviews Badge
Re: M and N are two positive integers and each of them has 20 factors. If  [#permalink]

Show Tags

New post 21 Apr 2019, 11:00
4
1
For the maximum value of r - s, let's find the maximum value of r and the minimum value of s.

Given that r is the total number of prime factors of M, and M is a positive integer that has 20 factors.
For the maximum value of r, let's assume that M = prime number \(p1^{1}p2^{1}p3^{4}\). In such a case, the number of factors of M is 20 and the number of prime factors is 3. We cannot have more than 3 prime numbers for the number of factors to be 20.
Hence, the lowest possible value of r is 3.

Also, Given that s is the total number of prime factors of N, and N is a positive integer that has 20 factors.
For the minimum value of s, let's assume that N = prime number \(p^{19}\). In such a case, the number of factors of N is 20 and the number of prime factors is 1.
Hence, the lowest possible value of s is 1.

Therefore, Max (r) - Min (s) = 3 - 1 = 2. So, the correct answer is option C. 2
_________________
In case my post helps you, please provide me with kudos. Thank you :-)
Signature Read More
General Discussion
Senior Manager
Senior Manager
User avatar
P
Joined: 28 Jul 2016
Posts: 373
Location: India
Concentration: Finance, Human Resources
Schools: LBS '19, ISB '18 (S), IIM-A"19
GPA: 3.97
M and N are two positive integers and each of them has 20 factors. If  [#permalink]

Show Tags

New post 21 Apr 2019, 11:01
4
A number with 20 factors can be written as
20 = 2*2*5 or\(a^1 * b^1 * c^4\)
20 = 4*5 or\(a^3 * b^4\)
20 = 10*2 or \(a^9 * b^1\)
20 = 20 or \(a^19\)

where a, b, c are prime factors
Hence a number with 20 factors can have a maximum of 3 and a minimum of 1 prime factors
3-1 = 2
Answer C
_________________
Please give Kudos. Kudos encourage active discussions and help the community grow
Signature Read More
VP
VP
avatar
V
Joined: 30 Jan 2016
Posts: 1052
Reviews Badge CAT Tests
Re: M and N are two positive integers and each of them has 20 factors. If  [#permalink]

Show Tags

New post 22 Apr 2019, 08:35
Hi axezcole92,

This question should be in the PS subforum. Please read here:
https://gmatclub.com/forum/rules-for-po ... 33935.html
_________________
Non progredi est regredi
Signature Read More
GMAT Club Bot
Re: M and N are two positive integers and each of them has 20 factors. If   [#permalink] 22 Apr 2019, 08:35
Print view
First unread post
Display posts from previous: Sort by

M and N are two positive integers and each of them has 20 factors. If

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

Moderators: chetan2u, Bunuel, VeritasKarishma, amanvermagmat, gmatbusters

Search for:


Copyright

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

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

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®.

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions