It is currently 24 Feb 2018, 07:51

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Integer m has 4 different prime factors and n has 3 different prime

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43896
Integer m has 4 different prime factors and n has 3 different prime [#permalink]

Show Tags

New post 22 Mar 2017, 11:07
Expert's post
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

66% (01:08) correct 34% (01:40) wrong based on 106 sessions

HideShow timer Statistics

Integer m has 4 different prime factors and n has 3 different prime factors. If m and n has the greatest common factor of 15, how many different prime factors does mn have?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
B
Joined: 17 May 2016
Posts: 21
 [#permalink]

Show Tags

New post 22 Mar 2017, 11:18
I guess that 3 and 5 are common to both m and n.
Besides that m has 2 unique prime factors and n has 1 unique factor making a total of 5 prime factors
IMO answer is B

Posted from my mobile device
Intern
Intern
avatar
B
Joined: 27 May 2016
Posts: 1
Re: Integer m has 4 different prime factors and n has 3 different prime [#permalink]

Show Tags

New post 22 Mar 2017, 11:27
Answer should be B as the there will be 3 prime numbers in addition, so in total we will have 5 different prime numbers,
Intern
Intern
avatar
Joined: 21 Mar 2017
Posts: 3
Re: Integer m has 4 different prime factors and n has 3 different prime [#permalink]

Show Tags

New post 22 Mar 2017, 11:36
I have a doubt my answer is coming out to be 4

Like I took m to be 210 which has 4 prime factors-2,3,5,7 and n to be 30 which has 3 prime factors-2,3,5

now mn is 6300 which has 4 prime factors-2,3,5,7
Intern
Intern
avatar
B
Joined: 25 Aug 2016
Posts: 4
Integer m has 4 different prime factors and n has 3 different prime [#permalink]

Show Tags

New post 22 Mar 2017, 13:05
johncath wrote:
I have a doubt my answer is coming out to be 4

Like I took m to be 210 which has 4 prime factors-2,3,5,7 and n to be 30 which has 3 prime factors-2,3,5

now mn is 6300 which has 4 prime factors-2,3,5,7


Hello, I took the same approach as yours i.e. by listing 2 sets of integers which have only prime factors. The answer must be B.

The error in the numbers you chose is as follows,
210 = 2x3x5x7
30 = 2x3x5
GCF of 210 and 30 is 2x3x5 = 30 and not 3 x 5 = 15.

Thus the numbers you selected should have been:
210 = 2x3x5x7 and
165 = 3x5x11 such that
GCF = 3 x 5 = 15.
With this combination now, Number of prime factors of mn = Count(2, 3, 5, 7, 11) = 5. Correct AC is B

Hope that helps.
Intern
Intern
avatar
Joined: 21 Mar 2017
Posts: 3
Re: Integer m has 4 different prime factors and n has 3 different prime [#permalink]

Show Tags

New post 22 Mar 2017, 19:12
ThePhDAspirant wrote:
johncath wrote:
I have a doubt my answer is coming out to be 4

Like I took m to be 210 which has 4 prime factors-2,3,5,7 and n to be 30 which has 3 prime factors-2,3,5

now mn is 6300 which has 4 prime factors-2,3,5,7


Hello, I took the same approach as yours i.e. by listing 2 sets of integers which have only prime factors. The answer must be B.

The error in the numbers you chose is as follows,
210 = 2x3x5x7
30 = 2x3x5
GCF of 210 and 30 is 2x3x5 = 30 and not 3 x 5 = 15.

Thus the numbers you selected should have been:
210 = 2x3x5x7 and
165 = 3x5x11 such that
GCF = 3 x 5 = 15.
With this combination now, Number of prime factors of mn = Count(2, 3, 5, 7, 11) = 5. Correct AC is B

Hope that helps.


Ah Got it! Thanks alot mate:)
2 KUDOS received
Senior Manager
Senior Manager
User avatar
G
Joined: 19 Apr 2016
Posts: 275
Location: India
GMAT 1: 570 Q48 V22
GMAT 2: 640 Q49 V28
GPA: 3.5
WE: Web Development (Computer Software)
Integer m has 4 different prime factors and n has 3 different prime [#permalink]

Show Tags

New post 22 Mar 2017, 22:01
2
This post received
KUDOS
1
This post was
BOOKMARKED
Bunuel wrote:
Integer m has 4 different prime factors and n has 3 different prime factors. If m and n has the greatest common factor of 15, how many different prime factors does mn have?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8


Since m has 4 different prime factors and n has 3 different prime factors

let the prime factors of m be a,b,3 and 5
let the prime factors of n be c,3 and 5

Since the GCD(m,n)=15, both m and n will have 3 and 5 as common prime factors

now m*n will have the following prime factors a,b,c,3 and 5 which are 5 in number.

Hence option B is correct.
Hit Kudos if you liked it 8-)
Senior Manager
Senior Manager
User avatar
G
Joined: 04 Sep 2015
Posts: 479
Location: India
WE: Information Technology (Computer Software)
Re: Integer m has 4 different prime factors and n has 3 different prime [#permalink]

Show Tags

New post 26 Mar 2017, 00:11
Integer m has 4 different prime factors and n has 3 different prime factors. If m and n has the greatest common factor of 15, how many different prime factors does mn have?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

Now M has 4 prime factors and n has 3.

the GCF is the greatest comman factore since it is 15 we see the prime factors for 15 and they are 3*5

so 2 of the Ms prime factor are 3 and 5 and left 2 other prime factors, 2 of the Ns prime factor are 3 and 5 left 1 other prime factor

2+(2)+1=5
Senior Manager
Senior Manager
User avatar
G
Joined: 06 Jul 2016
Posts: 437
Location: Singapore
Concentration: Strategy, Finance
GMAT ToolKit User Premium Member
Re: Integer m has 4 different prime factors and n has 3 different prime [#permalink]

Show Tags

New post 26 Mar 2017, 08:51
Bunuel wrote:
Integer m has 4 different prime factors and n has 3 different prime factors. If m and n has the greatest common factor of 15, how many different prime factors does mn have?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8


The Answer should be B.

m = A*B*C*D
n = X*Y*Z
Both have powers >= 1.

GCD (M,N) = 3*5 => 3 and 5 are common prime factors.
=> 2 + 3 additional factors so a total of 5 factors.

Correct?
_________________

Put in the work, and that dream score is yours!

Senior Manager
Senior Manager
avatar
B
Joined: 06 Dec 2016
Posts: 253
Re: Integer m has 4 different prime factors and n has 3 different prime [#permalink]

Show Tags

New post 26 Mar 2017, 10:13
M has 4 different prime factors
M - 2 x 3 x 5 x 7 = 210

N has 3 different prime factors
N - 3 x 5 x 11 = 165

MN = 210 x 165 = 34650

34650 has 5 different prime factors (2, 3, 5, 7 and 11).

The answer is B
Expert Post
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2016
Re: Integer m has 4 different prime factors and n has 3 different prime [#permalink]

Show Tags

New post 27 Mar 2017, 10:55
Bunuel wrote:
Integer m has 4 different prime factors and n has 3 different prime factors. If m and n has the greatest common factor of 15, how many different prime factors does mn have?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8


If m and n have a GCF of 15, they both share a prime of 3 and 5. Thus, m has 2 prime factors that differ from those of n and n has 1 other prime factor that differs from those of m.

Since mn has 2 common prime factors and 3 uncommon prime factors, mn has a total of 5 different prime factors.

Answer: B
_________________

Jeffery Miller
Head of GMAT Instruction

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

Re: Integer m has 4 different prime factors and n has 3 different prime   [#permalink] 27 Mar 2017, 10:55
Display posts from previous: Sort by

Integer m has 4 different prime factors and n has 3 different prime

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


cron

GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.