Find all School-related info fast with the new School-Specific MBA Forum

It is currently 23 Jul 2014, 00:09

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The greatest common factor of 16 and the positive integer n

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Manager
Manager
User avatar
Joined: 04 Jan 2008
Posts: 120
Followers: 2

Kudos [?]: 9 [1] , given: 0

The greatest common factor of 16 and the positive integer n [#permalink] New post 16 Sep 2008, 06:44
1
This post received
KUDOS
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

52% (02:17) correct 48% (01:54) wrong based on 163 sessions
The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210?

A. 3
B. 14
C. 30
D. 42
E. 70
[Reveal] Spoiler: OA
SVP
SVP
User avatar
Joined: 05 Jul 2006
Posts: 1542
Followers: 5

Kudos [?]: 65 [0], given: 39

Re: Zumit PS 021 [#permalink] New post 16 Sep 2008, 07:03
dancinggeometry wrote:
The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210?

3
14
30
42
70


n= 4x, n= 3y ie: n= 12z ie: 3*2*2*z , z cant be 5 or 2 or 3

210 = 5*2*3*7 from the choices 3 wins
Senior Manager
Senior Manager
avatar
Joined: 31 Jul 2008
Posts: 309
Followers: 1

Kudos [?]: 17 [0], given: 0

GMAT Tests User
Re: Zumit PS 021 [#permalink] New post 16 Sep 2008, 16:13
42

5 cannot be a factor of n (between n and 45 common factor is only 3 not 5)
1 KUDOS received
Director
Director
avatar
Joined: 14 Aug 2007
Posts: 735
Followers: 7

Kudos [?]: 96 [1] , given: 0

GMAT Tests User
Re: Zumit PS 021 [#permalink] New post 17 Sep 2008, 00:09
1
This post received
KUDOS
dancinggeometry wrote:
The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210?

3
14
30
42
70


since GCF of 16 and n is 4
16 = 2*2 * 2 * 2
n = 2*2 * ...

since GCF of 45 and n is 3
45 = 5 * 3 * 3
n = 3 * ...

thus n must be 2*2 *3 *...

210 = 7 * 3 * 5 * 2

n can not be 5, (otherwise GCF of 45 and 3 would have been 15)
it can be 7 though

7*3*2 = 42

D.
Manager
Manager
avatar
Status: Essaying
Joined: 27 May 2010
Posts: 156
Location: Ghana
Concentration: Finance, Finance
Schools: Cambridge
GMAT 1: 690 Q47 V37
GPA: 3.9
WE: Accounting (Education)
Followers: 1

Kudos [?]: 7 [0], given: 8

GMAT ToolKit User GMAT Tests User
Re: Zumit PS 021 [#permalink] New post 23 Sep 2011, 01:43
I believe it should be 3 based on the given data. "N" can be 12 and satisfy the two conditions(2,2,3).
Manager
Manager
avatar
Status: Meh, I can't take the GMAT before 2017.
Joined: 20 Aug 2011
Posts: 152
Followers: 3

Kudos [?]: 64 [0], given: 0

Re: Zumit PS 021 [#permalink] New post 23 Sep 2011, 01:58
The questions states "could be" & not "must be".

The greatest common factor of 16 and the positive integer n is 4
The prime factor of n will have exactly two 2s
The greatest common factor of n and 45 is 3
Exactly one 3 and exactly zero 5s
Because the question states that the GCD between n and 45 is only 3. Thus, 5 cannot be a factor of n, but 7 could be a factor.

Hence, 2*3*7=42.

_________________

Hit kudos if my post helps you.
You may send me a PM if you have any doubts about my solution or GMAT problems in general.

Director
Director
avatar
Joined: 01 Feb 2011
Posts: 770
Followers: 14

Kudos [?]: 80 [0], given: 42

GMAT Tests User
Re: Zumit PS 021 [#permalink] New post 25 Sep 2011, 13:10
GCF of 16 and n = 4 => n = 2^2(...) -----1
GCF of n and 45 = 3 => n =3(...) -------2

GCF of n and 210 = ?

= GCF of (2^2)*3(...) and 2*3*5*7 = 6

so GCF of n and 210 would be multiple of 6.

Answer is D as its the only possible option that is a multiple of 6.
Intern
Intern
avatar
Joined: 18 Mar 2012
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 65

GMAT Tests User
Re: Zumit PS 021 [#permalink] New post 18 May 2012, 03:11
Spidy001 wrote:
GCF of 16 and n = 4 => n = 2^2(...) -----1
GCF of n and 45 = 3 => n =3(...) -------2

GCF of n and 210 = ?

= GCF of (2^2)*3(...) and 2*3*5*7 = 6

so GCF of n and 210 would be multiple of 6.

Answer is D as its the only possible option that is a multiple of 6.


why should the GCF of n and 210 be multiple of 6?

Thank you all!!
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18684
Followers: 3232

Kudos [?]: 22230 [0], given: 2601

Re: Zumit PS 021 [#permalink] New post 18 May 2012, 06:58
Expert's post
mila84 wrote:
Spidy001 wrote:
GCF of 16 and n = 4 => n = 2^2(...) -----1
GCF of n and 45 = 3 => n =3(...) -------2

GCF of n and 210 = ?

= GCF of (2^2)*3(...) and 2*3*5*7 = 6

so GCF of n and 210 would be multiple of 6.

Answer is D as its the only possible option that is a multiple of 6.


why should the GCF of n and 210 be multiple of 6?

Thank you all!!


The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210?
A. 3
B. 14
C. 30
D. 42
E. 70

The greatest common factor of 2^4=16 and n is 4 --> n is a multiple of 2^2=4 but not the higher powers of 2, for example 2^3=8 or 2^4=16, because if it were then the greatest common factor of 16 and n would be more than 4;

The greatest common factor of 3^2*5=45 and n is 3 --> n is a multiple of 3 but not the higher powers of 3 and not 5, because if it were then the greatest common factor of 3^2*5=45 and n would be more than 3;

So, n is a multiple of 2^2*3=12, not a multiple of higher powers of 2 or 3, and not a multiple of 5 (so n=12x where x could be any positive integer but 2, 3, or 5). Now, as 210=2*3*5*7 then the greatest common factor of n and 210 could be 6 or 6*7=42 (if 7 is a factor of n).

Answer: D.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
User avatar
Status: struggling with GMAT
Joined: 06 Dec 2012
Posts: 310
Location: Bangladesh
Concentration: Accounting
GMAT Date: 04-06-2013
GPA: 3.65
Followers: 7

Kudos [?]: 90 [0], given: 46

The greatest common factor of 16 and the positive integer n [#permalink] New post 27 Mar 2013, 03:07
The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210?

(A)3
(B)14
(C)30
(D)42
(E)70

Need easy explanation to solve it quickly
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18684
Followers: 3232

Kudos [?]: 22230 [0], given: 2601

Re: The greatest common factor of 16 and the positive integer n [#permalink] New post 27 Mar 2013, 03:15
Expert's post
mun23 wrote:
The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210?

(A)3
(B)14
(C)30
(D)42
(E)70

Need easy explanation to solve it quickly


Merging similar topics. Please refer to the solutions above.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 23 Mar 2011
Posts: 474
Location: India
GPA: 2.5
WE: Operations (Hospitality and Tourism)
Followers: 11

Kudos [?]: 92 [1] , given: 59

GMAT Tests User
Re: The greatest common factor of 16 and the positive integer n [#permalink] New post 20 Apr 2013, 11:29
1
This post received
KUDOS
mun23 wrote:
The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210?

(A)3
(B)14
(C)30
(D)42
(E)70

Need easy explanation to solve it quickly


Hi, let me try to explain in simpler way:

GCF = 4 = 2^2
16 = 2^4
that means prime box of n = 2^2 , ? ? ?

GCF = 3
45 = 3^2*5
that means prime box of n = 3^1, ? ? ?

Overall prime box of n = 2^2, 3^1, ???

Now, 210 = 3*7*5*2
from above we know the prime factor and powers of n (not complete ??)
therefore GCF = 3^1 * 2^1 * 7^1 (not 5 - we have seen above, but at least a 7 is possible)
Thus at least a GCF of 42 is possible here

Hope this helps

_________________

"When the going gets tough, the tough gets going!"

Bring ON SOME KUDOS MATES+++



-----------------------------
Quant Notes consolidated: consolodited-quant-guides-of-forum-most-helpful-in-preps-151067.html#p1217652

My GMAT journey begins: my-gmat-journey-begins-122251.html

All about Richard Ivey: all-about-richard-ivey-148594.html#p1190518

1 KUDOS received
Manager
Manager
avatar
Joined: 09 Apr 2013
Posts: 214
Location: United States
Concentration: Finance, Economics
GMAT 1: 710 Q44 V44
GMAT 2: 740 Q48 V44
GPA: 3.1
WE: Sales (Mutual Funds and Brokerage)
Followers: 4

Kudos [?]: 55 [1] , given: 40

Re: The greatest common factor of 16 and the positive integer n [#permalink] New post 20 Apr 2013, 20:48
1
This post received
KUDOS
Simple explanation?

First, do a factor tree for each number.

You'll see that 5 can't be a factor of N (otherwise it would have been the highest factor between N and 45).

The highest factor that could theoretically exist between N and 210 is therefore all of the factors of 210 besides those we've ruled out. 210 is factored to 2 * 3 * 5 * 7. we've ruled out 5, so 2 * 3 * 7 = 42. Answer is D.

If the question asked "the highest factor that we KNOW exists" rather than "COULD" exist, the answer would be six since 2 and 3 are both factors of N, as well as of 210.
SVP
SVP
User avatar
Joined: 09 Sep 2013
Posts: 1708
Followers: 162

Kudos [?]: 33 [0], given: 0

Premium Member
Re: The greatest common factor of 16 and the positive integer n [#permalink] New post 09 Jul 2014, 06:20
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: The greatest common factor of 16 and the positive integer n   [#permalink] 09 Jul 2014, 06:20
    Similar topics Author Replies Last post
Similar
Topics:
2 If the greatest common factor of two integers, m and n, is rxs0005 7 20 Mar 2011, 08:52
The greatest common factor of 16 and the positive integer n rosgmat 0 04 Nov 2012, 14:01
13 Experts publish their posts in the topic The greatest common factor of 16 and the positive integer n ajit257 18 22 Feb 2011, 17:01
4 Experts publish their posts in the topic The greatest common factor of 16 and the positive integer n krishan 13 21 Dec 2008, 04:18
1 The greatest common factor of 16 and the positive integer n kman 3 09 Aug 2008, 17:42
Display posts from previous: Sort by

The greatest common factor of 16 and the positive integer n

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

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

Powered by phpBB © phpBB Group and phpBB SEO

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®.