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

It is currently 23 Oct 2018, 10:03

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

If n is a positive integer, what is the greatest common factor

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

Hide Tags

SVP
SVP
User avatar
D
Joined: 26 Mar 2013
Posts: 1842
Reviews Badge CAT Tests
If n is a positive integer, what is the greatest common factor  [#permalink]

Show Tags

New post 01 Aug 2018, 20:50
1
7
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

34% (01:53) correct 66% (02:37) wrong based on 125 sessions

HideShow timer Statistics

If n is a positive integer, what is the greatest common factor of n and 64?

(1) No two different factors of n sum to a prime number.

(2) The greatest common factor of n and 2,310 is 165.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50060
If n is a positive integer, what is the greatest common factor  [#permalink]

Show Tags

New post 01 Aug 2018, 20:59
3
3
If n is a positive integer, what is the greatest common factor of n and 64?

Notice that 64 = 2^6. So, the GCF of n and 2^6 is either 1 or some power of 2 (from 2 to 2^6).

(1) No two different factors of n sum to a prime number. This implies that 2 is NOT a factor of n, if it were then the sum of two factors of n, 1 and 2, would be a prime number. Since 2 is not a factor of n, then the GCF of n and 2^6 is 1. Sufficient.

(2) The greatest common factor of n and 2,310 is 165. So, the GCF of n and some even number is NOT even. This implies that 2 is NOT a factor of n. Since 2 is not a factor of n, then the GCF of n and 2^6 is 1. Sufficient.

Answer: D.

Hope it's clear.
_________________

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

General Discussion
Intern
Intern
avatar
B
Joined: 06 Feb 2018
Posts: 16
Re: If n is a positive integer, what is the greatest common factor  [#permalink]

Show Tags

New post 22 Sep 2018, 12:03
Hi Bunuel
I often struggle with such questions. What topic should I revisit to get better on such questions?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50060
Re: If n is a positive integer, what is the greatest common factor  [#permalink]

Show Tags

New post 23 Sep 2018, 02:39
1
hargun3045 wrote:
Hi Bunuel
I often struggle with such questions. What topic should I revisit to get better on such questions?


2. Properties of Integers




5. Divisibility/Multiples/Factors



For other subjects:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread
_________________

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: 23 Nov 2016
Posts: 18
If n is a positive integer, what is the greatest common factor  [#permalink]

Show Tags

New post 23 Sep 2018, 12:12
Bunuel wrote:
If n is a positive integer, what is the greatest common factor of n and 64?

Notice that 64 = 2^6. So, the GCF of n and 2^6 is either 1 or some power of 2 (from 2 to 2^6).

(1) No two different factors of n sum to a prime number. This implies that 2 is NOT a factor of n, if it were then the sum of two factors of n, 1 and 2, would be a prime number. Since 2 is not a factor of n, then the GCF of n and 2^6 is 1. Sufficient.

(2) The greatest common factor of n and 2,310 is 165. So, the GCF of n and some even number is NOT even. This implies that 2 is NOT a factor of n. Since 2 is not a factor of n, then the GCF of n and 2^6 is 1. Sufficient.

Answer: D.

Hope it's clear.


Hi Bunuel what if the n is in the form of 2^p where none of the two factors of 2^p will add to a prime number. but we do not know what is the value of P so we certainly can not determine GCF .So statement 1 is not sufficient.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50060
Re: If n is a positive integer, what is the greatest common factor  [#permalink]

Show Tags

New post 23 Sep 2018, 20:47
LoneSurvivor wrote:
Bunuel wrote:
If n is a positive integer, what is the greatest common factor of n and 64?

Notice that 64 = 2^6. So, the GCF of n and 2^6 is either 1 or some power of 2 (from 2 to 2^6).

(1) No two different factors of n sum to a prime number. This implies that 2 is NOT a factor of n, if it were then the sum of two factors of n, 1 and 2, would be a prime number. Since 2 is not a factor of n, then the GCF of n and 2^6 is 1. Sufficient.

(2) The greatest common factor of n and 2,310 is 165. So, the GCF of n and some even number is NOT even. This implies that 2 is NOT a factor of n. Since 2 is not a factor of n, then the GCF of n and 2^6 is 1. Sufficient.

Answer: D.

Hope it's clear.


Hi Bunuel what if the n is in the form of 2^p where none of the two factors of 2^p will add to a prime number. but we do not know what is the value of P so we certainly can not determine GCF .So statement 1 is not sufficient.


2^p is 2, 4, 8, ... For any of these values you can pick 1 and 2 as factors, which gives the sum of 3, which is a prime.
_________________

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: 24 Sep 2013
Posts: 23
Location: Saudi Arabia
GPA: 3.8
WE: Project Management (Energy and Utilities)
Re: If n is a positive integer, what is the greatest common factor  [#permalink]

Show Tags

New post 24 Sep 2018, 05:11
1
Dear Bunuel,

Can you elaborate more about the line

(1) No two different factors of n sum to a prime number. This implies that 2 is NOT a factor of n, if it were then the sum of two factors of n, 1 and 2, would be a prime number.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50060
Re: If n is a positive integer, what is the greatest common factor  [#permalink]

Show Tags

New post 24 Sep 2018, 05:16
vipulshahi wrote:
Dear Bunuel,

Can you elaborate more about the line

(1) No two different factors of n sum to a prime number. This implies that 2 is NOT a factor of n, if it were then the sum of two factors of n, 1 and 2, would be a prime number.


Any even number has at least the following factors: 1 and 2. The sum = 3 = prime.

(1) says that "No two different factors of n sum to a prime number". So, n is NOT even.
_________________

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

GMAT Club Bot
Re: If n is a positive integer, what is the greatest common factor &nbs [#permalink] 24 Sep 2018, 05:16
Display posts from previous: Sort by

If n is a positive integer, what is the greatest common factor

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


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®.