Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 21 Jan 2014
Posts: 99
GPA: 4

Which of the following could be the greatest common factor of positive
[#permalink]
Show Tags
01 Jun 2016, 08:52
Question Stats:
54% (00:37) correct 46% (00:40) wrong based on 357 sessions
HideShow timer Statistics
Which of the following could be the greatest common factor of positive integers a and b? I. 1 II. aIII. abA) II only B) I and II only C) I and III only D) II and III only E) I, II and III
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 47903

Re: Which of the following could be the greatest common factor of positive
[#permalink]
Show Tags
01 Jun 2016, 09:09
pepo wrote: which of the following could be the greatest common factor of positive integers a and b?
I. 1 II. a III. ab
A) II only B) I and II only C) I and III only D) II and III only E) I, II and III It could be 1 if a and b are coprime, for example, 1 and 2, 11 and 13... It could be a itself if a is a factor of b, for example, 2 and 4, 5 and 15... It could be ab, for example, when a=b+1: a=2 and b=1, a=3 and b=2... Answer: E.
_________________
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? Extrahard Quant Tests with Brilliant Analytics




Intern
Joined: 09 Nov 2015
Posts: 1

Re: Which of the following could be the greatest common factor of positive
[#permalink]
Show Tags
28 Jan 2017, 07:47
Bunuel wrote: pepo wrote: which of the following could be the greatest common factor of positive integers a and b?
I. 1 II. a III. ab
A) II only B) I and II only C) I and III only D) II and III only E) I, II and III It could be 1 if a and b are coprime, for example, 1 and 2, 11 and 13... It could be a itself if a is a factor of b, for example, 2 and 4, 5 and 15... It could be ab, for example, when a=b+1: a=2 and b=1, a=3 and b=2... Answer: E. Since greatest is asked it should be a single number not 3 numbers. Correct me if I'm wrong



Math Expert
Joined: 02 Sep 2009
Posts: 47903

Re: Which of the following could be the greatest common factor of positive
[#permalink]
Show Tags
28 Jan 2017, 07:50
Raahan wrote: Bunuel wrote: pepo wrote: which of the following could be the greatest common factor of positive integers a and b?
I. 1 II. a III. ab
A) II only B) I and II only C) I and III only D) II and III only E) I, II and III It could be 1 if a and b are coprime, for example, 1 and 2, 11 and 13... It could be a itself if a is a factor of b, for example, 2 and 4, 5 and 15... It could be ab, for example, when a=b+1: a=2 and b=1, a=3 and b=2... Answer: E. Since greatest is asked it should be a single number not 3 numbers. Correct me if I'm wrong The question asks which of the following could be the greatest common factor (GCF) of positive integers a and b? All three (for different cases) could be the greatest common factors of a and b. So, the answer is E.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Director
Joined: 02 Sep 2016
Posts: 734

Re: Which of the following could be the greatest common factor of positive
[#permalink]
Show Tags
30 May 2017, 22:43
BunuelIn the third case (ab), a and b can also be 6 and 4?
_________________
Help me make my explanation better by providing a logical feedback.
If you liked the post, HIT KUDOS !!
Don't quit.............Do it.



Math Expert
Joined: 02 Sep 2009
Posts: 47903

Re: Which of the following could be the greatest common factor of positive
[#permalink]
Show Tags
30 May 2017, 22:53



Intern
Joined: 23 Feb 2017
Posts: 37

Re: Which of the following could be the greatest common factor of positive
[#permalink]
Show Tags
31 May 2017, 16:45
The GCF of 4,10 is 2, which does not fall into any of the 3 categories right?



Manager
Joined: 27 Dec 2016
Posts: 202
Concentration: International Business, Marketing

Re: Which of the following could be the greatest common factor of positive
[#permalink]
Show Tags
31 May 2017, 18:36
Hi,
I am confused with the second option. If a and b were 2 and 3, their GCF would have been 1. How is second option still sufficient? Please explain!
Thanks!



Math Expert
Joined: 02 Sep 2009
Posts: 47903

Which of the following could be the greatest common factor of positive
[#permalink]
Show Tags
31 May 2017, 20:42



Manager
Joined: 27 Dec 2016
Posts: 202
Concentration: International Business, Marketing

Re: Which of the following could be the greatest common factor of positive
[#permalink]
Show Tags
01 Jun 2017, 06:58
Bunuel wrote: sasidharrs wrote: The GCF of 4,10 is 2, which does not fall into any of the 3 categories right? csaluja wrote: Hi,
I am confused with the second option. If a and b were 2 and 3, their GCF would have been 1. How is second option still sufficient? Please explain!
Thanks! Notice that the question asks "Which of the following COULD be the greatest common factor of positive integers a and b?" NOT "Which of the following MUST be the greatest common factor of positive integers a and b?" I see now, makes a lot of sense! Thanks a lot Bunuel!!



Manager
Joined: 17 Jun 2015
Posts: 236
GMAT 1: 540 Q39 V26 GMAT 2: 680 Q46 V37

Re: Which of the following could be the greatest common factor of positive
[#permalink]
Show Tags
18 Jun 2017, 04:17
I took the two positive integers to be 0 and 2. Proves right across all the three cases, hence E
_________________
Fais de ta vie un rêve et d'un rêve une réalité



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12175
Location: United States (CA)

Re: Which of the following could be the greatest common factor of positive
[#permalink]
Show Tags
04 Dec 2017, 13:55
Hi All, We're told that A and B are positive integers. We're asked which of the Roman Numerals COULD be the Greatest Common Factor of A and B. We can solve the problem by TESTing VALUES. I. 1 IF A=1 and B=2, then the GCF = 1. Roman Numeral 1 COULD be true. Eliminate Answers A and D. II. A IF A=1 and B=2, then the GCF = 1 (so the GCF = A). Roman Numeral 2 COULD be true. Eliminate Answer C. III. A  B IF A=2 and B=1, then the GCF = 1 (so the GCF = AB). Roman Numeral 3 COULD be true. Eliminate Answer B. Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3161
Location: United States (CA)

Re: Which of the following could be the greatest common factor of positive
[#permalink]
Show Tags
11 Jan 2018, 14:49
pepo wrote: Which of the following could be the greatest common factor of positive integers a and b?
I. 1 II. a III. ab
A) II only B) I and II only C) I and III only D) II and III only E) I, II and III Let’s analyze each Roman numeral. I. 1 If a = 4 and b = 7, then their greatest common factor is 1. So I is possible. II. a If a = 4 and b = 8, then their greatest common factor is 4, which is a. So II is possible. III. a  b. If b = 8 and a = 4, then their greatest common factor is 4, which is a  b. So III is possible. Answer: E
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Manager
Joined: 13 Jun 2012
Posts: 180
Location: United States
WE: Supply Chain Management (Computer Hardware)

Which of the following could be the greatest common factor of positive
[#permalink]
Show Tags
11 Jan 2018, 15:22
pepo wrote: Which of the following could be the greatest common factor of positive integers a and b?
I. 1 II. a III. ab
A) II only B) I and II only C) I and III only D) II and III only E) I, II and III The main thing to notice is COULD 1. Can it be 1? Yes if both the numbers are prime 2 Can it be a? Yes is a=2 and b=4 ..GCF is 2 3. Can it be ab? Yes, if a=8 and b=4. the GCF is 4. ab is also equal to 4




Which of the following could be the greatest common factor of positive &nbs
[#permalink]
11 Jan 2018, 15:22






