Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss!
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58450

Which of the following CANNOT be the greatest common divisor of two
[#permalink]
Show Tags
08 Feb 2011, 01:43
Question Stats:
82% (00:44) correct 18% (00:50) wrong based on 708 sessions
HideShow timer Statistics
Which of the following CANNOT be the greatest common divisor of two positive integers x and y? (A) 1 (B) x (C) y (D) x  y (E) x + y Problem Solving Question: 98 Category: Arithmetic Pro perties of numbers Page: 74 Difficulty: 600 The Official Guide For GMAT® Quantitative Review, 2ND Edition
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Math Expert
Joined: 02 Sep 2009
Posts: 58450

Which of the following CANNOT be the greatest common divisor of two
[#permalink]
Show Tags
08 Feb 2011, 03:28
Which of the following CANNOT be the greatest common divisor of two positive integers x and y?(A) 1 (B) x (C) y (D) x  y (E) x + y Divisor of a positive integer cannot be more than that integer (for example integer 4 doesn't have a divisor more than 4, the largest divisor it has is 4 itself), so greatest common divisor of two positive integers x and y can not be more than x or y. Answer: E.
_________________




Manager
Joined: 13 Feb 2012
Posts: 129
Location: Italy
Concentration: General Management, Entrepreneurship
GPA: 3.1
WE: Sales (Transportation)

Re: Which of the following CANNOT be the greatest common divisor of two
[#permalink]
Show Tags
24 Jul 2012, 10:42
Manhattan's way of visualizing the GCF comes in handy in this type of question. Even if you do not recall by theory that the GCF cannot be greater than either terms, you can figure that out.
_________________
"The Burnout"  My DebriefKudos if I helped you Andy



Intern
Joined: 01 Aug 2006
Posts: 31

Re: Which of the following CANNOT be the greatest common divisor of two
[#permalink]
Show Tags
07 Feb 2014, 21:49
Which of the following CANNOT be the greatest common divisor of two positive integers x and y?
method 1: use examples/counter examples. A. 1 (x=2;y=3) B. x (x=2; y = 4) C. y (x=4; y = 2) D. xy (x = 4; y =2) E. x+y > NOT POSSIBLE.
Concept: Factors of a number are always less than or equal to that number. HCF of x and y can never be greater than the smaller number.



eGMAT Representative
Joined: 04 Jan 2015
Posts: 3074

Which of the following CANNOT be the greatest common divisor of two
[#permalink]
Show Tags
27 Apr 2015, 05:50
Hi Everyone! Here's a question to further test your understanding of the concept of GCD: If A and B are distinct positive integers greater than 1 such that the GCD of A and B is A, then which of the following must be true?
(A) A is a prime number (B) A and B have the same prime factors. (C) A and B have the same evenodd nature (D) All the factors of B are divisible by A (E) The LCM of A and B is BWill post the solution in this thread on May 1, 2015. Till then, happy solving! Regards Japinder
_________________



eGMAT Representative
Joined: 04 Jan 2015
Posts: 3074

Which of the following CANNOT be the greatest common divisor of two
[#permalink]
Show Tags
01 May 2015, 06:13
EgmatQuantExpert wrote: Hi Everyone! Here's a question to further test your understanding of the concept of GCD: If A and B are distinct positive integers greater than 1 such that the GCD of A and B is A, then which of the following must be true?
(A) A is a prime number (B) A and B have the same prime factors. (C) A and B have the same evenodd nature (D) All the factors of B are divisible by A (E) The LCM of A and B is BWill post the solution in this thread on May 1, 2015. Till then, happy solving! Regards Japinder The correct answer is Option E.PFB the correct solution for this question: We are given that A and B are distinct positive integers greater than 1 such that the GCD of A and B is A The important thing to note is that the question is asking about must be true statements. Must be true statements are those that will hold for all possible values of A and B, without exception. So, our approach here will be to see if we can find any exceptions to the 5 given statements. Let's see. (A) A is a prime numberConsider A = 20 and B = 60. In this case, GCD(A,B) = A but A is not a prime number. Since we have found an exception to Statement A, it is clearly not a must be true statement. (B) A and B have the same prime factors.Once again, consider the case of A = 20 and B= 60. The prime factors of A are 2 and 5. The prime factors of B are 2, 3 and 5. So, clearly Statement B doesn't hold true for all possible values of A and B, and therefore, cannot be a must be true statement. (C) A and B have the same evenodd natureConsider A = 3 and B = 6. Here too, GCD(A,B) = A but the evenodd nature of A and B is opposite. So, Statement C is ruled out as well. (D) All the factors of B are divisible by A In the case of A= 20 and B = 60, 15 is a factor of B that is not divisible by A. Similarly, in the case of A = 3 and B = 6, 1 is a factor of B that is not divisible by A The existence of these exceptions indicates that Statement D is not a must be true statement. (E) The LCM of A and B is BWe know that LCM(A,B)*GCD(A,B) = A*B . . . (1) Given: GCD(A,B) = A . . . (2) On substituting (2) in (1), we get: LCM(A,B) = B Therefore, Statement E will always be true, for all values of A and B. Thanks and Best Regards Japinder
_________________



Manager
Joined: 29 Mar 2015
Posts: 74
Concentration: Strategy, Operations
WE: Research (Other)

Which of the following CANNOT be the greatest common divisor of two
[#permalink]
Show Tags
01 May 2015, 07:25
Thanks Jaspinder... I want to clarify two things which are what is the level of this question? and how to approach number system questions (I mean substituting values and working through is the best way to approach questions)?
_________________
If you like my post, Pl. do not hesitate to press kudos!!!!
Q51 on GMAT  PM me if you need any help with GMAT QUANTS!!!



eGMAT Representative
Joined: 04 Jan 2015
Posts: 3074

Re: Which of the following CANNOT be the greatest common divisor of two
[#permalink]
Show Tags
04 May 2015, 04:08
nailgmat2015 wrote:
Thanks Jaspinder...
I want to clarify two things which are what is the level of this question? and how to approach number system questions (I mean substituting values and working through is the best way to approach questions)?
Dear nailgmat2015Thank you for your questions. PFB my response. 1. This question is of GMAT 650 difficulty level. That said, I don't think the difficultylevel of a question is an important number. During the preparation stage, one should focus on the learning that one can glean from a question. And, every question that can teach you something  whether a conceptual point or a takeaway on how to attempt questions better  is an important question. By focusing in this manner on i) building concepts ii) learning to solve questions methodically in a stepbystep manner iii) learning from the mistakes that one makes along the way even the questions of the GMAT 700+ difficulty level will start seeming easy to you. 2. I am not too big a fan of solving questions by substituting numbers. This approach certainly appears appealing at the first look because it seemingly allows you to bypass conceptual understanding. And precisely there lies the problem with this approach  if, during your preparation, you solve questions by substituting numbers, you're depriving yourself of an opportunity to hone your conceptual understanding. I always advise my students to work through questions from the first principles. Since your question was specifically about Number Properties, I can actually share with you a tangible sample of what I mean: Our Number Properties Live Classroom session is a free session and likewise, its recording too is freely accessible by all. Please click here to go to the recording (the video takes about 45 seconds to load). The Number Properties part begins from the 20th minute onwards. In this session, you'll find both basic and very advanced questions from EvenOdd numbers, Prime Numbers and LCMGCD. And, you'll see for yourself how even the most difficult Number Properties questions can be solved by applying, in a stepbystep manner, the basic concepts that you already know. I hope you found this discussion useful. Please let me know if I can be of any further help Best Regards Japinder
_________________



Director
Joined: 02 Sep 2016
Posts: 649

Re: Which of the following CANNOT be the greatest common divisor of two
[#permalink]
Show Tags
17 Aug 2017, 06:45
Bunuel wrote: Lolaergasheva wrote: Which of the following cannot be the GCD of two positive integers x and y? a 1 b x c y d xy e x+y Divisor of a positive integer cannot be more than that integer (for example integer 4 doesn't have a divisor more than 4, the largest divisor it has is 4 itself), so greatest common divisor of two positive integers x and y can not be more than x or y. Answer: E. Bunuel Is this true only for positive integers because a negative integer can have divisors that are greater than the number. For example: 4 has divisors 1, 2, 2, 4, 4, 1 (1, 4) (2,2) (4,1) Is this understanding correct ?



Math Expert
Joined: 02 Sep 2009
Posts: 58450

Re: Which of the following CANNOT be the greatest common divisor of two
[#permalink]
Show Tags
17 Aug 2017, 06:48
Shiv2016 wrote: Bunuel wrote: Lolaergasheva wrote: Which of the following cannot be the GCD of two positive integers x and y? a 1 b x c y d xy e x+y Divisor of a positive integer cannot be more than that integer (for example integer 4 doesn't have a divisor more than 4, the largest divisor it has is 4 itself), so greatest common divisor of two positive integers x and y can not be more than x or y. Answer: E. Bunuel Is this true only for positive integers because a negative integer can have divisors that are greater than the number. For example: 4 has divisors 1, 2, 2, 4, 4, 1 (1, 4) (2,2) (4,1) Is this understanding correct ? Luckily you don't have to worry about that because every GMAT divisibility will tell you in advance that variables are positive integers only.
_________________



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2815

Re: Which of the following CANNOT be the greatest common divisor of two
[#permalink]
Show Tags
21 Aug 2017, 16:45
Lolaergasheva wrote: Which of the following CANNOT be the greatest common divisor of two positive integers x and y?
A. 1 B. x C. y D. xy E. x+y Since the greatest common divisor or greatest common factor (GCF) of any two positive integers must be no larger than the lesser of the two integers, the GCF can’t be sum of the two integers. That is, the GCF of x and y can’t be x + y. Answer: E
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Manager
Joined: 29 May 2016
Posts: 94
Location: Czech Republic
Concentration: Finance, Strategy
GPA: 3.94
WE: Corporate Finance (Investment Banking)

Re: Which of the following CANNOT be the greatest common divisor of two
[#permalink]
Show Tags
13 Aug 2019, 14:04
If I assume that x=y, wouldn't that make answer choice (D) nonsensical?
In other words if x=y then if x=2 22=0. But can zero be the greatest common divisor of positive integers?




Re: Which of the following CANNOT be the greatest common divisor of two
[#permalink]
13 Aug 2019, 14:04






