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

It is currently 21 Jun 2018, 18:26

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

If x and y are integers and x<y, is the greatest common factor (GCF) o

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

Hide Tags

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 5911
If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink]

Show Tags

New post 28 Apr 2016, 02:52
2
5
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

51% (00:55) correct 49% (00:48) wrong based on 97 sessions

HideShow timer Statistics

If x and y are integers and x<y, is the greatest common factor (GCF) of x and y greater than 1?

(1) x = 40!
(2) y = 40! + 1


Modified version of Bunuel's Q

_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


GMAT online Tutor

1 KUDOS received
SC Moderator
User avatar
D
Joined: 13 Apr 2015
Posts: 1689
Location: India
Concentration: Strategy, General Management
GMAT 1: 200 Q1 V1
GPA: 4
WE: Analyst (Retail)
GMAT ToolKit User Premium Member
Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink]

Show Tags

New post 28 Apr 2016, 03:08
1
chetan2u wrote:
If x and y are integers and x<y, is the greatest common factor (GCF) of x and y greater than 1?

(1) x = 40!
(2) y = 40! + 1


Modified version of Bunuel's Q
OA after 2-3 replies


x < y. GCF(x,y) > 1?

St1: x = 40! --> Insufficient as we do not know the value of y

St2: y = 40! + 1 --> Sufficient
40! contains all the factors from 1 to 40.
If all the integers from 1 to 40 are factors of 40!, the integers from 1 to 40 cannot be the factors of 40! + 1
Since x < y, x < 40! + 1
i.e x <= 40!
x can contain all the factors upto 40! But will always be coprime with 40! + 1
i.e say x = 37 or x = 37*2. x is factor of 40! so it cannot be a factor of 40! + 1
Hence GCF(x, y) = 1

Answer: B
Intern
Intern
avatar
Joined: 30 Aug 2016
Posts: 5
Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink]

Show Tags

New post 29 Sep 2016, 05:29
chetan2u - I am unable to understand the solution for this problem. It seems the ans is wrongly mentioned as B while it should be C.
Can you pls check & confirm.

The reason for my concern is, that would the same answer still holds if in option B, we change y= 5! + 1 just for the sake of easy calculation.
Since x can be any integer less than y, let say x = 5 then gcf would be 5, while if x = 24 then gcf would be 1. Hence B is insufficient.

Let me know your thoughts.

Thanks,
Nitin

Pls share Kudos if you like my post
SC Moderator
User avatar
D
Joined: 13 Apr 2015
Posts: 1689
Location: India
Concentration: Strategy, General Management
GMAT 1: 200 Q1 V1
GPA: 4
WE: Analyst (Retail)
GMAT ToolKit User Premium Member
Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink]

Show Tags

New post 29 Sep 2016, 05:42
nitswat wrote:
chetan2u - I am unable to understand the solution for this problem. It seems the ans is wrongly mentioned as B while it should be C.
Can you pls check & confirm.

The reason for my concern is, that would the same answer still holds if in option B, we change y= 5! + 1 just for the sake of easy calculation.
Since x can be any integer less than y, let say x = 5 then gcf would be 5, while if x = 24 then gcf would be 1. Hence B is insufficient.

Let me know your thoughts.

Thanks,
Nitin

Pls share Kudos if you like my post


Hi Nitin,

The answer is B and the solution is explained above. If you can point out the portion that you were not able to understand I can try to answer your queries.

In your first case, y = 5! + 1 = 121
You have taken x = 5
GCF(5, 121) = 1

In the second case, y = 121 and x = 24
GCF(24, 121) = 1

So B is sufficient
1 KUDOS received
Intern
Intern
avatar
Joined: 30 Aug 2016
Posts: 5
Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink]

Show Tags

New post 29 Sep 2016, 06:07
1
Vyshak, How about this one - y = 5! +1 = 121 and x = 11, then gcf (x,y) would be 11.
Manager
Manager
avatar
B
Joined: 09 Oct 2015
Posts: 106
Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink]

Show Tags

New post 29 Sep 2016, 06:29
Vyshak wrote:
nitswat wrote:
chetan2u - I am unable to understand the solution for this problem. It seems the ans is wrongly mentioned as B while it should be C.
Can you pls check & confirm.

The reason for my concern is, that would the same answer still holds if in option B, we change y= 5! + 1 just for the sake of easy calculation.
Since x can be any integer less than y, let say x = 5 then gcf would be 5, while if x = 24 then gcf would be 1. Hence B is insufficient.

Let me know your thoughts.

Thanks,
Nitin

Pls share Kudos if you like my post


Hi Nitin,

The answer is B and the solution is explained above. If you can point out the portion that you were not able to understand I can try to answer your queries.

In your first case, y = 5! + 1 = 121
You have taken x = 5
GCF(5, 121) = 1

In the second case, y = 121 and x = 24
GCF(24, 121) = 1

So B is sufficient


for simplicity,

y= 4! + 1 = 25
and if x<y, lets take x as 5.
In this case GCF is 5.
if x = 4,
GCF is 1

On the other hand, in the question if it results in a prime number, the answer is always GCF=1

chetan2u could you please tell us how it is B?
SC Moderator
User avatar
D
Joined: 13 Apr 2015
Posts: 1689
Location: India
Concentration: Strategy, General Management
GMAT 1: 200 Q1 V1
GPA: 4
WE: Analyst (Retail)
GMAT ToolKit User Premium Member
Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink]

Show Tags

New post 29 Sep 2016, 07:12
nitswat wrote:
Vyshak, How about this one - y = 5! +1 = 121 and x = 11, then gcf (x,y) would be 11.


Yes you are right. But 5! + 1 is composite. I am not sure whether 40! + 1 is prime or composite. All I know is 40! + 1 can be written in the form of 6k + 1 and may be prime. The answer can be concluded as C if 40! + 1 is composite.
Manager
Manager
avatar
B
Joined: 09 Oct 2015
Posts: 106
Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink]

Show Tags

New post 29 Sep 2016, 07:25
Vyshak wrote:
nitswat wrote:
Vyshak, How about this one - y = 5! +1 = 121 and x = 11, then gcf (x,y) would be 11.


Yes you are right. But 5! + 1 is composite. I am not sure whether 40! + 1 is prime or composite. All I know is 40! + 1 can be written in the form of 6k + 1 and may be prime. The answer can be concluded as C if 40! + 1 is composite.


How were you able to conclude that it's of the form 6n+1?
Besides,i don't think there is a way to conclude whether it's prime or composite.

Posted from my mobile device
SC Moderator
User avatar
D
Joined: 13 Apr 2015
Posts: 1689
Location: India
Concentration: Strategy, General Management
GMAT 1: 200 Q1 V1
GPA: 4
WE: Analyst (Retail)
GMAT ToolKit User Premium Member
Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink]

Show Tags

New post 29 Sep 2016, 07:34
rahulkashyap wrote:
Vyshak wrote:
nitswat wrote:
Vyshak, How about this one - y = 5! +1 = 121 and x = 11, then gcf (x,y) would be 11.


Yes you are right. But 5! + 1 is composite. I am not sure whether 40! + 1 is prime or composite. All I know is 40! + 1 can be written in the form of 6k + 1 and may be prime. The answer can be concluded as C if 40! + 1 is composite.


How were you able to conclude that it's of the form 6n+1?
Besides,i don't think there is a way to conclude whether it's prime or composite.

Posted from my mobile device


40! is divisible by 6 --> 40! = 6k --> 40! + 1 = 6k + 1
Intern
Intern
User avatar
B
Joined: 06 Jan 2016
Posts: 24
Location: Spain
Concentration: Operations, General Management
GMAT ToolKit User Premium Member
If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink]

Show Tags

New post 21 Oct 2017, 04:04
Vyshak correct me if I'm wrong. I think I know why the OA is C.

There is no indication in this problem that x or y are positive integers. Just that x<y

In the case of the Statement 2:
If x is positive will have to be a factor of y! and therefore there won't be any common factor besides 1
BUT if x is negative it could be equal to: x= -1 * (40! + 1) yielding a gcf of (40! + 1) therefore insufficient

When analyzing both statements together we get only one possible answer that is gcf=1 since both positive integers are co-primes
If x and y are integers and x<y, is the greatest common factor (GCF) o   [#permalink] 21 Oct 2017, 04:04
Display posts from previous: Sort by

If x and y are integers and x<y, is the greatest common factor (GCF) o

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


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®.