Last visit was: 04 Jun 2024, 02:37 It is currently 04 Jun 2024, 02:37
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

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

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11370
Own Kudos [?]: 33143 [9]
Given Kudos: 314
Send PM
Reviews Badge
If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink] If x and y are integers and x<y, is the greatest common factor (GCF) o   28 Apr 2016, 02:52
4
Kudos
5
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

64% (01:12) correct 36% (01:17) wrong based on 98 sessions
Hide Show DIFFICULTY AND 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
ShowHide Answer
Official Answer
C
User avatar
D
Kurtosis
Current Student
Joined: 13 Apr 2015
Posts: 1433
Own Kudos [?]: 4573 [2]
Given Kudos: 1228
Location: India
Send PM
GMAT ToolKit User Reviews Badge
Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink] If x and y are integers and x<y, is the greatest common factor (GCF) o   28 Apr 2016, 03:08
1
Kudos
1
Bookmarks
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
avatar
nitswat
Intern
Intern
Joined: 30 Aug 2016
Posts: 5
Own Kudos [?]: 5 [0]
Given Kudos: 0
Send PM
Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink] If x and y are integers and x<y, is the greatest common factor (GCF) o   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
User avatar
D
Kurtosis
Current Student
Joined: 13 Apr 2015
Posts: 1433
Own Kudos [?]: 4573 [0]
Given Kudos: 1228
Location: India
Send PM
GMAT ToolKit User Reviews Badge
Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink] If x and y are integers and x<y, is the greatest common factor (GCF) o   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
avatar
nitswat
Intern
Intern
Joined: 30 Aug 2016
Posts: 5
Own Kudos [?]: 5 [2]
Given Kudos: 0
Send PM
Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink] If x and y are integers and x<y, is the greatest common factor (GCF) o   29 Sep 2016, 06:07
2
Kudos
Vyshak, How about this one - y = 5! +1 = 121 and x = 11, then gcf (x,y) would be 11.
avatar
B
rahulkashyap
Manager
Manager
Joined: 09 Oct 2015
Posts: 174
Own Kudos [?]: 61 [0]
Given Kudos: 28
Send PM
Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink] If x and y are integers and x<y, is the greatest common factor (GCF) o   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?
User avatar
D
Kurtosis
Current Student
Joined: 13 Apr 2015
Posts: 1433
Own Kudos [?]: 4573 [0]
Given Kudos: 1228
Location: India
Send PM
GMAT ToolKit User Reviews Badge
Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink] If x and y are integers and x<y, is the greatest common factor (GCF) o   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.
avatar
B
rahulkashyap
Manager
Manager
Joined: 09 Oct 2015
Posts: 174
Own Kudos [?]: 61 [0]
Given Kudos: 28
Send PM
Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink] If x and y are integers and x<y, is the greatest common factor (GCF) o   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
User avatar
D
Kurtosis
Current Student
Joined: 13 Apr 2015
Posts: 1433
Own Kudos [?]: 4573 [0]
Given Kudos: 1228
Location: India
Send PM
GMAT ToolKit User Reviews Badge
Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink] If x and y are integers and x<y, is the greatest common factor (GCF) o   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
User avatar
B
EddyEd
Intern
Intern
Joined: 06 Jan 2016
Posts: 26
Own Kudos [?]: 15 [0]
Given Kudos: 88
Send PM
GMAT ToolKit User
If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink] If x and y are integers and x<y, is the greatest common factor (GCF) o   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
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 33299
Own Kudos [?]: 833 [0]
Given Kudos: 0
Send PM
Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink] If x and y are integers and x<y, is the greatest common factor (GCF) o   05 Nov 2023, 07:00
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 Club Bot
gmatclubot
Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink]
05 Nov 2023, 07:00
Moderator:
Bunuel
Math Expert
93486 posts