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If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink]
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28 Apr 2016, 02:52
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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
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Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink]
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28 Apr 2016, 03:08
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 23 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



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Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink]
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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



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Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink]
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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



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Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink]
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29 Sep 2016, 06:07
Vyshak, How about this one  y = 5! +1 = 121 and x = 11, then gcf (x,y) would be 11.



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Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink]
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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?



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Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink]
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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.



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Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink]
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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



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Re: If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink]
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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



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If x and y are integers and x<y, is the greatest common factor (GCF) o [#permalink]
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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 coprimes




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