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K is a set of integers such that if the integer r is in K, [#permalink]
 17 Oct 2010, 06:30
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K is a set of integers such that if the integer r is in K, then r + 1 is also in K. Is 100 in K? (1) 50 is in K. (2) 150 is in K.
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Last edited by Bunuel on 04 Aug 2012, 03:39, edited 1 time in total.
OA added.
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Re: Set of Integers [#permalink]
17 Oct 2010, 06:40
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Re: Set of Integers [#permalink]
17 Oct 2010, 07:14
questions such as the one above never mention the total number of terms in the set , wouldnt that matter , say if the set were to contain only 10 integers or say 50 , the answer to the question might change ....?
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Re: Set of Integers [#permalink]
17 Oct 2010, 15:24
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muditadixit81 wrote: questions such as the one above never mention the total number of terms in the set , wouldnt that matter , say if the set were to contain only 10 integers or say 50 , the answer to the question might change ....? Not really, because the way the set is defined, it will always be either the empty set or an infinite set. If the set contains any integer, it will have to contain all the integers greater than or equal to that integer. So the question of having exactly 50 or 100 integers never arises
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Re: Set of Integers [#permalink]
17 Oct 2010, 23:18
shrouded1 wrote: muditadixit81 wrote: questions such as the one above never mention the total number of terms in the set , wouldnt that matter , say if the set were to contain only 10 integers or say 50 , the answer to the question might change ....? Not really, because the way the set is defined, it will always be either the empty set or an infinite set. If the set contains any integer, it will have to contain all the integers greater than or equal to that integer. So the question of having exactly 50 or 100 integers never arises Well, that is some valuable information. Thank you and +1.
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Re: Set of Integers [#permalink]
17 Oct 2010, 23:54
Guys, would you mind explaining the solution bit more. How can 100 be in set, if 50 is in K. Wouldn't r+1, i.e., 51 should be there? Thanks!
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Re: Set of Integers [#permalink]
18 Oct 2010, 00:19
vibhutirs wrote: Guys, would you mind explaining the solution bit more. How can 100 be in set, if 50 is in K. Wouldn't r+1, i.e., 51 should be there? Thanks! If r is in the set, r+1 will be in it. So if 50 is in the set, 51 will be in it If 51 is in the set, by the same logic, 52 will be in it If 52 is in the set, 53 will be in it .... AND SO ON So basically what the condition implies is if r is in the set, all the integers greater than r will also have to be in the set. Hence, 50 being in there is sufficient for 100 to be in there. But 150 being in there, is not necessarily sufficient
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K is a set of integers such that if the integer r is in K, then r + 1 is also in K. Is 100 in K?
(1) 50 is in K.
(2) 150 is in K.
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Re: please explain [#permalink]
26 Oct 2012, 02:55
From 1 If 50 is in a part of K then 51 is a part of k and if 51 is a part of k then 52 is also a part of k so the possible values of k are k>=50 From 2 k>=150 so from 1 we can say that 100 is a part of k but from 2 we are not sure if it is contains 100 or not... Ans: A)
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Re: please explain [#permalink]
26 Oct 2012, 03:04
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Re: please explain
[#permalink]
26 Oct 2012, 03:04
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