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K is a set of integers such that if the integer r is in K,

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dkverma
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K is a set of integers such that if the integer r is in K, [#permalink] New post   Updated on: 04 Aug 2012, 03:39
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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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A

Originally posted by dkverma on 17 Oct 2010, 06:30.
Last edited by Bunuel on 04 Aug 2012, 03:39, edited 1 time in total.
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K is a set of integers such that if the integer r is in K, [#permalink] New post   17 Oct 2010, 06:40
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dkverma wrote:
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.


(1) 50 is in K --> integers more than or equal to 50 are in the set K, so 100 is in the K. Sufficient.

(2) 150 is in K --> integers more than or equal to 150 are in the set K, so 100 may or may not be in the K (if the source integer is 100 or less then 100 is in K but if the source integer is more than 100 then 100 is not in K). Not sufficient.

Answer: A.

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https://gmatclub.com/forum/if-p-is-a-set ... 96630.html
https://gmatclub.com/forum/k-is-a-set-of ... 03005.html

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Re: Set of Integers [#permalink] New post   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] New post   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] New post   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] New post   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] New post   18 Oct 2010, 00:19
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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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Re: please explain [#permalink] New post   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: K is a set of integers such that if the integer r is in K, [#permalink] New post   26 Nov 2013, 06:31
Bunuel,
Hi I understood your explanation.However , I think if you were to classify statement 2 as insufficient then statement 1 would also be
if 50 is in set the 51,is also in the ,same as 52...... all the way to a hundred.
if 150 is in set then 149 must have been part of the set, 148 .. all the way to possibly 0.
But following your explanation you mentioned in statement two that there is no way of knowing if 100 was part of the set? Well i agree with you but how are we to know if statement 1 goes all the way to 100?
I was thinking that E would have been the answer.no?
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Re: K is a set of integers such that if the integer r is in K, [#permalink] New post   26 Nov 2013, 08:24
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mumbijoh wrote:
Bunuel,
Hi I understood your explanation.However , I think if you were to classify statement 2 as insufficient then statement 1 would also be
if 50 is in set the 51,is also in the ,same as 52...... all the way to a hundred.
if 150 is in set then 149 must have been part of the set, 148 .. all the way to possibly 0.
But following your explanation you mentioned in statement two that there is no way of knowing if 100 was part of the set? Well i agree with you but how are we to know if statement 1 goes all the way to 100?
I was thinking that E would have been the answer.no?


We know that if r is in K, then r + 1 is also in K.

(1) says that 50 is in K, thus every integer more than 50 is also in K: 51 because 50 is there, 52 because 51 is there, ..., 100 because 99 is there.

Similar questions to practice:
for-a-certain-set-of-numbers-if-x-is-in-the-set-then-both-161920.html
for-a-certain-set-of-numbers-if-x-is-in-the-set-then-x-136580.html
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if-p-is-a-set-of-integers-and-3-is-in-p-is-every-positive-96630.html
k-is-a-set-of-numbers-such-that-i-if-x-is-in-k-then-x-96907.html

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Re: K is a set of integers such that if the integer r is in K, [#permalink] New post   26 Nov 2013, 11:50
Bunuel wrote:
mumbijoh wrote:
Bunuel,
Hi I understood your explanation.However , I think if you were to classify statement 2 as insufficient then statement 1 would also be
if 50 is in set the 51,is also in the ,same as 52...... all the way to a hundred.
if 150 is in set then 149 must have been part of the set, 148 .. all the way to possibly 0.
But following your explanation you mentioned in statement two that there is no way of knowing if 100 was part of the set? Well i agree with you but how are we to know if statement 1 goes all the way to 100?
I was thinking that E would have been the answer.no?


We know that if r is in K, then r + 1 is also in K.

(1) says that 50 is in K, thus every integer more than 50 is also in K: 51 because 50 is there, 52 because 51 is there, ..., 100 because 99 is there.

Similar questions to practice:
for-a-certain-set-of-numbers-if-x-is-in-the-set-then-both-161920.html
for-a-certain-set-of-numbers-if-x-is-in-the-set-then-x-136580.html
a-set-of-numbers-has-the-property-that-for-any-number-t-in-t-98829.html
if-p-is-a-set-of-integers-and-3-is-in-p-is-every-positive-96630.html
k-is-a-set-of-numbers-such-that-i-if-x-is-in-k-then-x-96907.html

Hope this helps.


Hi Bunuel,

Can you explain again why B is insufficient? If 150 is in K, 151, .152... resulting from ( r + 1) also is in K. That means 100 will be out of K because K includes only value > 150. B helps to always answer: NO (100 is always NOT in K: Sufficient).

Thanks.
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Re: K is a set of integers such that if the integer r is in K, [#permalink] New post   26 Nov 2013, 11:58
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yenpham9 wrote:
Bunuel wrote:
mumbijoh wrote:
Bunuel,
Hi I understood your explanation.However , I think if you were to classify statement 2 as insufficient then statement 1 would also be
if 50 is in set the 51,is also in the ,same as 52...... all the way to a hundred.
if 150 is in set then 149 must have been part of the set, 148 .. all the way to possibly 0.
But following your explanation you mentioned in statement two that there is no way of knowing if 100 was part of the set? Well i agree with you but how are we to know if statement 1 goes all the way to 100?
I was thinking that E would have been the answer.no?


We know that if r is in K, then r + 1 is also in K.

(1) says that 50 is in K, thus every integer more than 50 is also in K: 51 because 50 is there, 52 because 51 is there, ..., 100 because 99 is there.

Similar questions to practice:
for-a-certain-set-of-numbers-if-x-is-in-the-set-then-both-161920.html
for-a-certain-set-of-numbers-if-x-is-in-the-set-then-x-136580.html
a-set-of-numbers-has-the-property-that-for-any-number-t-in-t-98829.html
if-p-is-a-set-of-integers-and-3-is-in-p-is-every-positive-96630.html
k-is-a-set-of-numbers-such-that-i-if-x-is-in-k-then-x-96907.html

Hope this helps.


Hi Bunuel,

Can you explain again why B is insufficient? If 150 is in K, 151, .152... resulting from ( r + 1) also is in K. That means 100 will be out of K because K includes only value > 150. B helps to always answer: NO (100 is always NOT in K: Sufficient).

Thanks.


I guess you did not follow the links provided...

We don't know which is the source integer in the set, if it's 150, then 100 won't be in the set but if the source integer is say 10 or 20 (basically if the source integer is less than or equal to 100), then 100 will be in the set. So, 100 may or may not be in the set. Consider below two examples of the set:

{150, 151, 152, ...}
{1, 2, 3, 4, ..., 100, ..., 150, ...}

Notice that both sets satisfy the second statement.

Hope it's clear.
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Re: K is a set of integers such that if the integer r is in K, [#permalink] New post   18 May 2014, 10:49
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If r is in K, r+1 is in K. So if 50 is in K, 51 is in K. But if 51 is in K, so is 52, and then so is 53, and so on. Indeed, if you know 50 is in K, you know that every positive integer larger than 50 must also be in K. So 1) is sufficient.

If 150 is in K, all we know for certain is that every positive integer greater than or equal to 150 must be in K. We don't know if 100 is in K. So 2) is insufficient.

Thus, A.
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Re: K is a set of integers such that if the integer r is in K, [#permalink] New post   28 Aug 2019, 07:17
Why is it not C ?
We don't know how many integer there is in the set...
Maybe it's a set of 10 intergers, maybe a set of 500 ? Thus with 1) and 2) we know for sure 100 is in K
What am I missing ?
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K is a set of integers such that if the integer r is in K, [#permalink] New post   Updated on: 28 Aug 2019, 11:54
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Coggi wrote:
Why is it not C ?
We don't know how many integer there is in the set...
Maybe it's a set of 10 intergers, maybe a set of 500 ? Thus with 1) and 2) we know for sure 100 is in K
What am I missing ?


Hi Coggi,

Option A alone is SUFFICIENT. If 50 is in the set, then 51, 52,..,100,...,to the infinity must be in the same set. 100% sure, and no additional data is even necessary.

Of course, option (C) must not be correct answer, because in Option (C), Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

One golden rule of thumb in DS is not to make any own assumption other than stated in the question stem. For this case, the question doesn't state nor explicitly indicate that there are finite number of the set.

Originally posted by freedom128 on 28 Aug 2019, 08:30.
Last edited by freedom128 on 28 Aug 2019, 11:54, edited 1 time in total.
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Re: K is a set of integers such that if the integer r is in K, [#permalink] New post   28 Aug 2019, 11:44
Okay I get it, so if no detail added always consider the set is infinite ?
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K is a set of integers such that if the integer r is in K, [#permalink] New post   28 Aug 2019, 12:26
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Coggi wrote:
Okay I get it, so if no detail added always consider the set is infinite ?


Yes, it is natural to do that. You can try this better but similar PS/DS questions here:

1) https://gmatclub.com/forum/each-of-64-w ... 03791.html
2) https://gmatclub.com/forum/if-n-is-a-po ... 03255.html

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Re: K is a set of integers such that if the integer r is in K, [#permalink] New post   21 Oct 2020, 10:56
this is badly worded question. If r is in K then r+1 is in k meaning 51 is in k. Why would 51 be considered r then. I thought the same thing earlier but there is no reason to consider the new 51 as r. It could be anything like f or how do we even know that this set is infinite. Not all information is given!
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Re: K is a set of integers such that if the integer r is in K, [#permalink] New post   20 Dec 2020, 08:43
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dkverma wrote:
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.


(1) \(50;50+1=51...100,101\) we can progress is in the way. Sufficient.

(2) If \(r=99, then \ 99+1= 100\), and progressing this way \(150 \) is in K, But if \(r=149\) then \(149+1=150\) is the k but \(100 \) is not in the k. Yes and No; Insufficient.

The answer is \(A\)
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Re: K is a set of integers such that if the integer r is in K, [#permalink] New post   23 Nov 2023, 00:08
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