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Set S contains N integers. Is S a set of distinct consecutive integers

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New post 17 Dec 2017, 02:44
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Set S contains N integers. Is S a set of distinct consecutive integers?

(1) The range of S is N

(2) The range of S is less than N+1

Source: expertsglobal

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Set S contains N integers. Is S a set of distinct consecutive integers  [#permalink]

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New post 17 Dec 2017, 04:18
NandishSS wrote:
Set S contains N integers. Is S a set of distinct consecutive integers?

(1) The range of S is N

(2) The range of S is less than N+1

Source: expertsglobal


Statement 1: if \(S\) is a set of distinct consecutive integers, then \(S ={a,a+1,a+2..........,a+(N-1)}\), where \(a\) is the first element of the set

Range of consecutive elements in set \(S =[a+(N-1)]-a=N-1\)

As per this statement \(N-1=N => -1=0\), which is not possible. Hence elements in set \(S\) are NOT consecutive. Sufficient

Statement 2: We know nothing about the elements in Set \(S\) and as explained in Statement 1, range of consecutive elements will be \(N-1\).

As per this statement range can be \(N\) or \(N-1\) or any other number. Insufficient

Option A

--------------------------------------------------------

Alternatively take few examples of consecutive set and test the statement. For eg. let S={1,2,3}, here N=3

Statement 1: Range of S = 3-1=2 but as per this statement range =3. hence S is not consecutive. Sufficient

Statement 2: implies Range<3+1, so range can be 3 or 2 or 1 etc. Insufficient
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Re: Set S contains N integers. Is S a set of distinct consecutive integers  [#permalink]

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New post 17 Dec 2017, 05:24
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Re: Set S contains N integers. Is S a set of distinct consecutive integers  [#permalink]

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New post 17 Dec 2017, 05:45
NandishSS wrote:
Set S contains N integers. Is S a set of distinct consecutive integers?

(1) The range of S is N

(2) The range of S is less than N+1

Source: expertsglobal



Not a very good formatting of question by the source..
consecutive integers have to be distinct, so mere "Is S a set of consecutive integers?" should have been sufficient.
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Re: Set S contains N integers. Is S a set of distinct consecutive integers  [#permalink]

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New post 26 Jun 2018, 22:07
pushpitkc wrote:
Set S contains N integers. Is S a set of distinct consecutive integers?

1. The range of S in N
2. The range of S is less than N+1

Source: Experts Global


So S contains N integers, which could be distinct or there could be repetitions. We have to determine whether S contains distinct consecutive integers or not.
Range of a list of numbers is the: (Max Value in that list) - (Min Value in that list)

(1) So N integers, and range is N only.
Lets take an example. Say there are 5 integers in this list and range is also 5. Can these 5 be consecutive?
NO. Because if we write 5 consecutive integers (x, x+1, x+2, x+3, x+4) then range of these would be '4' (1 less than 5).
So basically if we have N consecutive integers (x, x+1, x+2, x+3... , x+N-1) then their range would be 'N-1' (1 less than N).
Thus we can conclude that this list does NOT contain all distinct consecutive integers. This is thus sufficient to answer the question with a NO.

(2) There are N integers and range is less than N+1.
As explained in analysis of first statement, these integers could be all distinct consecutive, in which case range would be N-1 (which is less than N+1).
Or we could have all integers as same, in which case range would be '0' (still less than N+1).
So we cannot conclude whether this list contains distinct consecutive integers or not. Not sufficient.

Hence A answer
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Re: Set S contains N integers. Is S a set of distinct consecutive integers  [#permalink]

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New post 27 Jun 2018, 02:13
pushpitkc wrote:
Set S contains N integers. Is S a set of distinct consecutive integers?

1. The range of S in N
2. The range of S is less than N+1

Source: Experts Global



I dont get the 1st statement, is there a typo?
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Re: Set S contains N integers. Is S a set of distinct consecutive integers  [#permalink]

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New post 27 Jun 2018, 04:49
LevanKhukhunashvili wrote:
pushpitkc wrote:
Set S contains N integers. Is S a set of distinct consecutive integers?

1. The range of S in N
2. The range of S is less than N+1

Source: Experts Global



I dont get the 1st statement, is there a typo?


There is no typo.

if S is a set of N distinct consecutive integers, the range will be N - 1.
For example, let S = {1, 2, 3, 4, 5}
Number of elements in S = 5. So, N in this case is 5.
Range = 5 - 1 = 4.

If the first of the integers is a, the second one will be a + 1, the third will be a + 2 and the Nth will be a + (N - 1).
So, the range will be a + (N - 1) - a = (N - 1).

If the range as given in statement 1 is N and not (N - 1) {what it will be if these are N consecutive integers}, then the N integers in set S CANNOT be consecutive integers.
So, statement 1 is sufficient.
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Set S contains N integers. Is S a set of distinct consecutive integers  [#permalink]

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New post 27 Jun 2018, 05:50
Set S contains N integers. Is S a set of distinct consecutive integers?

1. The range of S in N

Range a(n)-a(1)=n,

1)Consecutive: "Consecutive integers" means arithmetic progression, in which a(n)=a(1)+(n-1)*d
In our case d=1, because numbers are aconsecutive (+1), hence a(n)=a(1)+n-1a(1)+n-1-a(1)=n, -1=0 - which is NEVER true, so our set S can not be a set of distinct consecutive integers. Sufficient

2. The range of S is less than N+1

Range a(n)-a(1)<n+1

1)Consecutive: a(1)+n-1-a(1)<n+1, -1<1 -set S can be a set of distinct consecutive integers
2)Non-consecutive:let d=2, then a(1)+(n-1)*2-a(1)<n+1, 2n-2<n+1, n<3 - set S can be a set of distinct non-consecutive integers. Let's check {2,4}, where 4-2<2+1. Not sufficient

Answer (A)
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Re: Set S contains N integers. Is S a set of distinct consecutive integers  [#permalink]

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Re: Set S contains N integers. Is S a set of distinct consecutive integers   [#permalink] 10 Aug 2019, 06:11
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