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

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

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26 Jun 2018, 14:00
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29% (02:16) correct 71% (01:42) wrong based on 25 sessions

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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

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

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26 Jun 2018, 21:07
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.

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

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27 Jun 2018, 01:13
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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27 Jun 2018, 03:49
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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27 Jun 2018, 04:50
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

Set S contains N integers. Is S a set of distinct consecutive integers &nbs [#permalink] 27 Jun 2018, 04:50
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