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

Question

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

(1) The range of S is greater than N-1

(2) The range of S is not N

chetan2u · Accepted Answer

S contains N integers.
We have to find   whether S is a set of distinct consecutive integers .

a) R=N-1  : If S contains 4 consecutive integers, say a, a+1, a+2, a+3, then range is a+3-a=3=4-1 or N-1.  Consecutive and distinct. 
 b) R >N-1 , the numbers are not consecutive. Also some elements may be same or may not be same.  Not consecutive but may or may not be distinct 
 c) R <N-1 , the numbers are again not consecutive. But some elements will surely be same, that is there is some repetition for sure.  Neither consecutive nor distinct.

(1) The range of S is greater than N-1
This is case (b), so the set may contain distinct integers but they are not consecutive.
Suff

(2) The range of S is not N
Any of the three cases above

A

GMATinsight · Answer

Question: Is S a set of distinct consecutive Integers?

STatement 1 : The range of S is greater than N-1 
 
For Range, N-1 with distinct terms in set
for N = 3, Set could be {1, 2, 3}
for N = 4, Set could be {1, 2, 3, 4}
for N = 5, Set could be {1, 2, 3, 4, 5}

Range = N-1 with N distinct terms in set confirms that set has consecutive Integers

But in the given statement, we acknowledge that Range > N-1 i.e Terms are DEFINITELY NOT distinct and Consecutive hence answer to teh question is DEFINITELY NO

SUFFICIENT

Statement 2 :The range of S is not N

But there is no certainty whether set has Range N-1 or something else such as N+1 hence

NOT SUFFICIENT

Answer: Option A

rajatchopra1994 · Answer

GMATinsight  , Please explain highlighted part.
For Consecutive integers, range will be always N-1. and your example explains same. So how statement 1 is sufficient, as it say it is greater than N-1

DhruvS · Answer

GMATinsight  >> Please help me understand the following scenario for option 1:

(1) The range of S is greater than N-1

Since Set S contain N integers
What if N=3 and S={1,4,4}
Range= 4-1 =3
and N-1=3-1=2
Therefore Range>N-1 holds true.
But, set S does not consists of distinct consecutive integers.
Will this not fail Option (1) ?

Regards,
Dhruv

chetan2u · Answer

Statement 1 confirms otherwise that the answer will be NO, they are not consecutive integers.

GMATinsight · Answer

rajatchopra1994   DhruvS

The range N-1 with distinct terms in set confirms that the set has consecutive numbers

But statement 1 confirms that Range > N-1 i.e Terms are definitely NOT CONSECUTIVE (Definite Answer) therefore

SUFFICIENT

rajatchopra1994 · Answer

GMATinsight  , Earlier u have written yes yes yes in explanation with examples. So I got confused. 
I was thinking about whether my explanation is wrong. Because I typed the whole answer then deleted it after seen your explanation.

Thanks for your correction.

Regards,
Rajat Chopra

firas92 · Answer

Let's assume S is a set of consecutive integers {a,a+1,a+2,a+3,...,a+N-1}. The range of S is a+N-1-a=N-1

So if S is a set of N consecutive integers, the range of S should be N-1

(1) The range of S is greater than N-1

Since the range of S is not N-1, S is not a set of consecutive integers

1 is sufficient

(2) The range of S is not N

The range may or may not be N-1. So S may or may not be a set of consecutive integers

2 is not sufficient

Answer is (A)

Posted from my mobile device

DhruvS · Answer

Just tried solving it with examples to get a better understanding. Anyone who needs more clarity by examples can refer this post.

(1) The range of S is greater than N-1 Since Set S contain N integers Case 1: if N=3 and S={1,4,4} Range= 4-1 =3 and N-1=3-1=2 Therefore Range>N-1 holds true. Set S does not consists of distinct consecutive integers. Answer: DEFINITE NO Case 2: if N=4 and S=0,1,2,3,4 Range=4-0=4 N-1=4-1=3 Therefore Range>N-1 holds true. Set S does not consists of distinct consecutive integers. Answer: DEFINITE NO Case 3: if N=4 and S={-2,0,3,5} Range=5-(-2)=7 N-1=4-1=3 Therefore Range>N-1 holds true. Set S does not consists of distinct consecutive integers. Answer: DEFINITE NO Case 4: if N=3 and S={1,2,3} Range=3-1=2 N-1=3-1=2 Since Range is not greater than N-1, this case does not apply. Case 5: if N=5 and S={-2,-1,0,1,2} Range=2-(-2)=4 N-1=5-1=4 Since Range is not greater than N-1, this case does not apply. We got a Answer: DEFINITE NO for Cases 1,2, and 3. Hence SUFFICIENT. (2) The range of S is not N Set can have a Range N-1, N+1, N+2 hence Case 1: N=4 and S={1,2,2,4} Range=4-1=3 N=4 Range!=N --->> True And Set S does not consists of distinct consecutive integers. Case 2: N=4 and S={1,2,3,4} Range=4-1=3 N=4 Range!=N --->> True And Set S consists of distinct consecutive integers. Hence NOT SUFFICIENT Final Answer (A)

DhruvS · Answer

Same happened with me I got confused because of "Yes" and when I tried solving it I got "No" as the answer

But this helped me to deep dive in the question and solve it through more examples.

Papist · Answer

S1: Let's take a look at some test values. If N=5, {1,2,3,4,5} and {-1,0,1,2,3} are both possible sets. In both cases, the range is 4, so we can conclude that the range of a set of consecutive integers will always be N-1. Since we are told the range of S is greater than N-1, the numbers in set S cannot be consecutive integers. SUFFICIENT.

S2: This isn't helpful. The range could be N-1 in which case the answer is yes, but if it is anything else the answer will be no. NOT SUFFICIENT.

ANSWER: A

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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

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