A set S contains N elements. Is S a set of distinct consecutive even

Question

A set S contains N elements. Is S a set of distinct consecutive even integers?

(1) The range of S is 2(N-1).

(2) When arranged in increasing order, the difference between any two consecutive terms is 2.

JerryAtDreamScore · Answer

Rephrase the question:   
>  Is S an arithmetic sequence of even integers?  
> Note this is quite hard to achieve. We need the set to have even integers only, and the even integers must be consecutive. 
> Therefore we focus on trying to DENY that S could be an arithmetic sequence of even integers. (If we successfully deny this, the statement(s) would be sufficient)

Statement 1 Alone:   
> The range is even. If we have N integers in the set, there would be  N - 1  gaps for the range. Thus if S was a set of distinct consecutive even integers, each gap would be 2 and the range is indeed  2*(N - 1) .
> However, this does not confirm that all integers in the middle of the range follow the consecutive trend.
> Thus we cannot deny that S could be an arithmetic sequence of even integers; this statement is insufficient.

Statement 2 Alone:   
> This is the exact scenario of an arithmetic sequence. 
> However we did not specify if the terms are all odd or all even.
> We still cannot deny that S could be an arithmetic sequence of even integers. Thus this statement is insufficient.

Both Statements Combined:   
> The given info still cannot specify if the terms are all odd or all even.
> Combining statements is still insufficient.

Answer: E

IanStewart · Answer

We don't even know the elements in the set are integers, so of course we can't tell if the set contains consecutive even integers, and the answer is E.

pappal · Answer

sir,
N is certainly an integer positive as well
1. so 2*N is an even integer and so is 2 
2. its an AP of d=2
 Hence combined both will justify the statement to be proven.
please correct me if incorrect.

Bunuel · Answer

Consider the sets below, all of which satisfy the statements:
 
{1.5, 3.5, 5.5} - answer NO.
{1, 3, 5} - answer NO.
{2, 4, 6} - answer YES.
 
Answer: E.

pappal · Answer

Thanks for clarifying

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A set S contains N elements. Is S a set of distinct consecutive even

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A set S contains N elements. Is S a set of distinct consecutive even

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