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13 Oct 2021, 07:30
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
61% (01:43) correct
39%
(01:24)
wrong
based on 188
sessions
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Not Attempted Yet
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.
(1) The range of S is 2(N-1).
(2) When arranged in increasing order, the difference between any two consecutive terms is 2.
13 Oct 2021, 14:13
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Bunuel
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
13 Oct 2021, 15:21
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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.
