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26 Aug 2023, 13:42
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C
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Difficulty:
65%
(hard)
Question Stats:
49% (01:38) correct
51%
(01:21)
wrong
based on 98
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S is a set of positive integers. Is the median of the set S an integer in S?
(1) When arranged in an increasing order, the difference between any two consecutive terms is a positive odd integer.
(2) The number of terms in S is even
(1) When arranged in an increasing order, the difference between any two consecutive terms is a positive odd integer.
(2) The number of terms in S is even
27 Aug 2023, 05:07
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srishin
Statement 1
(1) When arranged in an increasing order, the difference between any two consecutive terms is a positive odd integer.
Inference: The members are equally spaced (i.e. the members are in Arithmetic Progression). The difference between any two consecutive terms is a positive odd integer.
If the number of terms in the set is odd, the median is a member of the set. Hence, the median is an integer.
If the number of terms in the set is even, the median is the arithmetic mean of the \((\frac{n}{2})\)th and \((\frac{n}{2}+1\))th term. As one of the two terms is even and the other term is odd, the average is not an integer.
As we are getting two contradicting answers, the statement alone is not sufficient. We can eliminate A and D.
Statement 2
(2) The number of terms in S is even
As the number of terms in the set is even, the median is the arithmetic mean of the \((\frac{n}{2})\)th and \((\frac{n}{2}+1\))th term. If both the terms have the same even-odd nature, the median is an integer. If one of the terms is even and the other term is odd, the median is not an integer.
As we have no information on the even-odd nature of the two terms, we cannot comment on whether the median is an integer.
The statement alone is not sufficient and we can eliminate B.
Combined
From statement 2, we know that the number of terms in the set is even.
From statement 1, we know that one of the two terms is odd and the other term is even.
Hence, the median is not an integer.
The statements combined are sufficient.
Option C
27 Aug 2023, 21:52
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gmatophobia
Hi,
Thanks for the reply. In S2: if number of terms of set S is even, then the median will never be present in the set S right? Whether the median is fraction/decimal/integer? So, for S2, the answer should always be no and hence option (B)?
