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16 Sep 2014, 00:58
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Is the median of set \(S\) even?
(1) Set \(S\) consists of consecutive odd integers.
(2) The average (arithmetic mean) of set \(S\) is even.
(1) Set \(S\) consists of consecutive odd integers.
(2) The average (arithmetic mean) of set \(S\) is even.
16 Sep 2014, 00:58
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Official Solution:
Is the median of set \(S\) even?
(1) Set \(S\) consists of consecutive odd integers.
The above implies that set \(S\) is evenly spaced. For every evenly spaced set, the mean equals the median. However, we don't have any information about the actual value of the median, making this statement insufficient.
(2) The mean of set \(S\) is even.
On its own, this statement is insufficient.
(1)+(2) From (1), we have that \(mean=median\). From (2), we have that \(mean=even\). Hence, \(mean=median=even\). Sufficient.
Answer: C
Is the median of set \(S\) even?
(1) Set \(S\) consists of consecutive odd integers.
The above implies that set \(S\) is evenly spaced. For every evenly spaced set, the mean equals the median. However, we don't have any information about the actual value of the median, making this statement insufficient.
(2) The mean of set \(S\) is even.
On its own, this statement is insufficient.
(1)+(2) From (1), we have that \(mean=median\). From (2), we have that \(mean=even\). Hence, \(mean=median=even\). Sufficient.
Answer: C
14 Jan 2015, 18:21
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Hi there, isn't statement 1 sufficient? given that mean=median, and since all numbers in the set are odd, we can definitevely say "no" the median of set S is never going to be even.
Thanks!
Thanks!
