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# Is the median of set S even?

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Is the median of set S even? [#permalink]  07 Feb 2012, 12:59
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Is the median of set S even?

(1) Set S is composed of consecutive odd integers
(2) The mean of set S is even
[Reveal] Spoiler: OA
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Re: club 13 - q1 [#permalink]  07 Feb 2012, 13:04
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teal wrote:
Is the median of set $$S$$ even?

1. Set $$S$$ is composed of consecutive odd integers
2. The mean of set $$S$$ is even

Can someone please explain the correct approach for this one?

Is the median of set S even?

(1) Set S is composed of consecutive odd integers --> set S is evenly spaced --> for any every evenly spaced set mean=median. But still insufficient.

(2) The mean of set S is even. Insufficient on its own.

(1)+(2) From (1) mean=median and from (2) mean=even --> mean=median=even. Sufficient.

Hope it helps.
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Re: Is the median of set S even? [#permalink]  07 Feb 2012, 13:44
can you please give me an example of a set in which mean is even and median is odd for statement 2?
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Re: Is the median of set S even? [#permalink]  07 Feb 2012, 13:46
Expert's post
teal wrote:
can you please give me an example of a set in which mean is even and median is odd for statement 2?

Sure: {1, 1, 4} --> mean=(1+1+4)/3=2=even and median=1=odd.
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Re: Is the median of set S even? [#permalink]  11 Feb 2014, 04:47
why isn't the correct answer A?

from statement 1 we know that S is a set containing consecutive odd integers, hence, it is an evenly spaced set. For all evenly spaced sets --> Mean = Median . Also, for all evenly spaced sets, Mean = Sum of first and last Number/ 2. Since we know that all numbers in the set are odd, we know that the first and the last number are odd, too, therefore odd + odd = even. Even/2=even --> the mean, and therefore the median of the set are even. Statement 1 is sufficient. If i did make a mistake, can someone please explain?

Cheers,
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Re: Is the median of set S even? [#permalink]  11 Feb 2014, 05:00
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damamikus wrote:
why isn't the correct answer A?

from statement 1 we know that S is a set containing consecutive odd integers, hence, it is an evenly spaced set. For all evenly spaced sets --> Mean = Median . Also, for all evenly spaced sets, Mean = Sum of first and last Number/ 2. Since we know that all numbers in the set are odd, we know that the first and the last number are odd, too, therefore odd + odd = even. Even/2=even --> the mean, and therefore the median of the set are even. Statement 1 is sufficient. If i did make a mistake, can someone please explain?

Cheers,

Why wouldn't you check your theories with simple examples?

{1, 3} --> median = 2 = even.
{1, 3, 5} --> median = 3 = odd.

Mistake in your reasoning is that even/2 = integer, not necessarily even. For, example, 4/2 = 2 = even, but 6/2 = 3 = odd.

Does this make sense?
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Re: Is the median of set S even? [#permalink]  11 Feb 2014, 05:08
thanks Bunuel!! you're right, i assumed even/2=even when in fact, as you pointed out, even/2=integer. thanks for the advice, i'll try to double-check my answers next time with some simple examples
Re: Is the median of set S even?   [#permalink] 11 Feb 2014, 05:08
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# Is the median of set S even?

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