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Is the median of set S even?

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Is the median of set S even?  [#permalink]

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New post 07 Feb 2012, 12:59
2
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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
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Re: club 13 - q1  [#permalink]

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New post 07 Feb 2012, 13:04
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2
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.

Answer: C.

Hope it helps.
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Re: Is the median of set S even?  [#permalink]

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New post 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]

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New post 07 Feb 2012, 13:46
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Re: Is the median of set S even?  [#permalink]

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New post 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]

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New post 11 Feb 2014, 05:00
1
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]

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New post 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 :)
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