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# Is the median of set S even?

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Manager
Joined: 13 May 2010
Posts: 110
Is the median of set S even?  [#permalink]

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07 Feb 2012, 13:59
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Difficulty:

35% (medium)

Question Stats:

65% (01:17) correct 35% (01:20) wrong based on 191 sessions

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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
Math Expert
Joined: 02 Sep 2009
Posts: 55266
Re: club 13 - q1  [#permalink]

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07 Feb 2012, 14:04
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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]

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07 Feb 2012, 14:44
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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Joined: 02 Sep 2009
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Re: Is the median of set S even?  [#permalink]

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07 Feb 2012, 14:46
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]

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11 Feb 2014, 05:47
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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Joined: 02 Sep 2009
Posts: 55266
Re: Is the median of set S even?  [#permalink]

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11 Feb 2014, 06:00
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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11 Feb 2014, 06:08
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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Is the median of set S even?  [#permalink]

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24 Mar 2019, 10:23
Bunuel wrote:
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.

Bunuel wrote:
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.

If you tested cases for stmt 2 instead of using theory, then you'll need to consider the 3 cases mentioned below:

3 Cases

1) When list just has one item: Mean = Median
2) When list has even # of items:

(x + y)/2 = even
x + y = even

So x & y could be both even or both odd.
In either case, median = even.

3) When list has odd # of items:

(x + y + z)/3 = even
(x + y + z) = even

If x & z are both even or odd, then (x + z) = even and y = even.
If x & z are opposite, then (x + z) = odd and y = odd.
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Is the median of set S even?   [#permalink] 24 Mar 2019, 10:23
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