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# Is the median of set S even? 1. Set S is composed of

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Manager
Joined: 13 May 2010
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Is the median of set S even? 1. Set S is composed of [#permalink]

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12 Jun 2010, 11:51
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Question Stats:

53% (00:54) correct 47% (00:57) wrong based on 63 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

Oa is
[Reveal] Spoiler:
c

I think there is some problem with OA here.

Using only statement II we can solve this Q as follows:

Assuming

I. the set as {2,4,6} -------statement II required
Mean = 4 , even
Median = 4 even

II. Set as {2,4,6,8}
Mean = 5
Median = 5

III. Set {1,3,5,7} -------statement II required
Mean = 4
Median = 4

Hence we do not require the info provided in statement I and we can solve with statemetn II only. Can anybody comment on this ?

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Math Expert
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Re: Gmat club test 16 [#permalink]

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12 Jun 2010, 12:20
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Expert's post
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gmatcracker2010 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

Oa is
[Reveal] Spoiler:
c

I think there is some problem with OA here.

Using only statement II we can solve this Q as follows:

Assuming

I. the set as {2,4,6} -------statement II required
Mean = 4 , even
Median = 4 even

II. Set as {2,4,6,8}
Mean = 5
Median = 5

III. Set {1,3,5,7} -------statement II required
Mean = 4
Median = 4

Hence we do not require the info provided in statement I and we can solve with statemetn II only. Can anybody comment on this ?

Your reasoning is not correct. Are you saying that all sets with even mean have even median? What about: {1, 1, 4} --> $$mean=2=even$$ and $$median=1=odd$$ OR {0.6, 1.2, 4,2, } --> $$mean=2=even$$ and $$median=1.2\neq{integer}$$.

Is the median of set S even?

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

(2) The mean of set S is even. Insufficient as shown above.

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

Hope it helps.
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Manager
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Re: Gmat club test 16 [#permalink]

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13 Jun 2010, 14:54
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I think this question is better done conceptually rather than with thru trial and error.
Like in this example, the first statement tells us the set has all odd integers while the second says it has an even number of ingers, taken together, should be enough to answer the question.

But thanks for posting the question
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Manager
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Re: Gmat club test 16 [#permalink]

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14 Jun 2010, 05:09
Bunuel, very good explanation. It was easier one compared to tough ones you had explained earlier.
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Manager
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Re: Gmat club test 16 [#permalink]

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10 Oct 2010, 16:45
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C

1) depending of the number of elements, the median can be odd or even. not suff.

2) mean = even does not tell you anything about the middle number or middle 2 nums

together:
even mean of consecutive odd ints =>even num of elements
consecutive odd ints => let middle be 21, 23 => median is even
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Manager
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Re: Gmat club test 16 [#permalink]

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16 Oct 2010, 05:10
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yes...should be C..

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Re: Is the median of set S even? 1. Set S is composed of [#permalink]

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26 Sep 2015, 04:40
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Re: Is the median of set S even? 1. Set S is composed of   [#permalink] 26 Sep 2015, 04:40
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