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Manager  Joined: 13 May 2010
Posts: 86
Is the median of set S even? (1) Set S is composed of consecutive odd  [#permalink]

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2 00:00

Difficulty:   55% (hard)

Question Stats: 62% (01:18) correct 38% (01:34) wrong based on 92 sessions

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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=medianmean=median. But still insufficient.

(2) The mean of set S is even.

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 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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Joined: 02 Sep 2009
Posts: 58453
Re: Is the median of set S even? (1) Set S is composed of consecutive odd  [#permalink]

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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

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  Joined: 24 Mar 2010
Posts: 79
Re: Is the median of set S even? (1) Set S is composed of consecutive odd  [#permalink]

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1
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  Joined: 07 Oct 2006
Posts: 55
Location: India
Re: Is the median of set S even? (1) Set S is composed of consecutive odd  [#permalink]

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Bunuel, very good explanation. It was easier one compared to tough ones you had explained earlier.
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Manager  Joined: 07 Aug 2010
Posts: 54
Re: Is the median of set S even? (1) Set S is composed of consecutive odd  [#permalink]

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1
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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Re: Is the median of set S even? (1) Set S is composed of consecutive odd  [#permalink]

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_________________ Re: Is the median of set S even? (1) Set S is composed of consecutive odd   [#permalink] 22 Mar 2018, 00:05
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