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# If S is a finite set of consecutive even numbers, is the

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Manager
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If S is a finite set of consecutive even numbers, is the [#permalink]  22 Nov 2006, 12:20
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If S is a finite set of consecutive even numbers, is the median of S an odd number?

(1) The mean of set S is an even number.

(2) The range of set S is divisible by 6.

Ans : A
VP
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[#permalink]  22 Nov 2006, 16:02
from (1) we can answer this

Say S= {2.4.6} Mean =4 and Median =4

Say S= {2.4.6,8} Mean =5 and Median =5

If the number of terms in the set is even then the Median is odd and viceversa

So A satisfies

From(2)

we cannot deduce anything so should be A alone
VP
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[#permalink]  22 Nov 2006, 19:11
It is A.

it is asking the number of elements is odd or even.
For such a set, the median is equal to the mean.

So for A, it is Suff.

For B, u gotta work it out. not as it looks so simple.
consider: {2, 4, 6, 8, 10, 12, 14}. median is always even.
and {-4, -2, 2} median is even.
and {-4, -2, 2, 4, 6, 8}. median is odd.

If it says it is all POSITIVE integers, then the answer would be D.
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Re: MGMAT DS: Median [#permalink]  23 Nov 2006, 01:52
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sujayb wrote:
If S is a finite set of consecutive even numbers, is the median of S an odd number?

(1) The mean of set S is an even number.

(2) The range of set S is divisible by 6.

Ans : A

Suppose the first integer is 2k and there are n integers in the list. The last element in S is 2k+2(n-1), and the mean of S (the average of the first and last terms) is 2k+n-1 and the range is 2(n-1)
The median of S will be odd if and only if n is even.

(1) 2k+n-1 is even, so n-1 is even and n is odd SUFF
(2) 2(n-1) is divisible by 6, so n-1 is a multiple of 3 i.e. n=3m+1 for some integer m NOT SUFF

A
VP
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[#permalink]  23 Nov 2006, 04:24
sorry. it was a mistake. it is insuff even if they are all positive.
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[#permalink]  23 Nov 2006, 11:36
Tennis_ball : Can you explain it with an example? (that the solution doesn't depend if the # is positive or negative)
VP
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[#permalink]  23 Nov 2006, 17:09
try the following cases:

2, 4, 6, 8. odd median and average.

2, 4, 6, 8, 10, 12, 14. even median and average.

6, 8, 10, 12. odd.

-4, -2, 0, 2 odd.
-4, -2, 0, 2, 4, 6, 8. even.
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[#permalink]  23 Nov 2006, 17:51
[quote="tennis_ball"]try the following cases:

2, 4, 6, 8. odd median and average.

2, 4, 6, 8, 10, 12, 14. even median and average.

6, 8, 10, 12. odd.

-4, -2, 0, 2 odd.
-4, -2, 0, 2, 4, 6, 8. even.[/quote]

The first statement is clear that is suff, but isn't that clear that the second is always insuff.
I agree with your first answer (if the number are all Positive the answer is D), but not with the correction that you make after (Insuff for Pos and Neg)
VP
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[#permalink]  23 Nov 2006, 19:05
I said in the previous post that it was a mistake. sorry about the comment about 'positive'.
[#permalink] 23 Nov 2006, 19:05
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# If S is a finite set of consecutive even numbers, is the

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