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

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If S is a finite set of consecutive even numbers, is the [#permalink] New post 28 May 2012, 05:01
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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.
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Re: If S is a finite set of consecutive even numbers, is the [#permalink] New post 28 May 2012, 05:13
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If S is a finite set of consecutive even numbers, is the median of S an odd number?

The set of consecutive even integers is an evenly spaced set (aka arithmetic progression). Now, for any evenly spaced set mean=median.

(1) The mean of set S is an even number --> mean=median=even. Sufficient.
(2) The range of set S is divisible by 6 --> if S={0, 2, 4, 6} then median=(2+4)/2=3=odd but if S={0, 2, 4, 6, 8, 10, 12} then median=6=even. Not sufficient.

Answer: A.
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Re: If S is a finite set of consecutive even numbers, is the   [#permalink] 28 May 2012, 05:13
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