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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]

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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]

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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]

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New post 19 Dec 2016, 13:17
Hello i have a question here: Regarding statement 1 "the mean of set S is an even number"

it does not define the (evenly spaced) set so.. if the set is { 2 4 6 8 10} median=6(even) mean = 30/5=6
if the set is { 2 4 6 8 10 12} median =(6+8)/2 = 14/2=7(odd) mean=7

I consider statement 1 as INSUFFICIENT since it gives even number or odd number we cannot answer with yes or no

every correction or explanation is welcome!
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Re: If S is a finite set of consecutive even numbers, is the  [#permalink]

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New post 20 Dec 2016, 14:24
1
Great Question.
Here is what i did in this one =>
For consecutive odds => AP series with Common difference =2
Hence Mean = Median = Average of the first and the last terms.
The question is asking us if median is odd.
If median is odd = number of integers in the set must be Even .


Statement 1
Mean = even
But mean = median
Hence Sufficient = NO.


Statement 2=>
Range is divisible by 6
Lest use test cases

0
2
4
6
=> Median = 3 => Odd
0
2
4
6
8
10
12
Median = 6= Even

Hence not sufficient

Hence A

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Re: If S is a finite set of consecutive even numbers, is the  [#permalink]

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New post 20 Dec 2016, 14:39
clever one , thank you stonecold !
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Re: If S is a finite set of consecutive even numbers, is the  [#permalink]

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New post 20 Dec 2016, 14:45
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Re: If S is a finite set of consecutive even numbers, is the  [#permalink]

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New post 23 Mar 2017, 01:37
venmic 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.



Bunuel please tell if my reasoning is correct for statement 2

Let a be first number in set
then
last number = a+(n-1)d
since d=2
Last Number=a+(n-1)2

Range = a+(n-1)2 - a= 2(n-1)
Range => 6k = 2(n-1)
n=3k+1
if k =1 ,n= Even number
if k =2 , n= Odd number
So Insufficient
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Re: If S is a finite set of consecutive even numbers, is the &nbs [#permalink] 23 Mar 2017, 01:37
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