Is the median of set S even?

Question

(1) Set S is composed of consecutive odd integers 
(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 ?

Bunuel · Accepted Answer

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
eq{integer} .

Is the median of set  S  even? 
 
(1) Set  S  consists of consecutive odd integers.
 
The above implies that set  S  is evenly spaced. For every evenly spaced set, the mean equals the median. However, we don't have any information about the actual value of the median, making this statement insufficient.
 
(2) The mean of set  S  is even. 
 
On its own, this statement is insufficient.
 
(1)+(2) From (1), we have that  mean=median . From (2), we have that  mean=even . Hence,  mean=median=even . Sufficient.

Answer: C

Hope it helps.

vinay.kaipra · Answer

Bunuel, very good explanation. It was easier one compared to tough ones you had explained earlier.

teal · Answer

can you please give me an example of a set in which mean is even and median is odd for statement 2?

Bunuel · Answer

Sure: {1, 1, 4} --> mean=(1+1+4)/3=2=even and median=1=odd.

damamikus · Answer

why isn't the correct answer A?

from statement 1 we know that S is a set containing consecutive odd integers, hence, it is an evenly spaced set. For all evenly spaced sets --> Mean = Median . Also, for all evenly spaced sets, Mean = Sum of first and last Number/ 2. Since we know that all numbers in the set are odd, we know that the first and the last number are odd, too, therefore odd + odd = even. Even/2=even --> the mean, and therefore the median of the set are even. Statement 1 is sufficient. If i did make a mistake, can someone please explain?

Cheers,

Bunuel · Answer

Why wouldn't you check your theories with simple examples?

{1, 3} --> median = 2 = even.
{1, 3, 5} --> median = 3 = odd.

Mistake in your reasoning is that even/2 = integer, not necessarily even. For, example, 4/2 = 2 = even, but 6/2 = 3 = odd.

Does this make sense?

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Is the median of set S even?

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Is the median of set S even?

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