If the total income of a family per month is $6000

As it is given that the middle value or median is $2000, hence two cases are possible:
i) When there are even number of members.
In such case, answer choices A, C and E are being considered.
Since for sets consisting of even number of elements, the mean of middle two values is the mean. Hence ATLEAST these two values must sum to $4000. The largest value has to be atleast $2000 and the lowest value has to be atmost $2000. Thus sum would be more than $6000. Hence C and E are eliminated. For answer choice A, where there are 2 elements, the mean of these two elements must be $2000 or sum is $4000. Eliminate A too.
Answer choice B is the only possible answer, in which either all the three elements are the same or the largest is more than $2000 and the smallest is less than $2000.
In case of E, the sum would become more than $6000.
+1B

if 2000 is the median and 6000 is your total you know right away that you have an odd number of family members - eliminate A,C and E.
furthermore, there is no way you could have 5 members with a median of 2000.
there are several ways you could have distributed the money with 3 family members;
1000,2000,3000
2000,2000,2000
Answer: B

Hi,

Actually the value can not only be 0 but also be negative too, say, if one the members is engaged in a business and incurs loss.

But does not income mean earnings? For example replace "income" with "earnings". So in this case, you are talking of earnings of the members of the family and it would not be incorrect to assume that all the members do earn. So I think only in the case when any member does not earn you need to state that explicitly.

Just removed the zero's from the numbers

Total income = 6

Median = 2


1 .......... 2 ............. 3 >>>>> Total = 6

No other combination possible

Answer = B

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.