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

Question

If the total income of a family per month is $6000 and the median income is $2000, how many members are there in the family?

A. 2
B. 3
C. 4
D. 5
E. 6

KarishmaB · Accepted Answer

One good thing about PS questions - you know only one option will satisfy the conditions i.e. there will be only one answer.

Total Income - 6000
Median - 2000

Assume number of people is 2. Median = Avg salary of the two people.
Since total income is 6000, the avg will be 3000 hence number of people cannot be 2.

Now assume number of people is 3. We can easily see that if each person makes $2000, the total will be $6000 and median will be $2000. This fits our question. Hence answer has to be (B).

We don't need to check any other options.

Note: The question should have mentioned that every family member earns. Otherwise no of people can be 4 or 5 too.
0, 2000, 2000, 2000
0, 0, 2000, 2000, 2000

Marcab · Answer

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

sambam · Answer

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

SVaidyaraman · Answer

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.

KarishmaB · Answer

Here is my opinion on this issue:

The question only states: how many members are there in the family?

Say, there is a family with 3 adults and 2 kids - there are 5 members in the family - but this info is not given to us.

Given information:
All three adults earn $2000 each
Total income of the family members => 6000
Median income of the family members => 2000

So given this information, how many family members will you say there are? 3 or 5? Do we count the kids as family members or not?

All I want to say is that if this were a DS question, I would not have said that there can be only 3 family members. There could be non-earning family members. The only reason I will go with 3 is because it is a PS question so I make the assumption that I need to.

PareshGmat · Answer

Just removed the zero's from the numbers

Total income = 6

Median = 2

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

No other combination possible

Answer = B

kokareva2002 · Answer

what if 1000/2000/2000/1000
Me=2000+2000/2=2000
Hence 4 members is also right

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

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GMAT Problem Solving (PS) Questions

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

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