Friends

[shashank.ism]

Abhash, Balu, Chandan and Dinesh are 4 friends each of whom weighs less than 100 kg. From amongst them they form a group and find the total weight of the group. If the sum of the total weights of all possible distinct groups, each having the same number of members as in the first is 882 kg, then the average weight of the 4 friends is

A) 41.75 kg
B) 63.5 kg
C) 73.5 kg
D) 83.5 kg
E) None

[ajith]

Abhash, Balu, Chandan and Dinesh are 4 friends each of whom weighs less than 100 kg. From amongst them they form a group and find the total weight of the group. If the sum of the total weights of all possible distinct groups, each having the same number of members as in the first is 882 kg, then the average weight of the 4 friends is

A) 41.75 kg
B) 63.5 kg
C) 73.5 kg
D) 83.5 kg
E) None

AB+AC+AD+BC+BD+CD+ ABC+ACD+BCD= 882

5(A+B+C+D) =882

(A+B+C+D) = 882/20 = 44.1

[lalmanistl]

Hi Ajit,

Can you please explain the logic to form the group.

I guess one 3 people group 'ABD' is missed in calculation.

-Lalmani

[Cinji18]

I'm not sure I understand the question.

[ajith]

Hi Ajit,

Can you please explain the logic to form the group.

I guess one 3 people group 'ABD' is missed in calculation.

-Lalmani

I am confused about the wording too... In my opinion the group can have 2 or three members

AB represents the group with the members and B
ABD is the group with A, B and D ..

so on .. and so forth..

But, the question is really ambiguous .... Probably thread starter can post, OA and OE

[Stuart@KaplanGMAT]

I am confused about the wording too... In my opinion the group can have 2 or three members

AB represents the group with the members and B
ABD is the group with A, B and D ..

so on .. and so forth..

But, the question is really ambiguous .... Probably thread starter can post, OA and OE

Since each of the possible groups must have the same number of members as the original group formed, we're talking about all the 2 person groups or all the 3 person groups.

So, either:

(A+B) + (A+C) + (A+D) + (B+C) + (B+D) + (C+D) = 882

or

(A+B+C) + (A+B+D) + (A+C+D) + (B+C+D) = 882

At first glance, it may seem like this provides 2 possible solutions. However, if we add up the As Bs Cs and Ds in each possible sum, we see that they are in fact identical!

In both scenarios, each person appears in 3 groups; so if we look at the sum of the individuals, we have:

3A + 3B + 3C + 3D = 882

3(A + B + C + D) = 882

A + B + C + D = 882/3 = 294

We want the average weight, so:

avg = (sum of terms)/(# of terms) = 294/4 = 146/2 = 73.5... choose (C).

As an aside, we know that the original group chosen can't have 1 member of 4 members; if it was 4 groups of 1 person per group, the max sum would be under 400kg; if it was 1 group of 4 people, again the max sum would be under 400kg.

What's the source?