Question

11 politicians have formed a number of committees. Every committee has exactly 6 members. the first 10 politicians in exactly 7 communities each. If the 11 politician is in exactly n committees, what is the sum of all possible values of n?​

Answer 1

Given : 11 politicians have formed a number of committees.

Every committee has exactly 6 members. The first 10 politicians are in exactly 7

committees each.

the 11th politician is in exactly 'n' committees,

To Find : sum of all possible values of n

Solution:

Let say number of committees = x Every committee has exactly 6 members

=> Total members = 6x

The first 10 politicians are in exactly 7 committees

Hence 10 x 7 = 70

11th politician is in exactly 'n' committees,

=> Total Members = 70 +n

6x = 70 + n

x = 12 => n = 2

The first 10 politicians are in exactly 7

committees

Math

5 points

Hence 10 x 7 = 70

11th politician is in exactly 'n' committees,

=> Total Members = 70 + n

6x = 70 + n

x = 12 => n = 2

x = 13 => n = 8

x = 14 => n = 14

x = 15 => n = 20 but n must be always less than x

Hence possible values of n are

2,8 and 14

Sum of all possible values of n = 2 + 8 + 14 =

24

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