11 politicians have formed a number of committees. Every committee has exactly 6 members. The first 10 politicians are in exactly 7 committees each. If the 11th politician is in exactly 'n' committees, what is the sum of all possible values of 'n'??
Answers
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,
0 ≤ n ≤ x
=> 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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Answer:
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,
0 ≤ n ≤ x
=> 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
Step-by-step explanation: