There are 65 members of an organization. The plan for disseminating news requires one member to contact two others with the information. Each member who receives the news contacts two members who have not yet gotten the news. This continues until all members have the information. How many members contact others?
A)64
B)48
C)32
D)16

Question

Quizplus · Accepted Answer

We can create a diagram to represent the distribution of news:

1st round: 1 member contacts 2 members (2 members total have the news)
2nd round: 2 members each contact 2 members (4 new members total have the news)
3rd round: 4 members each contact 2 members (8 new members total have the news)
4th round: 8 members each contact 2 members (16 new members total have the news)
5th round: 16 members each contact 2 members (32 new members total have the news)
6th round: 32 members each contact 2 members (64 members total have the news)

Therefore, it takes 6 rounds of communication for all 65 members to receive the news. The question is asking how many members in total will be contacted. To find this, we can add up the number of members contacted in each round:

1st round: 1 member contacts 2 members = 2
2nd round: 2 members each contact 2 members = 4
3rd round: 4 members each contact 2 members = 8
4th round: 8 members each contact 2 members = 16
5th round: 16 members each contact 2 members = 32
6th round: 32 members each contact 2 members = 64

Adding these up, we get:

2 + 4 + 8 + 16 + 32 + 64 = 126

Therefore, a total of 126 members will be contacted. However, the question is asking how many members contact others, not how many members are contacted. Every member except for the first one contacts others, so the answer is:

65 - 1 = 64

Therefore, the answer is (A) 64.

There Are 65 Members of an Organization