A committee of k members was formed from the n members of a certain

Question

A committee of k members was formed from the n members of a certain company's board of directors. Each member of the committee sent exactly one email summarizing his or her perspective on the committee's findings to each board member who was not a member of the committee, and to no one else. The total number of these email summaries sent was 35.

Select values for k and for n that are jointly consistent with the given information. Make only two selections, one in each column.

Kinshook · Answer

Given: A committee of k members was formed from the n members of a certain company's board of directors. Each member of the committee sent exactly one email summarizing his or her perspective on the committee's findings to each board member who was not a member of the committee, and to no one else. The total number of these email summaries sent was 35.

Asked: Select values for k and for n that are jointly consistent with the given information. Make only two selections, one in each column.

Total number of email summaries = k(n-k) = 35 = 5*7
If k = 5; n = 12; k(n-k) = 5*7 = 35
 
k:
4
 5 
6
10
12

n:
4
5
6
10
 12

CEdward · Answer

How come we need to multiply k x (n - k)?

waritamorn · Answer

Hi, 
number of board = n,
number of comittee = k (k person from n person) ==> k< n
each k send e-mail to board member who was not a member of the committee (n-k)
so total e-mail will be 
k*(n-k) = 35 = 7*5

Is this the correct approach?
Thanks

Sajjad1994 · Answer

Yes it is.

TargetMBA007 · Answer

* Each board member sent 1 email to "each of the other members" and we are given the total no. of emails. So we should ask, what should this total equal to?

Total no. of emails = No. of people sending the emails (k) * no. of people receiving the emails (n-k).
35 = k (n-k). 
7*5 = k (n-k), so one of them is a multiple of 5 and one of them is a multiple of 7. 
We know k<n, as we are choosing k from n, so k must be 5, which means, n-k=7 or n=12.

Bunuel  - Tag: EA

Bunuel · Answer

________________
Done. Thank you!

Apk641 · Answer

This problem gave me a lot of trouble at first, but once I stopped focusing only on the math and thought logically about how the 35 emails are created, it clicked.

We’re told each committee member sends emails to everyone  not  on the committee. So how can we get a total of 35 emails?

The only product that makes sense is  5 × 7  = 35. But 7 isn’t one of the answer choices for n or k... so where is it coming from?

The only way to get it 7 is from 12-5. Now we have this narrowed down to to possible answers once we realize this.

And since the committee must be  a subset  of the board, k has to be less than n. Therefore n=12, k=5

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A committee of k members was formed from the n members of a certain

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