From a committee of 25 legislators, n members formed a task force.

Question

From a committee of 25 legislators, n members formed a task force. Each member of the task force sent a report to each committee member who was not on the task force. If a letter was sent in response to each report, which of the following represents the combined number of reports and letters sent?

A. \(n(25 - n)\)

B. \(n(26 - n)\)

C. \((n + 1)(25 - n)\)

D. \(n^2(25 - n)^2\)

E. \(2n(25 - n)\)

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Bunuel · Answer

Given that there are n members on the task force, then there are 25 - n members who are not on the task force. Since each member of the task force sent a report to each committee member who was not on the task force, then the total number of reports sent is n(25 - n). Since the same number of letters were sent as the reports, then the combined number of reports and letters sent is 2n(25 - n).

Answer: E.

gmatophobia · Answer

Number of members on the task force =  n

Number of members who are not on the taskforce =  (25-n)

Each member of the task force sent a report to each committee member who was not on the task force.

Number of reports sent =  n*(25-n)

If a letter was sent in response to each report

Number of letters sent = Number of reports sent =  n*(25-n)

The combined number of reports and letters sent =  2 * n*(25-n)

Option E

ShilpiAgnihotrii · Answer

The statement "If a letter was sent in response to each report" suggests that the question is asking for all the 25-n members have sent a letter in response.

Bunuel · Answer

The phrase "If a letter was sent in response to each report" means that for each report sent by a task force member, there is one corresponding response. There are n(25 - n) reports, and since each report gets a response, there are also n(25 - n) responses. Thus, the total number of reports and responses is 2n(25 - n).

If you are confused with the letters, substitute some numbers to understand better. Assume 5 members formed a task force. Then each of these 5 members sends a report to each of the remaining 20 committee members. This results in 5 * 20 = 100 reports. Each of these 100 reports receives a response, adding another 100 letters (each of the 20 committee members receives 5 reports and thus sends 20 * 5 = 100 letters in response). Therefore, the total number of reports and letters sent is 5 * 20 + 20 * 5 = 2 * 5 * 20 = 200.

Hope it's clear.

AnkurGMAT20 · Answer

Use smart numbers here:

Say out of 25 members, 24 members formed task force. Hence, n= 24 and person who is not in task force = 1.

Each of the n i.e. 24 members will send report to that '1' person who is not in the task force. So, total reports = 24

Now that '1' person will send letters to 24 members in response of their report. So, total letters = 24

Reports + Letters = 48

Now check all the options by taking n= 24. Option B, C, and D will be eliminated. Only A and E are left.

We can now check the remaining options again by taking n = 23 and calculating the total reports and letters.

Correct Option is E.

bumpbot · Answer

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From a committee of 25 legislators, n members formed a task force.

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From a committee of 25 legislators, n members formed a task force.

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