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

­ 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. 

­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.

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.­

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