Alright, this one was a pain. But I will go with C.
Explanation:
Fact - A weeklong alumni calling spree results in 400 alumni signing up as mentors each year.
Conclusion - if phone-a-thon is discontinued, the result will be a ~400 decline in the number of sign-ups.
Let's go through each answer choice.
A -
The phone-a-thon costs the university less than the value of 400 alumni mentors’ time. Wrong. Do I NEED this to be true for the conclusion to hold? No. It does not matter how much it costs the university versus the value of mentors' time.
B -
The university would still be able to contact alumni through email if the phone-a-thon were discontinued. Wrong. Not a requirement for the conclusion to hold, even if email isn't a possible way to contact - we will still see a decline of 400, attributable to the discontinued phone-a-thon.
C -
Few alumni who currently sign up to mentor through the phone-a-thon would sign up through other university outreach efforts if the phone-a-thon were discontinued. Correct.This one is a good answer choice. If
I don't assume that only a few of the alumni will sign up to the mentor program if the university don't call them, it opens up the possibility that more than a few/most/a substantial number of these alumni sign up for the program. Therefore, C's absence brings my conclusion to a doubtful place.
D -
The alumni who sign up to mentor through the phone-a-thon are not substantially more likely than other alumni to sign up to mentor in any given year, regardless of how they are contacted. Wrong. Oh boy, this answer choice refused to be eliminated easily. Here's my best effort - even if these phone-a-thon alumni are substantially more likely than others to sign up as a mentor regardless of how they are contacted, it doesn't necessarily imply that most of them would sign up.
For example, if the likelihood of the other mentors is 1%, and the ones who sign up through the phone-a-thon are 10 times more likely to sign up - 10%; then discontinuing the calling strategy would still lead to a decline in the number of mentors.
My main problem with this answer choice is - I don't know how likely a random alumnus is to sign up. So substantially higher could mean 10% or 100%, I just don't have enough data to go on. With a heavy heart, I will eliminate this.
E -
The university’s other mentoring sign-up channels would not become significantly more effective at attracting mentors if the phone-a-thon were discontinued. Wrong.Similar problem as D, I don't know effective these channels currently are and how much the significant increase in effectiveness would impact the mentor numbers - cannot assume that the increase will be enough to cover the 400 mentor delta.