At the company picnic, all of the employees who participated in more than four of the scheduled events, and only thos...

SamA on November 8, 2019

Hello @Lucie,

Keep in mind that this is an "if and only if" scenario, which is different from a sufficient - - - - - > necessary format. In this case, each term is both sufficient and necessary. I'll demonstrate.

If an employee was eligible for the raffle (ER), then they participated in more than four of the scheduled events (5+).
ER - - - - - - > 5+

If an employee participated in more than four of the scheduled events (5+), then they were eligible for the raffle (ER).
5+ - - - - - - -> ER

Therefore: 5+ < - - - - - - - -> ER

Only a small proportion of employees were eligible for the raffle. So what can we conclude? Only a small proportion of employees participated in 5+ events.

less than half (ER) - - - - - - -> less than half (5+)

So what mistake does the argument make? It forgets those who participated in exactly 4 events. It says, "most of the employees must have participated in fewer than four of the scheduled events." We cannot conclude this! If it said "4 or fewer," then it would be ok.

Usually it is helpful to diagram a flaw-in-reasoning question, but in this case I worry that it makes things more complicated. I would simply look for an answer choice that assumes there are only two categories, and fails to see a third category, such as "exactly 4."

E makes this same mistake. Which category does it forget? Swimmers whose racing times stayed exactly the same.