"At the company picnic, all of the employees who participated in more than four of the scheduled events, and only those employees, were eligible for the raffle held at the end of the day."
So, let's place numbers into the argument so it'll be easier to comprehend.
Let's say 25 employees out of 100 participated in more than four of the scheduled events. So, 25 people were eligible for the raffle, meaning 75 were not.
We know that if you are not eligible for the raffle, you did not participate in more than four events. We can agree that 75 out of 100 does compose a majority, so we can use the word "most."
The conclusion states: because 25 out of 100, i.e. "only a small proportion," of employees were eligible, most of the employees must have participated in fewer than four events.
But, we know that "not participated in more than four events," does not necessarily mean participating in "fewer than four events."
Not participating in more than four events could mean participating in EXACTLY four events. What if 60 employees participated in four events, 15 participated in two events and 25 participated in more than four events? Then, even though a small proportion of employees were eligible for the raffle, it is not true that most of the employees must have participated in fewer than four of the events.
Answer choice (E) has the same flaw.
We know that all of the swim team members who had decreased their racing times during the season were given awards that no other members were given. A small amount of the team members were given such awards, so the argument concludes that most of the team members must have increased during the season.
Alright, so again, just because a team member does not decrease their racing time, does not mean that they necessarily increased their racing time. Couldn't their racing time just have stayed the same?
Thus, even though 25 out of 100 swim team members have decreased their racing times, 60 swim team members could have just kept their times the same, while 15 increased their time.
Thus, it is not necessarily true that more than half the team members must have increased their times during the season.
As you can see, answer choice (E) has the same flawed pattern of reasoning that is exhibited in the argument.
Hope that clears things up! Please let us know if you have any other questions.
Karen-NorrisJanuary 20, 2022
I got the right answer, but I approached the question a different way. Did I just get lucky?
I saw this as a quantifier flaw since an "all" (Sufficient and Necessary) statement and a "some" statement could not produce a "most" conclusion.
Stimulus:
Premise: If participated in more than 4 events --> participate in raffle.
Premise: Employees - some - not participate in raffle.
Conclusion: Employees - most - not more than 4 events.
Answer Choice E:
Premise: If Team Member with decreased time --> receive award.
Premise: Team members - some - received award
Conclusion: Team members - most - not decreased time.
RaviFebruary 5, 2022
@Karen-Norris, I think what you're getting at is that the argument is overlooking the possibility of there being other options. Some swim team members might have not had a change in their racing times. A time that didn't change is the overlooked possibility between and increase and decrease.
