Self-study
Support 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. █████ ████ █ █████ ██████████ ██ ███ █████████ ████ ████████ ███ ███ ███████ ████ ██ ███ █████████ ████ ████ ████████████ ██ █████ ████ ████ ██ ███ █████████ ███████
Stimulus Breakdown: Flawed Reasoning
The stimulus tells us that all employees who participated in more than four scheduled events at the picnic were eligible for the raffle, and that only those employees were eligible. The stimulus then notes that only a small proportion of employees were eligible for the raffle. Thus, the stimulus concludes that most of the employees must have participated in fewer than four scheduled events.
Analysis: Flawed Reasoning Pattern
Let's examine the logic here. First, we're told that all the employees who participated in more than four events were eligible for the raffle, and only those employees were eligible. In other words, participating in more than four events is both a sufficient and necessary condition for being eligible for the raffle. You could restate this as saying that if and only if employees participate in more than four events, they will be eligible for the raffle:
more than 4 events ↔ eligible
The stimulus then tells us that only a small proportion of employees were eligible. This implies that most employees were not eligible, which tells us that most employees did not participate in more than four events:
/eligible → /more than 4 events
This might sound similar to what the stimulus concludes, but it's important to see that it's not the same thing. Remember that "more than four" means "five or more," and "not more than four" means "four or fewer." The stimulus concludes that most employees participated in "fewer than four" events — i.e., three or fewer. So the stimulus incorrectly negates "more than four" and overlooks the possibility that most employees could have participated in exactly four events.
So the answer we're looking for will probably contain a similar flaw, negating "more than X" to "less than X" rather than "equal to or less than X" (or vice-versa, negating "less" to "more" instead of "equal to or more than").
25.
Which one of the following █████████ ████████ █ ██████ ███████ ██ █████████ ████ ████ ████ █████████ ██ ███ ████████ ██████
a
Only third- and ███████████ ████████ ███ ███████ ██ ████ ████ ██ ███████ █████ ███ ███████ ██ ███ ██████████ ████████ ████ ████ ██ ██████ ███ ███ ████ ██ ███ ███████████ ████████ ████ ████ ██ ███████ ██ ████ ██ ████ █████ ██████████ ████████ ████ ███████████ ████████ ████ ████ ██ ███████
Incorrect. This is a flawed argument because it assumes that since the proportion of third-years who keep cars on campus is smaller than the proportion of fourth-years who do so, the absolute number of third-years versus fourth-years who do so must be smaller. But there could be significantly more third-years overall than fourth-years, so that one quarter of third years could still be more people than one half of fourth years. So (A) contains a flaw, but not the same one as in the stimulus.
b
Only those violin ████████ ███ ████████ █████ █████████ ████████ ████ ████████ ███ █████████ ██ █████████ █████ ███ ██ ███ ██████ ████████ ████ ████████ ██ █████████ █████ ███ ████ ████ ████ ███ ████ ██████ ████████ ███ ████████ ███ █████ █████████
Incorrect. This argument mistakes a necessary condition for a sufficient one. In order to reach the conclusion that since these two students were chosen as soloists, only those two students must have attended the extra sessions, we would need to know that attending the extra sessions guaranteed (i.e., was a sufficient condition for) becoming a soloist:
attend sessions → soloist
Then we would know that no one else must have met the sufficient condition of attending the sessions. But the premise actually states that only those who attended the extra sessions could become soloists, not that all those who attended would become soloists:
soloist → attend sessions
So there could have been others who attended the sessions (met the necessary condition) and didn't become soloists, for whatever reason. This is a sufficiency/necessity confusion flaw, not an incorrect negation of a quantifier. So (B) isn't what we're looking for.
c
The only students ███████ ██ █ ███████ ███████ ████ ███ ████ ███████ ███ ████ ███ ████████ ████ ████ █████████ █████ ████ ██ ███ ████ ███████ ████ ████████ ████ ██ ███ ████ ███████ ████ ████ ████ ███ ████████ █████
There's no flaw in this argument. If the only students honored at the banquet were band members who made the dean's list:
honored → band member AND dean's list
And most of the band members were honored:
band members –most→ honored
Then we can legitimately conclude that most of the band members must have made the dean's list, since that's a necessary condition for being honored:
band members –most→ honored → dean's list
Since (C) is a valid argument, it certainly doesn't contain the flaw we're looking for.
d
All of the ███████ ██ ███ ███████ ████ ███ ███████████ ██ ███ ████████ ████ ██████ ████ ███████ ███████ █████ ███ ██ ███ ████ ███████ ███ ███████ ███████ █████ ███ ███████ ████ ████ ███████████ ██ ███ ████████ ████ ███████
This is a different flaw than what we're looking for. Since all the statements in this argument are about members of the service club, let's kick that idea up into the domain (i.e., assume that the condition "member of the service club" is already met, and leave it out of our diagramming). In that case, the first sentence tells us that:
volunteered at hospital last summer → biology major
But the next sentence concludes that all ten members who were biology majors must therefore have volunteered at the hospital last summer, which assumes:
biology major → volunteered at hospital last summer
So (D) confuses sufficient and necessary conditions, which is a flaw, but not the one we're looking for.
e
All of the ████ ████ ███████ ███ ███ █████████ █████ ██████ █████ ██████ ███ ██████ ████ █████ ██████ ████ ██ █████ ███████ ████ ██████ █████ █████ ████ ████ ███ ████ ███████ ████ █████ ████ ███████ ███ ██████ █████ ██ ████ ████ ████ ███ ████ ███████ ████ ████ █████████ ██████ ███ ███████
(E) is the answer we want. We're told that all the members who decreased their time, and only those members, were given these awards:
decrease time ↔ award
Since less than half the employees received these awards, we know that more than half did not receive these awards, and therefore must not have decreased their time:
/award → /decrease time
But "not decreasing time" could mean keeping their time the same. Meanwhile, (E) incorrectly concludes that these employees must have increased their time. This answer choice incorrectly negates a "less" statement (decrease time) to a "more" statement (increase time), which mirrors the flaw in the stimulus.