Self-study
Support Ann will either take a leave of absence from Technocomp and return in a year or else she will quit her job there; but she would not do either one unless she were offered a one-year teaching fellowship at a prestigious university. ██████████ ████ █████ ███ ██ ████ █ █████ ██ ███████ ██ ██ ████ ███ ████ ███ ████ ███ ███ ████ ███████ ███ ███████████ ███ ███ ██████████ ██████████ ███ ████ ████ ███ ███ ██ ██████████ ████ ██ ██████████ █████ ███ ███ ███ ████ ███████ ███ ███████████
Argument Summary
Premise 1: Ann will either take a leave (and return in a year) or quit. Notice these two options are mutually exclusive by nature: "taking a leave and returning" means she keeps her job, while "quitting" means she ends it. So if she quits, she didn't take a leave.
Premise 2: Technocomp will allow her to take a leave if it doesn't find out about the fellowship, but not otherwise. The "but not otherwise" adds the second half: if Technocomp does find out, it won't allow the leave. Combine that with the first half ("if doesn't find out, allow"), and we get an if-and-only-if: Technocomp allows leave if and only if it doesn't find out about the fellowship. Equivalently, leave is not allowed if and only if Technocomp found out.
Third, the conclusion: if Ann quits, Technocomp found out.
To get from "Ann quits" to "Technocomp found out," we want to establish this chain: quit → no leave → leave not allowed → Technocomp found out.
The first step (quit → no leave) is established by Premise 1 (from the mutually exclusive options). The third step (leave not allowed → Technocomp found out) is established by Premise 2. The middle step is where the argument has a gap. Just because Ann doesn't take a leave doesn't mean leave wasn't allowed. She might have been allowed to take leave and chosen to quit anyway. The argument needs to close that gap.
The Missing Link Between Premises
We want an assumption that says: if Ann doesn't take a leave, then leave wasn't allowed. Equivalently (contrapositive): if leave was allowed, Ann would have taken it. With that piece, the chain runs cleanly from "Ann quits" all the way to "Technocomp found out."
20.
Which one of the following, ██ ████████ ██████ ███ ██████████ █████ ██ ██ ████████ ██████
a
Technocomp will find ███ █████ ███ █████ ███████ ███ ██████████ ████ ██ ███████ ███████ ██ ████
This tells us what's required for Technocomp to find out (someone has to inform on her). But that's a necessary condition for finding out, not a way to prove that quitting implies Technocomp found out. The argument needs to derive "Technocomp found out" from "Ann quits," which means closing the gap between "Ann doesn't take leave" and "leave wasn't allowed." (A) doesn't close that gap.
b
The reason Ann █████ ███ ██████████ ██ ██ ███ ███ ████ ███ ███ ██ ███████████
This is about Ann's motivation. This doesn't connect the two premises in a way that allows us to get from "quits job" to "Technocomp found out." Also, if Ann specifically wants the fellowship so she can quit, she might prefer to quit even when Technocomp would have let her take leave. That's the opposite of what the argument needs to bridge "no leave" to "leave not allowed."
c
Technocomp does not █████ ███ ██ ███ █████████ ██ ████ █ █████ ██ ███████ ██ █████ ██ ████ ███ ███ ██ ███ ████████████
Irrelevant. The fellowship is a teaching position, not a job at a competitor. The premises already specify the ONLY condition for Technocomp's leave decision (whether it finds out about the fellowship), so a special rule about competitor employment doesn't apply here.
d
Ann will take █ █████ ██ ███████ ██ ██████████ ██████ ███ ██ ████ █ █████ ██ ████████
This is the answer. (D) says: if Technocomp allows the leave, Ann takes it. The contrapositive is exactly the bridge we want: if Ann doesn't take a leave, leave wasn't allowed. With (D) plugged in, the chain runs cleanly:
Ann quits
↓ leave of absence and come back OR quit (so quitting means no leave)
Ann doesn't take leave
↓ (D)'s contrapositive (the assumption)
Technocomp didn't allow leave
↓ allow ↔ didn't find out
Technocomp found out about fellowship
e
Ann would be ███████ ███ ██████████ ████ ██ ███ ████ ███ ███ ██ ███████████
Wrong direction. (E) says: if Ann is offered the fellowship, she quits. Even granted, that doesn't give us "if she quits, Technocomp found out." (E) starts from the fellowship offer and ends at quitting. We need an assumption that starts from quitting and ends at Technocomp finding out.