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The question stem states that if the stimulus is true what will help draw the conclusion of the argument that :"Maggie will share an apartment with her college roommate only if her parents know that she has accumulated excessive credit card debt during college". This is turn means that we need to find the assumption that will help hold this conclusion true.

Analyzing answer options:

A) Maggie's college roommate is willing to share an apartment only because Maggie accumulated excessive credit card debt during college.( we already know this from the stimulus and keeping this as our assumption doesn't let us derive the conclusion that we need.)

B) If Maggie shares an apartment with her college roommate, her parents will know that she accumulated excessive credit card debt during college. (I considered this to be a contender initially but on thinking about a little more this option isn't a contender, what if Maggie's parents do not know about her credit card debt would she still move in with her room mate, this option doesn't answer this question.)

C) If Maggie had not accumulated excessive credit card debt in college, she would neither move into her old bedroom at her parents' house nor share an apartment with her college roommate. (irrelevant, the stimulus clearly helps us understand that if Maggie wouldn't have accumulated credit card debt she wouldn't have to consider either options in the first place.)

D) If Maggie's parents do not allow her to move into her old bedroom at their house, she will share an apartment with her college roommate. (This is the conclusion that we are trying to prove hence this definitely cannot be our assumption.)

E) If Maggie's parents allow her to move into her old bedroom at their house, she will do so. (This is our OA because if Maggie's parents are not aware that she has a huge credit card debt then they will let her move into her old bedroom but if they are aware that she has excessive credit card debt then she will have to move in with her college room mate, hence making the conclusion in the question stem hold true.)
Hey There,
I am still unable to understand the explanation of the answer choice E and confused between D and E .
Would you please elaborate it so that the missing areas of the answers can be joint.
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What is the scenario Maggie would go home to stay with her parents.. “ she runs out of money” that was her criteria to go
Back home. In choice E she would take it however if her parents came to know that she has credit debt they would ask her to
Leave when she will end up with her roommate.

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Hi experts,
Please help to explain why each choice is right or wrong. Thanks.
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This is a very poor quality question. Options don't match with the conclusion. The assumption depends on Maggie's debt during college not on her parent's permission.
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This is an excellent question!

Premises/facts that we know:
- Maggie has accumulated credit card debt in college
- So she will either move back home or share an apartment with her roommate
- If her parents know about the debt, they will not allow her to move back home

Conclusion:
Maggie will share an apartment with her college room mate only if her parents get to know about the debt

Assumption:
The conclusion can be restated this way: if her parents do not get to know of the debt, she will move back home.
Remember, the roommate has not imposed any conditions.
From the conclusion we can infer that if her parents allow her to move home, that would be her first choice

- Matches Answer Choice E

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Let's dig deeper and look at every statement for the correct answer. Let me share why this question is difficult for some. The reason is that it's so basic. We sometimes overthink when we see complex statements and exam writers know that. So, one way to make a question difficult is to make it so basic that the solution is always in front of our eyes, but we still miss it. But let's get to the core of it. :). If we can drive home a message that thinking just right is what we need (no overthinking and, of course, no less thinking), that'll become handy in solving such complex questions dealing with fundamental deceptions.

Maggie will either move into her old bedroom at her parents' house to save money or else she will share an apartment with her college roommate. - Ok, this only shares two options that Maggie has
1. Move into her old bedroom or
2. Share an apartment

However, she would not do either one unless she had accumulated excessive credit card debt during college. So this is "UnlessX, Y" conditional. This means X is necessary for not Y. So, expansion of this statement. Maggie's accumulation of excessive debt is a necessary condition for her to choose either.

Maggie's parents will allow her to move into her old bedroom at their house if and only if they do not know that she has accumulated excessive credit card debt during college. Ok. This is another conditional. Notice "if and only if," so this is both a necessary and sufficient condition.

Necessary condition -
Only if they do not know do parents allow her to move into her bedroom. (They do not knowing is a necessary or a minimum condition for her to move to her bedroom)
It implies
Parents allowing her to move into her bedroom implies that they dont know about her debt.
If they know, parents, dont allow her to move into her bedroom.

Sufficient Condition - If they don't know, they'll 100% (guarantee) allow her.

Question Stem - If all of the above statements are true, which of the following would allow the conclusion that Maggie will share an apartment with her college roommate only if her parents know that she has accumulated excessive credit card debt during college to be properly drawn? - Conclusion - Maggie will share an apartment with her college roommate only if her parents know that she has accumulated excessive credit card debt during college.

Expansion - Only if her parents know she'll share an apartment. (expansion is not required as we'll not get that much time on the exam, but just sharing if you want to understand the implications else, ignore this part)
It implies that is she shares an apartment, her parents know that she has debt.
Or If her parents don't know that she has debt, she doesn't share an apartment. And rather take her bedroom.

So, we are looking for a sufficient condition (not a minimum condition), a missing premise for the conclusion to follow, which is

In a nutshell, we need to find a missing premise for the conclusion: "Maggie will share an apartment with her college roommate only if her parents know or they don't allow" So it means knowing that she wants to live with her parents (if they allow) is important. See option E's explanation to understand it better.

A) Maggie's college roommate is willing to share an apartment only because Maggie accumulated excessive credit card debt during college. - Bringing a new condition is okay, but this isn't related to the scope of the argument, which is establishing a condition: Only if her parents know she'll share an apartment. Wrong.

B) If Maggie shares an apartment with her college roommate, her parents will know that she accumulated excessive credit card debt during college. - Let me explain why this is atrociously wrong.

The 3rd Fact in the argument says that "Maggie's parents will allow her to move into her old bedroom at their house if and only if they do not know that she has accumulated excessive credit card debt during college."

So here, parents not knowing is a MINIMUM condition to allow her. But she can STILL CHOOSE to live with her college roommate? Isn't it? Yes. There is no SUFFICIENT condition in the argument that if her parents do not know, she'll 100% move with her parents. (there is a sufficient condition that her parents will 100% allow her, but will she 100% move in? We don't know. By the way, this is a critical gap, which is what option E pugs beautifully) So, in this statement, "will" is wrong. There is no way we can deduce this from the argument.


C) If Maggie had not accumulated excessive credit card debt in college, she would neither move into her old bedroom at her parents' house nor share an apartment with her college roommate. - Yes, that's what the entire argument is based on, but this is also stated in the argument. The assumption is about what's missing from the conclusion and not about stating the facts already stated or implied in the argument. Wrong.

D) If Maggie's parents do not allow her to move into her old bedroom at their house, she will share an apartment with her college roommate. - already implied in the statements.

E) If Maggie's parents allow her to move into her old bedroom at their house, she will do so. Suppose she doesn't do that. Instead, she goes to live in an apartment instead of moving to her old bedroom, and the conditional conclusion is invalid.

Let's look at the flow here to understand it better.

Fact 1 - Maggie has two options: either
1. Move into her old bedroom or
2. Share an apartment

Fact 2 - Maggie's accumulation of excessive debt is a necessary condition for her to choose either.

Fact 3 - The parents not knowing is a necessary and sufficient condition for her parents to allow her. (Maggie's parents will allow her if and only if they do not know about her debt)

Let me give an analogy. If 760 is necessary to enter the Dream Business School (DBS). Suppose we get a score of 760. Is it 100% sure that we get into (DBS)? No. Likewise, if Maggie has met the minimum condition, can she still live with her college roommate? Yes. Isnt it? If that is the case, she chooses to stay with her roommate even after meeting the minimum condition. We can't then deduce the conclusion (that she will live with her roommate only if her parents know) as she is already staying with her college roommate. Isn't it.? So, we need confirmation that she will stay with her parents when she meets the minimum conditions.

Missing Premise - If Maggie's parents allow her to move into her old bedroom at their house, she will do so. Exactly. Suppose she chooses to stay with her roommate even after meeting the minimum condition. In that case, we can't deduce the conclusion (that she will live with her roommate only if her parents know) as she is already staying with her college roommate.

Conclusion - Maggies will share an apartment when? Only if her parents know.

I hope this helps.
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