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Please let me know if I'm thinking about the difference between these two conditions correctly.

I wrote the following stimulus since I have learned that posting LSAT questions is a no-no.

Most people who lose weight do not exercise at all. In fact exercising will be of little value to your weight goals if you eat 99 fried chickens each day.

If all of the statements are true, which one of the following must be true?

(A) Exercising is neither a sufficient nor a necessary condition to lose weight.

I would choose this answer since the first sentence shows that exercising is not a necessary condition. If it was necessary, then there would not be any people who had lost weight.

The last sentence shows that it is also not a sufficient condition since it does not guarantee that if you exercise you will lose weight.

Am I thinking about this correctly?

Here is a recent post of mine which explains the difference (the last line doesn't necessarily apply to you):

Be very clear what you are looking for in each type of question.

A necessary assumption is something that absolutely must be there or else the argument falls apart. It functions like a life vest in that it serves to keep the argument just above water, and without it, the argument drowns. Thus, the necessary assumption is something that you need to make it possible for the conclusion to make sense. The necessary assumption is not part of the conclusion. Rather, it is an unstated premise that must be within the argument, or else the conclusion cannot logically follow. A necessary assumption does not guarantee that the given conclusion will follow, but it makes it possible.

A sufficient assumption is one that guarantees the truth of the conclusion. Dont think of it as a mere life vest because it is much more. It makes it not just possible for the conclusion to follow (like a necessary assumption), but makes it so the conclusion given absolutely has to follow. A sufficient assumption makes it so the conclusion deductively follows from the premises, whereas a necessar assumption merely makes it possible for the conclusion to follow.

This is how you conceptualize assumption questions, so be very clear with what you are looking for since I think you are over complicating and over thinking it.

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