This question is from an LSAT Logical Reasoning section (#22) and is not asking for the necessary assumption, but the sufficient assumption. And these don’t show up on GMAT CR.
As you indicate, negating (E) (there are no moons that orbit Alpha) would indeed kill the argument. In fact, it would make the entire argument moot.
But a Sufficient Assumption asks for an answer that guarantees/proves the conclusion to be true. (E) clearly does not prove the conclusion to be true. In fact, E barely even strengthens the argument if at all.
I just wrote about this earlier in reference to another question. Please note that I’ve been teaching both GMAT and LSAT since the 20th century. Here’s what I wrote:
Students need to be very careful about doing questions phrased like this, especially because it’s from an LSAT Logical Reasoning section. Specifically, LSAT preptest 62, section 4, number 18.
This question type doesn’t really exist in GMAT CR. “Really” is a weird term, I realize. But check it out...
For LSAT Logical Reasoning, this question type is known as a Sufficient Assumption, where the correct answer, when combined with the argument in the stimulus, creates a valid argument.
To paraphrase: The correct answer will guarantee/prove that the conclusion is true based on the evidence/premises. This different from a Necessary Assumption question.
Sufficient Assumption questions (unlike 95% of Necessary Assumption questions) will NOT contain a synonym for necessary (depends, relies, required). They will most often employ the phrase “if assumed”, along with “conclusion follows logically” or “enables the conclusion to be properly inferred”.
PLEASE fact check me (only OG material): for GMAT CR (unlike LSAT LR), any Sufficient Assumption question will be also be asking for a Necessary Assumption.
CR questions phrased as a Sufficient Assumption are extremely rare. If anyone ever sees such a question where the correct answer does not appear to be necessary, I would appreciate a notification. You’ll probably be wrong (heh), but perhaps I’m wrong (I’m not, though).
In other words, it’s entirely possible that a sufficient assumption will also be necessary. But this absolutely does not have to be the case.
For the GMAT, the correct answer to any assumption question will be a necessary assumption as shown by the negation test (beyond the scope of this reply).
But for the LSAT, the correct answer to many Sufficient Assumption questions will NOT be necessary (the negation test will be of no help).
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This is why students need to be careful about doing an LSAT Logical Reasoning. Several question types that look familiar actually do not show up on GMAT critical reasoning.
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