Self-study
Brown dwarfs—dim red stars that are too cool to burn hydrogen—are very similar in appearance to red dwarf stars, which are just hot enough to burn hydrogen. ██████ ████ █████ ███████ ███████ ███████████ ███████ ██ ███ ███████ ████████ ███ █████ ███ ███ ███████ ██ ███ █████ ██████ ███ ███ ██████ ██ ███████ ███████ ██████████ ██ ██████████ ██ ██ ███████ ████████████ ███ ████ █████ ████ ████████ ██ ███████ ██ ███ ███ ██ █████ ███████ █████ ███████
Summary
The author here is just throwing a bunch of information about stars at us, so we should start by figuring out exactly what that information is. We're talking about stars, but more specifically about brown dwarf stars. The stimulus gives us various facts about brown dwarf stars: (1) they're too cool to burn hydrogen; (2) they look similar to red dwarf stars; (3) they contain lithium when first formed—because all stars do. Then we learn something about a subset of brown dwarf stars, specifically the coolest brown dwarfs: they have all the properties we've already identified, but they also are the only stars too cool to burn lithium.
From all this, the author concludes that any star lacking lithium cannot be one of the coolest brown dwarfs. We know that all stars contain lithium when they first form, but recall that all stars except the coolest brown dwarfs are hot enough to destroy lithium completely. So the author's reasoning is that if a star is hot enough to have burned away all its lithium, it can't possibly be one of the coolest brown dwarfs.
Objective: Find the Necessary Assumption
This might seem like a solid argument now that we've broken it down, but there has to be a gap somewhere to give rise to a necessary assumption. However, the author directly states that the coolest brown dwarfs can't destroy lithium, so that can't be it. As with many Necessary Assumption questions, it might be hard to predict the answer here, so if nothing jumps out straight away a good strategy is to go straight to the answer choices and see what they offer us. We just need to keep in mind that the correct answer must be truly necessary to the argument. If we take the correct answer and tell the argument “you’re not allowed to have this,” the argument will completely fail.
To check whether each answer choice is necessary if it's not immediately clear, we can use one of our tried and true approaches: the "must be true" test or the negation test. Either way, what we're testing that the argument truly requires that assumption.
16.
The argument depends on assuming █████ ███ ██ ███ ██████████
a
None of the ███████ █████ ██████ ███ ████ ████ ███ ██████ ██ ███████ ████████
Here's our necessary assumption, and we can see why using negation. If (A) weren't true, and even one of the coolest brown dwarfs used to be hot enough to destroy lithium, then it would be possible to find one of the coolest brown dwarfs that contained no lithium. Since negating (A) would weaken the argument, (A) must be necessary to assume.
b
Most stars that ███ ███ ████ ██ ████ ████████ ███ ███ ████ ██ ███████ ███████ ███████████
From the premises, we do know that brown dwarfs are too cool to burn hydrogen, and the coolest of these also can't burn lithium. This makes the coolest brown dwarfs (non-lithium-burning) a subset of stars that can't burn hydrogen.
So (B) sounds like it aligns with the stimulus, but the issue is that the size of this subset doesn't matter to the argument. The author is concerned with drawing a line between stars that can burn lithium and stars that can't; how many stars there are in each category makes no difference. So (B) isn't necessary to assume.
c
Brown dwarfs that ███ ███ ███ ██████ ██ ███████ ███████ ███ ███ ██████ ██ ███████ ███████
The conclusion is simply that a lack of lithium proves that a given star is not one of the coolest brown dwarfs. The author only mentions helium in passing as the result of burning lithium, but the argument doesn't depend on this in any way, so it's not necessary to assume anything about helium.
d
Most stars, when █████ ███████ ███████ ███████ ███ ████ ██████████ ██ ████████
Based on the premises, any star that's hot enough will destroy all of its lithium completely; any star that doesn't burn out all its lithium just isn't hot enough to do so. How much lithium the star contained to begin with doesn't matter because the premises are so absolute. So it's not necessary to assume anything about the inital amounts of lithium.
e
No stars are ████ ███████ ██ ██████████ ██ ███ ██████ ████ ███ █████ ███████
The lithium content of a star is what matters; its appearance is irrelevant. The author mentions the similar appearance of brown and red dwarfs as context, but the argument doesn't depend on that information, so we don't need to make any assumptions about it.