A is actually really simple, and I think you might slap yourself when you realize it:

The argument states "students are bored by history courses as they are currently taught" and that "the best way to teach history" is to avoid dates and statistics (in other words, the things that bore students). As a result, the argument is in essence assuming that minimizing boredom is part of the best way to teach history, as you should avoid doing things that are boring.

Your reasoning, in fact, is moreso tied to the reason why B cannot be the answer: it is a necessary assumption that you can teach history with a lesser focus on dates and statistics for that to be the best way to teach.

@joelatennyson369

This makes perfect sense. Thank you!

I don't believe it's a good idea to be involving numbers in your problem solving method. Time is a luxury, and any kind of setup like this that will increase the mental load of thinking about the problem will serve only to slow you down, right or wrong. Instead, think about the groups involved in this question and the direction of the variable being tracked (known crime rate).

Going with this approach, we have two groups: local police departments and random citizens. Seeing from the paragraph that local PDs report on crimes reported to them, we know that the direction of PD "perceived crime" statistics will follow the number of police reports given. As the local PDs are reporting increased crime, this means reported crime is going up.

Meanwhile, from our intuition (and the lack of any information given to the contrary), we assume the random citizen group gets their "perceived crime" variable data from ambient crime levels exclusively, in other words representing the number of reported AND unreported crimes occurring. As their survey indicates a downward trend, we can conclude the total number of crimes is going down or not moving.

If reported crime is going up compared to total crime, the proportion of reported crimes is increasing. This leads us to E as an answer.

In many logical reasoning questions, I often find myself returning to the same logic in my answers: how much information do I need to abstract from the question to reach this conclusion? Given that I'm sure you've already figured out why the other choices are incorrect, I will focus exclusively on B and E.

First, let's talk about why B is wrong. Look over the passage carefully. If it helps, split the paragraph into a bulleted list made only of statements of fact. Notice that B is in fact saying the opposite of what the passage tells us. A manufacturer chooses stabilizers, a low cost option, at the expense of flavor. This means when minimizing costs, manufacturers prefer consistency to flavor. B says the opposite of this and therefore cannot be correct.

Take it a step further, though - let's say B in fact did match the logic we could possibly infer from the paragraph. It would still be incorrect. Despite the fact that we can make a decently logical estimate in favor of this hypothetical B, the fact remains that we don't actually have enough information. We don't know if companies choose stabilizers because consumers prefer consistency, if it's the only option they can afford at all, or otherwise. In choosing our hypothetical B, we assume one of many possibilities.

Compare this to E. E uses only information directly in the paragraph. Nothing is assumed besides "ice cream should be cold", which is such a basic fact of life you are expected by the test creators to know it. As a result, E is the most direct, correct inference of all the choices and must be the correct answer.

I hope this helps.

Now, for the word explanation: D as a question is providing information with a scope far too wide to be a concise answer to this question. What we need to assume is whatever will logically connect "cannot be observed" and "cannot be true". The most concise language to this end would be "whatever cannot be observed cannot be true". E is essentially saying exactly this, but in another form (contrapositive). What D is saying, on the other hand, is "everything that cannot be proven true must not be able to be observed". This statement is effectively unrelated to the question at hand, and is also in the wrong order. This is reflected in the logic above.

Both D and E are statements that, if true, would make the statement provided follow logically. However, D "overreaches" in its meaning, so to speak. The statement only needs one piece of information to be proven true - that a proposition being true requires it to be observable.

This logic takes the form of:

Math Props Cannot Be observed → ?

? → Math Props Cannot Be True (excuse my awkward writing, since I don't normally think of this stuff directly in lawgic).

Anyway, what we're looking for is the answer choice that logically connects these statements. To do so, it should have sufficient condition of the first statement and a necessary condition of the second statement.

cannot be known true → cannot be observed (D) - When we look at D, we observe that the order of the sufficient and necessary conditions is incorrect. We could take the contrapositive, but it would still fail to connect the points given.

knowing statement to be true → can be observed (E) - When we look at E, it does not appear to be correct at first. However, when we take the contrapositive, we get cannot be observed → cannot be known to be true - a general statement almost exactly matching the logic form of the question stem. Therefore, E is the assumption that, if true, makes the statement true.