#25 - Roberta is irritable only when she is tired

[Administrator]

Complete Question Explanation

Flaw in the Reasoning—SN. The correct answer choice is (E)

As with the last stimulus, this stimulus contains conditional reasoning. We are given a rule, that if Roberta is irritable, then she is tired:

• Sufficient Necessary
  irritableroberta tiredroberta

Next, we are given factual information, that Roberta has been yawning and just lost her keys. Based on this information, the argument concludes that Roberta must be irritable. This conclusion is flawed for two reasons. First it assumes that since Roberta has been yawning and just lost her keys, then she must be tired. Second, even if the facts were to establish that Roberta is tired, the conclusion results from a Mistaken Reversal, treating (supposed) evidence that the necessary condition was met as proof that the sufficient condition is satisfied as well.

This is a Flaw in the Reasoning question. Our is prephrase is that the argument contains the two flaws described above. The correct answer choice could test either or both of those flaws.

Answer choice (A): This answer choice describes a causal reasoning flaw. However, the argument was not causal, so this answer choice is incorrect.

Answer choice (B): Here, the answer choice refers to circular reasoning. However, the premise and the conclusion were not logically identical, so the argument was not circular.

Answer choice (C): In this case, the answer choice describes an over-generalization from a potentially atypical example. However, the conclusion was not general. Instead, it was very narrow, confined to the issue of whether Roberta is tired on this particular occasion.

Answer choice (D): This answer choice is very tricky, and is designed to catch those who are simply looking for conditional reasoning keywords rather than considering the entire context of the answer choice. However, this choice is incorrect because it has to do with Roberta losing things, which is irrelevant to the conclusion.

Answer choice (E): This is the correct answer choice because it describes the argument’s use of a Mistaken Reversal to reach the conclusion.

[ltoulme]

Hi!

I'd like to make sure I diagrammed this question correctly!

I diagrammed the stimulus as:

Tired Loses Things
Tired Irritable

So, since the stimulus then takes this to mean that since she's tired and has lost her keys, she must be irritable, they are incorrectly combining the diagrams to be:

Loses Things Tired Irritable

This is a mistaken reversal of the original tired and loses things chain, so the author took the necessary condition (loses things) to be a sufficient condition of being irritable.

Is this correct??

Thanks so much for your help!
Laura

[Jonathan Evans]

Laura,

Good work, but you've actually got your own Mistaken Reversal going on here! From the stimulus we know she's irritable only if she's tired. She loses things only if she's tired.

Irritable OR Loses Things Tired

The conclusion is a Mistaken Reversal. Diagrammed it looks like this:

Tired & Losing Things Irritable

To prephrase, we would say that the author is mistakenly treating the Necessary Condition "Tired" as Sufficient to know she's "Irritable."

[ltoulme]

So the "only" is really modifying "tired" rather than "losing things" or "irritable." I made the mistake of thinking "when" was modifying "tired" so the "only" went with the other conditions. But, really, "only when" is really like "only if"?

Thanks very much for your help!

[Dave Killoran]

So the "only" is really modifying "tired" rather than "losing things" or "irritable." I made the mistake of thinking "when" was modifying "tired" so the "only" went with the other conditions. But, really, "only when" is really like "only if"?

Thanks very much for your help!

Hi Laura,

Yes, you are exactly right: as far as diagramming conditional statements, "only if" operates in identical fashion to "only when," and both introduce necessary conditions.

Good job!

[Marc94]

Hello,

I was able to see the mistaken reversal, but the wording of the right answer confused me.

I had diagrammed:

I -> T
L -> t

Y(T) and L -> I

So isn't being (I)rritable sufficient (a guarantee) that Roberta is tired?
And based on this I figured answer E should have said the opposite. "Takes a sufficient condition for Roberta's being irritable to be a necessary condition."

Unfortunately, the terms necessary and sufficient often lead to slight confusion for me.

[Adam Tyson]

Your diagram looks great, Marc94, but then your interpretation of it breaks down a bit. Being irritable IS a sufficient condition for being tired, but in the conclusion they have it as a necessary condition! Answer E is referring to being tired, which is a necessary condition whenever she is irritable, and treats it as a sufficient condition, proving that she is irritable.

Answer E could have been reworded to say "takes a sufficient condition for being tired to be a necessary condition for being tired" , and the condition referred to in such an answer would be "irritable."

Try plugging in the conditions in the stimulus to that answer and you'll see how it relates to your diagrams. E would then read "takes being tired as necessary when she is irritable for being sufficient to show she is irritable." That's your diagrams!

[T.B.Justin]

I understand that irritable is sufficient and tired is necessary, and that the author is concluding that irritable is a necessary condition, however the wording of the correct answer choice I do not understand.

"Takes a necessary condition for Roberta's being irritable to be a sufficient condition."

I think this says the author has mistakenly concluded that Roberta's being irritable is necessary when it is in fact sufficient.

[Charlie Melman]

Hi Justin,

You have it exactly right. The way to understand answer choices worded in this way (and they appear frequently) is to think of it as saying: "The author could only have reached the conclusion she did if she mistakenly..."

And here, the only way for her to reach her mistaken conclusion was to do precisely what you described.

[Henry Z]

This conclusion is flawed for two reasons. First it assumes that since Roberta has been yawning and just lost her keys, then she must be tired.

Why is this a flaw? The stimulus says Roberta "loses things only when she is tired." I think it's a legit inference that if she lost her keys, she must be tired.