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#73602
Complete Question Explanation

Parallel Flaw. The correct answer choice is (A).

The argument is based on Formal Logic, which bears a strong resemblance to Conditional Reasoning but which differs in one important respect: where conditional reasoning is absolute and guaranteed (the sufficient condition guarantees the necessary condition), in formal logic the relationship is less than 100% certain. Most commonly, Formal Logic is indicated by the use of words like "some" and "most."

We are told in the stimulus that most of the people who disapprove of the Prime Minister share a certain trait (their disapproval is based on opposition to a tax increase). One person, we are told, does not share that trait, and the author concludes that she probably approves of the Prime Minister. The problem is that without knowing more about the group of people who DO approve, or if there are in fact any people who do, we cannot know the probability of Theresa being in that other group. (For more about the important aspects of this stimulus that must be paralleled in the correct answer, see Clay's excellent summary in this thread.) Another problem is that the argument ignores the possibility that there exists a third group, people who neither approve nor disapprove, and this is a type of False Dilemma.

Answer choice (A): This is the correct answer choice. Like in the stimulus, we have a group of people most of whom share a certain trait, a person who does not share that trait, and a conclusion that the person is probably in an opposite group. The Formal Logic flaw is there, because we know nothing about the size or characteristics, or even the existence, of that opposite group, and the False Dilemma is also present because the author failed to consider a possible third group who are neutral on the subject.

Answer choice (B): A bit of a shell game happens in this answer choice. Instead of a premise that the person does not share the popular trait and a conclusion that she is in a different group, we have a premise that she is in a different group and a conclusion that she does not share that trait. There is also no false dilemma present.

Answer choice (C): The same shell game found in answer B is present in this answer, with the person in question being in a different group and the author then concluding that they do not share the popular trait. This is backwards compared to what happened in the stimulus.

Answer choice (D): This answer actually looks valid, and thus cannot be parallel to the flawed argument in the stimulus. Here, we have someone who IS in the group being discussed, and a conclusion that she probably shares the trait that most members of the group share.

Answer choice (E): Here we have someone who IS a member of the group in question, which already makes it a bad answer, since we want a conclusion that they are probably in an opposing group. The conclusion is flawed, in that it changes terms from the belief being based on a news report to a claim about having actually seen the report (instead, of, say, hearing about the report second-hand).
 carnegie49
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#25326
Hi,

I was wondering if staff would recommend conditional diagramming for this question, and, if so, how to diagram.

I was able to solve it by reading the question and remembering the flow of the argument but this can be difficult to keep in one's head, particularly under testing conditions. I realize what is best for some test takers will not be best for all but generally speaking, how should one approach this question?

Thanks!!!
 David Boyle
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#25413
carnegie49 wrote:Hi,

I was wondering if staff would recommend conditional diagramming for this question, and, if so, how to diagram.

I was able to solve it by reading the question and remembering the flow of the argument but this can be difficult to keep in one's head, particularly under testing conditions. I realize what is best for some test takers will not be best for all but generally speaking, how should one approach this question?

Thanks!!!

Hello,

This is something of a Mistaken Negation, though there may be some causal reasoning. (Sometimes causal and conditional may overlap, or seem to.)
One could diagram the stimulus as, or something close to,

Disapprove of income-tax raise :most: disapprove of prime minister overall
slash disapprove of income-tax raise (subscript Theresa) :arrow: approve of prime minister overall (subscript Theresa)

Or you could think of it a a numbers/percentages issue: just because most who don't approve of the prime minister do so because of the tax raise, there still could be some folks--even Theresa--who disapprove of the prime minister for reasons besides the tax raise.

David
 mpoulson
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#25998
Hello,

I narrowed down my answer choices to A and B. However, I couldn't chose between the two and simply guessed B wrong. Can you explain why the answer is A and not B? Thank you.

V/r,

Micah
 Clay Cooper
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#26007
Hi Micah,

Sure. Thanks for your question.

Answer choice A is correct because it parallels the stimulus in doing the following:

Mentioning a group with a trait (disapprove of job performance/support logging)
Saying most members of that group share another trait (dislike income tax/believe will reduce risk of a fire)
Mentioning a member of the group who does not share the second trait (Theresa/Andy)
Mistakenly concluding that this person is therefore not a member of the original group (Theresa probably approves of PM's performance/Andy probably opposes logging)

While answer choice B diverges from these two by doing the following:

Mentioning a group with a trait (expect population to increase)
Saying most members of that group share another trait (think new school is good idea)
Mentioning a person who is not a member of the original group (Bonita)
Mistakenly concluding that this person does not share the second shared trait.

So both A and B contain logically invalid arguments; however, A perfectly parallels the argument in the stimulus, while B does not.

Does that help?
 harvoolio
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#45793
I got this wrong (really running out of time). If I were to try to apply PowerScore's technique for parallel reasoning (in the Logical Reasoning Bible) would this be correct?

Conclusion in the stimulus: "So, Theresa probably approves of the prime minister's overall job performance." Check five answer choices for equivalent (a) qualifier of "probably" and (b) no negation. Eliminate (B) for negation.

(A) "Andy probably opposes allowing limited logging there."
(B) "She probably does not favor building a new school."
(C) "He probably believes that his own financial situation has worsened."
(D) "She probably supports building the Valley Freeway."
(E) "He probably saw the weather report on the Channel 9 news.

Premise 1: "Of the citizens who disapprove of the prime minister's overall job performance most (citizens) disapprove of the prime minister's support for increasing the income tax." Check four remaining answer choices for equivalent (a) quantity of "most" and (b) part of a whole (i.e. "support for increasing the income tax" is a part of "overall job performance".) Eliminated (D) because the premise is two parts and not part of a whole.

(A) "Of the people who support allowing limited logging in the Grizzly National Forest, most support it because they think it will reducer the risk of fire in the forest."
(C) "Of the people who believe that the overall economy has improved, most believe it because they believe that their own financial situation has improved."
(D) "Of the people who oppose funding a study to determine the feasibility of building a light rail line in the Loffoch Valley, most also believe that the Valley Freeway should be built."
(E) "Of the people who believe that there will be a blizzard tomorrow, most believe it because of the weather report on the Channel 9 news."

Premise 2: "However, Theresa believes that the income tax should be increased." Check three remaining answer choices for equivalent negation of the part (and not the whole). Eliminate (C) and (E) for negating the whole (instead of the part). Choose (A).

(A) "Andy thinks that the risk of limited logging will not reduce the risk of fire in the forest,"
(C) "Chung believes that the economy has worsened."
(E) "Eduardo believes that there will be a blizzard tomorrow,"

Thanks in advance.
Last edited by harvoolio on Mon Jun 04, 2018 10:23 pm, edited 1 time in total.
 Daniel Stern
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#46209
I think your application of PowerScore principles to this parallel reasoning question is perfect!

Keep it up!

Best,
Dan
 ashnicng
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#68289
David Boyle wrote: This is something of a Mistaken Negation, though there may be some causal reasoning. (Sometimes causal and conditional may overlap, or seem to.)
One could diagram the stimulus as, or something close to,

Disapprove of income-tax raise :most: disapprove of prime minister overall
slash disapprove of income-tax raise (subscript Theresa) :arrow: approve of prime minister overall (subscript Theresa)
Hello! I was wondering how we determine that "Disapprove of income-tax raise" goes on the left side of the arrow!
Thanks!
 Jeremy Press
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#70946
Hi ash,

Not to touch off too big a dispute here, but the most diagram should actually be:
Disapprove of P.M.'s overall performance :most: Disapprove because of P.M. support for higher income tax

What precedes the "most" arrow in "most" statements, is (1) in a grammatical sense, the term that is directly "modified" by the most; and (2) in a logical sense, the broader category from which the smaller 51%+ subset is being drawn. Consider a simple example: Most dogs are friendly. In a grammatical sense, the "most" directly modifies the term dogs (so the term "dogs" would precede the arrow). In a logical sense, "dogs" are the broader category from which the 51%+ subset of "friendly (dogs)" are being drawn (so, again, "dogs" would precede the arrow).

In the first sentence of the stimulus we could rephrase to state: "Most of the citizens who disapprove of the prime minister's overall job performance disapprove because of the prime minister's support for increasing the income tax." Notice the "most" is the direct grammatical modifier of "citizens who disapprove of the prime minister's overall job performance," so that should be the term that precedes the "most" arrow. In a logical sense, that is also the broader group (the group of overall disapprovers) from which the smaller 51%+ subset (the group whose disapproval is rooted in their objection to the higher income tax) is being drawn.

The mistake in the stimulus is trying to create a "contrapositive" type of relationship from a most statement, which is not logically valid. Consider this simple example as a parallel to the stimulus: "Most dogs are friendly. Rufus is not friendly. Thus, Rufus is not a dog." That would be a mistake of logic because it's not necessarily true that all dogs are friendly, thus Rufus (as an unfriendly dog) might just be the exception to the dominant trend.

I hope this helps!

Jeremy

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