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#32587
Complete Question Explanation
Justify the Conclusion—SN. The correct answer choice is (A)
This is a difficult question involving a sophisticated conditional reasoning inference. Many people found this question to be difficult, and it provides a good example of how diagramming complicated conditional relationships can help you identify inferences.
The stimulus begins with a conditional rule that includes a compound sufficient condition. The order of presentation of this rule, with the necessary condition coming first in the sentence, makes the rule that much more difficult to understand quickly. Reordered, the rule states that if students are taught with methods appropriate to their learning style, then if they also devote significant effort to their studies, they will achieve broad mastery of the curriculum.
TMA = students taught methods appropriate to their learning styles
DSE = students devote significant effort to their studies
ABM = students achieve broad mastery of the curriculum
Sufficient Necessary
TMA
+ 
ABM
DSE
Next, the stimulus concludes that if the students in a particular school do not achieve broad mastery of the curriculum (ABM), then it must be the case that those students are not taught with methods appropriate to their learning styles (TMA):
ABM TMA
This conclusion partially describes the contrapositive of the conditional premise presented above. However, the actual contrapositive of that relationship is:
TMA
ABM or
DSE
Written out, the contrapositive provides that if the students do not achieve broad mastery in the curriculum (ABM), then: 1) the students are not taught with methods appropriate to their learning styles (TMA); or, 2) the students do not devote significant efforts to their studies; or, 3) the students are neither taught with methods appropriate to their learning styles nor do they devote significant efforts to their studies (TMA and DSE).
By comparing the argument’s conclusion with the contrapositive, we can see that the author explicitly identifies one of the three necessary condition options, i.e., TMA, without providing any evidence to support this choice. What makes this question particularly tricky, however, is that the author’s explicit statement that the students are not being taught with methods appropriate to their learning styles (TMA), does not rule out the possibility that they also fail to devote significant effort to their studies (DSE). Because the options are not mutually exclusive, explicitly identifying one option does not inherently preclude the other option from being the case.
The question stem tells us that this is a Justify the Conclusion question, meaning the correct answer choice will contain information proving the conclusion is valid. To have such a strong effect in this conditional argument, the correct answer will provide a conditional relationship requiring that, no matter what, if the students do not achieve a broad mastery of the curriculum, then they are not being taught with methods appropriate to their learning style. In other words, regardless of which necessary condition option is selected, the term TMA must ultimately be in the diagram as a necessary condition. Here is how we can diagram that conditional relationship, with this expanded representation of the contrapositive in bold:
TMA
ABM or
DSE TMA
So, the prephrase for this Justify the Conclusion question is that if a student does not devote significant effort to their studies, then it must be the case that they are not being taught with methods appropriate to their learning styles.
Answer choice (A): This is the correct answer choice, because it contains the contrapositive of our prephrased relationship. Again, the prephrased relationship would be diagrammed as:
DSE TMA
The contrapositive to this relationship is:
TMA DSE
In other words, if the students are taught with methods appropriate to their learning styles, then they will devote significant effort to their studies—a restatement of the relationship described in this answer choice.
Answer choice (B): Do not be confused by the beginning of this answer choice. The “even if” language essentially tells you to set aside for the moment any evidence that secondary school students are taught with methods appropriate to their learning styles, i.e., disregard evidence that TMA. Instead, the choice says, focus on this relationship—if students do not devote significant effort to their studies, then they will not achieve broad mastery of the curriculum. We can diagram this as:
DSE ABM
This relationship does not fit the relationship identified in our prephrase, and it is one part of a Mistaken Negation of the relationship provided in the premise.
Answer choice (C): As with answer choice (B), this choice also presents a partial Mistaken Negation of the conditional rule provided by the premise in the stimulus. Here, the sufficient condition is the students not being taught with methods appropriate to their learning styles (TMA), which can be diagrammed as:
TMA ABM
Answer choice (D): This answer choice is incorrect, in part because it deals causal reasoning, which was not used in the stimulus. The language “does not always result in” is saying that teaching secondary school students with methods appropriate to their learning skills (TMA), one of the sufficient conditions from the original rule, does not always cause students to achieve a broad mastery of the curriculum. This choice is attractive to those who fail to recognize the difference between causal and conditional reasoning.
Also, this choice is attractive to those who misunderstood the task. Assuming the language in this answer choice were not causal, it would come close to being a valid Must Be True inference. It would be accurate to say that if only one of the sufficient conditions were met, then the necessary condition may not be met. In the context of this answer choice, it would be a valid Must Be true inference if it were to say that “teaching secondary school students with methods appropriate to their learning styles may not always indicate a broad mastery of the curriculum by those students.”
Answer choice (E): As with answer choice (D), this information invokes one of the two sufficient conditions and could be attractive to someone who misinterpreted this as a Must Be True question.
Justify the Conclusion—SN. The correct answer choice is (A)
This is a difficult question involving a sophisticated conditional reasoning inference. Many people found this question to be difficult, and it provides a good example of how diagramming complicated conditional relationships can help you identify inferences.
The stimulus begins with a conditional rule that includes a compound sufficient condition. The order of presentation of this rule, with the necessary condition coming first in the sentence, makes the rule that much more difficult to understand quickly. Reordered, the rule states that if students are taught with methods appropriate to their learning style, then if they also devote significant effort to their studies, they will achieve broad mastery of the curriculum.
TMA = students taught methods appropriate to their learning styles
DSE = students devote significant effort to their studies
ABM = students achieve broad mastery of the curriculum
Sufficient Necessary TMA + ABM DSENext, the stimulus concludes that if the students in a particular school do not achieve broad mastery of the curriculum (ABM), then it must be the case that those students are not taught with methods appropriate to their learning styles (TMA):
ABM TMAThis conclusion partially describes the contrapositive of the conditional premise presented above. However, the actual contrapositive of that relationship is:
TMA ABM or DSEWritten out, the contrapositive provides that if the students do not achieve broad mastery in the curriculum (ABM), then: 1) the students are not taught with methods appropriate to their learning styles (TMA); or, 2) the students do not devote significant efforts to their studies; or, 3) the students are neither taught with methods appropriate to their learning styles nor do they devote significant efforts to their studies (TMA and DSE).
By comparing the argument’s conclusion with the contrapositive, we can see that the author explicitly identifies one of the three necessary condition options, i.e., TMA, without providing any evidence to support this choice. What makes this question particularly tricky, however, is that the author’s explicit statement that the students are not being taught with methods appropriate to their learning styles (TMA), does not rule out the possibility that they also fail to devote significant effort to their studies (DSE). Because the options are not mutually exclusive, explicitly identifying one option does not inherently preclude the other option from being the case.
The question stem tells us that this is a Justify the Conclusion question, meaning the correct answer choice will contain information proving the conclusion is valid. To have such a strong effect in this conditional argument, the correct answer will provide a conditional relationship requiring that, no matter what, if the students do not achieve a broad mastery of the curriculum, then they are not being taught with methods appropriate to their learning style. In other words, regardless of which necessary condition option is selected, the term TMA must ultimately be in the diagram as a necessary condition. Here is how we can diagram that conditional relationship, with this expanded representation of the contrapositive in bold:
TMA ABM or DSE TMASo, the prephrase for this Justify the Conclusion question is that if a student does not devote significant effort to their studies, then it must be the case that they are not being taught with methods appropriate to their learning styles.
Answer choice (A): This is the correct answer choice, because it contains the contrapositive of our prephrased relationship. Again, the prephrased relationship would be diagrammed as:
DSE TMAThe contrapositive to this relationship is:
TMA DSEIn other words, if the students are taught with methods appropriate to their learning styles, then they will devote significant effort to their studies—a restatement of the relationship described in this answer choice.
Answer choice (B): Do not be confused by the beginning of this answer choice. The “even if” language essentially tells you to set aside for the moment any evidence that secondary school students are taught with methods appropriate to their learning styles, i.e., disregard evidence that TMA. Instead, the choice says, focus on this relationship—if students do not devote significant effort to their studies, then they will not achieve broad mastery of the curriculum. We can diagram this as:
DSE ABMThis relationship does not fit the relationship identified in our prephrase, and it is one part of a Mistaken Negation of the relationship provided in the premise.
Answer choice (C): As with answer choice (B), this choice also presents a partial Mistaken Negation of the conditional rule provided by the premise in the stimulus. Here, the sufficient condition is the students not being taught with methods appropriate to their learning styles (TMA), which can be diagrammed as:
TMA ABMAnswer choice (D): This answer choice is incorrect, in part because it deals causal reasoning, which was not used in the stimulus. The language “does not always result in” is saying that teaching secondary school students with methods appropriate to their learning skills (TMA), one of the sufficient conditions from the original rule, does not always cause students to achieve a broad mastery of the curriculum. This choice is attractive to those who fail to recognize the difference between causal and conditional reasoning.
Also, this choice is attractive to those who misunderstood the task. Assuming the language in this answer choice were not causal, it would come close to being a valid Must Be True inference. It would be accurate to say that if only one of the sufficient conditions were met, then the necessary condition may not be met. In the context of this answer choice, it would be a valid Must Be true inference if it were to say that “teaching secondary school students with methods appropriate to their learning styles may not always indicate a broad mastery of the curriculum by those students.”
Answer choice (E): As with answer choice (D), this information invokes one of the two sufficient conditions and could be attractive to someone who misinterpreted this as a Must Be True question.