Sufficient & Necessary Questions - - Question 16

It is clear that none of the volleyball players at yesterday's office beach party came to work today since everyone w...

Dalaal February 25, 2020

question 16's answer choices

1- Why is E flawed, why couldn't we consider the variable "not the same job for the past five years" to be the same as "frequently changes jobs"? 2- when encountering a parallel reasoning question, do we merely look for the structure, or do we also take into consideration the use of contrapositive instead of the positive in determining the parallel answer choice? 3- I am facing difficulty in diagramming sentences that include more than one conditional statement, for example, in answer choice A, the sentence "since everyone employed by TRF who was given the opportunity to purchase dental insurance did so" was diagrammed as TRF & O -> PDI whereas I diagrammed it as TRF -> PDI. Moreover, in answer choice B, the sentence "none of the office managers attended the banquet this year, since they were all denied promotion" was diagrammed as 1) OM -> not AB since OM -> not P whereas I diagrammed it as not P -> not AB. I have noticed this difficulty which I am encountering in many questions. Any advice would be appreciated.

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SamA February 26, 2020

Hello @Dalaal,

My diagram of the stimulus:
Premise: PV - - - - - -> BSB (not BSB - - - > not PV)
Premise: W - - - - - - > not BSB
Conclusion: W - - - - -> not BSB - - - - > not PV

This conclusion is valid.

The correct answer is D:

Premise: 2F - - - -> WFP
Premise: WFP - - - -> no JV
Conclusion: 2F - - - - > WFP - - - > no JV

To your first question:
We can consider those terms to be the same, so that is not the problem with E. The problem with E is "likely to be hired." We do not know about future likelihood. We could only conclude: "No one who frequently changes job is currently employed by MXM."

To your second question:
Remember that a contrapositive carries the exact same logic as its counterpart. We rearrange them only to make certain relationships easier to understand. I see where your question comes from. For the stimulus I used a contrapositive, but for answer choice D I didn't. This did not prevent me from choosing the right answer, because I am only looking at the structure.

The necessary condition of one premise is the sufficient condition for the other premise. That is the structure that allows us to make a chain and draw the conclusions.
P1: A - -> B
P2: B - -> C
P3: A - -> B - -> C

Because the contrapositive carries the exact same logic, it doesn't matter if one of the premises was written differently. P1 could be (not B - -> not A) and the logic is the same.

To your third question:
That was the tricky part of answer choice A. You just have to pay attention to the specific wording. This would have been correct if it was about all employees of TRF. However, it said "employees who were given the opportunity." This might not be all employees, so the conclusion is not valid. This is only one conditional statement, but you didn't notice one of the sufficient conditions.

SamA February 26, 2020

As for answer choice B, I think you were partially correct. This is how I would have diagrammed it:

Premise: P - - -> AB
Premise: OM - - -> not P
Conclusion: Om - - > not AB

This is flawed because a promotion is sufficient for attending the banquet. This does not mean that an un-promoted person cannot attend the banquet.
P - - > AB is not the same as AB - - >P