Students at Lincoln High School will boycott graduation ceremonies unl

Here is the comprehensive explanation

Remember, “A unless B” is the equivalent of ~B—>A. The first sentence in the passage can be depicted as ~BD—>BG where B D stands for “the administration allows the band director to keep his teaching position” and BG stands for “Students at Lincoln High School will boycott graduation ceremonies.” The second sentence contains an implied if-then statement. It can be stated as follows: “If the administration allows the band director to keep his teaching position, then it will have to eliminate one of the new coaching positions.” This can be depicted as BD—>EC Of course, EC stands for “it will have to eliminate one of the new coaching positions.” As presented, the two diagrammed statements cannot be connected. However, let’s suppose the high school students do not boycott graduation ceremonies, which is selection (C). If we apply the contrapositive to the first diagram, ~BD—>BG, the statement becomes ~BG—>BD Then we can use the transitive property to combine ~BG—>BD with BD—>EC to yield the following diagram: ~BG—>EC That is, if the students don’t boycott graduation ceremonies, then a new coaching position will be eliminated. Thus, the correct assumption is that the students will not boycott graduation ceremonies. The answer is selection (C).

The problem with D is that it is a necessary assumption, but we are looking for a sufficient assumption--something that makes the argument valid. (This is a question type that is much more likely to show up on the LSAT than the GMAT.) While the argument fails without D, adding that information doesn't make the argument correct. It just patches one hole.
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rish2708 We do have to accept the premises as true, but notice that these premise are conditional. They don't tell us whether these things will actually happen. I could say "If you crash my car, you will owe me a lot of money," even though it's pretty unlikely that you will ever crash my car. In this case, we know that IF the band director is not allowed to stay, THEN the students will boycott. If the students do not boycott, that must mean the band director IS allowed to stay. (This is what we call a contrapositive, as diagrammed in the OE.) That sets off a logic chain leading to the conclusion: No boycott --> band director stays --> new coaching position cut

I see your point about the additional assumption. Technically, the chain we really have is as follows, with the (-->) representing the link we don't actually have: No boycott --> band director ALLOWED to stay (-->) band director continues to teach --> new coaching position cut. So yes, ideally the answer would cover that additional assumption. Either the question writer didn't think of this, or they consider it implied that if you are allowed to keep a job, you do actually stay in that job. However, given what we have to work with, C is the clear winner.
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Responding to a pm:

Premises:
Unless band director is retained, students will boycott ceremonies. (This means "retaining band director" is necessary for no boycott. Mind you, it may still not be enough. Students may still boycott if they, say, don't like the guest speaker)
If band director is retained, then one new coaching position will be eliminated. 

Conclusion: New coaching position will be eliminated. 

We need that option which leads to the conclusion. You can properly draw the conclusion once you put in that option with your premises. 


(A) Students will drop out of the band program.

Irrelevant. No info about students dropping out of band program. The discussion is about students boycotting ceremonies.

(B) The administration will insist that the high school band director retire.

If band director retires, students will boycott ceremonies. The new coaching position is likely to be retained (it may be eliminated for another reason, hence the use of "likely to be"). So our conclusion does not follow from this statement. 

(C) The students will not boycott graduation ceremonies.

Retaining band director was necessary for no boycott. If students will not boycott, it means the band director was retained. If the band director was retained then the new position is eliminated. Hence our conclusion follows. 

Note that negating this statement has no impact on our conclusion. It is a sufficient assumption but not necessary. 
Negated: The students will boycott graduation ceremonies.
Does it tell us anything about whether the band director was retained or not? No. As we discussed, the boycott could happen because of any other reason too. Band director may or may not have been retained in this case. So we don't know whether the new coaching position was eliminated. So our conclusion does not break. 

(D) The administration has the authority to allow the band director to keep his teaching position.

We don't know what happens if the admin does not have the authority to allow the band director to keep his position. If the band director retires, students boycott. But what happens to the new coaching position? Is it retained or eliminated, we don't know. Hence it does not lead to our conclusion. 

(E) The high school students will not drop their threat to boycott graduation ceremonies if other student benefits are offered.

We already know that retaining the band director ­is necessary to avoid boycott. This option doesn't lead us to the conclusion. 

Answer (C)­

Here are some discussions on sufficient and necessary conditions: 

https://youtu.be/MmlwcTlHZz8

https://youtu.be/BW8Ijrhjjq8

https://youtu.be/yQYkL1DSslA­
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Having the authority ot retain does not mean that the admin will retain him. In fact, the argument implies that the admin is forcing him to retire at the end of the year. 

...the administration allows the band director to keep his teaching position rather than forcing him to retire at the end of the school year.

Nothing in option (D) indicates that the admin will change its mind. They have the authority but that doesn't mean they will change their mind.

In option (C), we are given that the students will not boycott which means that the admin has changed its mind. Otherwise the students would have boycotted. If the admin will retain him, it means that the new position will be eliminated and that is how we reach the conclusion. 
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Hi Please explain why C is the correct answer

hi,
sajid your explanation above seems quite acceptable , but can you clarify what i am thinking about it
if the administrator allows band director then high schools students will not boycott ceremonies , which means students want band director to keep teaching .
that's why if new position will be eliminated then it must be true that the band director is still teaching so this can be true when we assume that students are not boycotting .

but i have a doubt too , say students want the band director and the administration does not , then how it can be true that without boycotting administration allows band director to keep teaching , i am so confused , please help

Hi

You should focus on the last line of the conclusion of the question stimulus that is

So, the new coaching position will be eliminated.

Now focus on the right option that is

The students will not boycott graduation ceremonies.

there is a swap of the order which confusing you

1st the administration will have to eliminate one of the new coaching positions it planned for next year then after this The students will not boycott graduation ceremonies and then the new coaching position will be eliminated.

Stimulus:
Students at Lincoln High School will boycott graduation ceremonies unless the administration allows the band director to keep his teaching position rather than forcing him to retire at the end of the school year. If the band director continues to teach at the high school, however, then the administration will have to eliminate one of the new coaching positions it planned for next year. So, the new coaching position will be eliminated.

Question Stem:
The conclusion stated in the passage above is properly drawn if which one of the following assumptions is made?

Premise 1: Students will boycott ceremonies unless the administration allows the band director to keep his teaching position rather than forcing him to retire at the end of the school year.

Premise 2: If the band director continues to teach at the high school, however, then the administration will have to eliminate one of the new coaching positions it planned for next year.

Conclusion: So, the new coaching position will be eliminated.

My take on this is: So the band director isn't leaving? Great! why? cuz the admin is allowing him to keep his teaching position. Wait.
that means the students won't boycott the graduation ceremonies.

Answer: (C) The students will not boycott graduation ceremonies.

Okay, what about if the director quits himself.
The logical flaw fails here then right?
This assumption needs to be made because it connects all the premises and conclusion together.

Anyways the students will boycott is a premise and we have studied that premises can't be wrong?

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I have doubt in understanding why D is not the answer? If Admininstration has the authority then Band Director can be retained and if this happens the new coaching position will be eliminated.

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