#20 - University president: We will be forced to reduce

[Administrator]

Complete Question Explanation

Justify the Conclusion—SN. The correct answer choice is (D)

This is a rather challenging question, in part because the premises are split between the first and the third sentences of the stimulus. The conclusion resides in the second sentence (note the conclusion indicator “so”), and the entire argument is conditional in nature. After applying the Unless Equation to the last sentence, the argument can be diagrammed as follows:

• Premise (1): Increase enrollment Reduce spending
  
  Premise (2): Increase enrollment Marketing
  
  Conclusion: Maintain quality Marketing

The question stem asks us to identify a statement that, if assumed, would allow the conclusion to be properly drawn. Despite the word “assumed” in the stem, this is a Justify question because our job is not to identify a statement upon which the argument depends, but rather to prove the conclusion by adding a piece of information to the premises. The sufficient condition indicator (“if”) in the question stem is a reminder that you must select an answer that is sufficient to prove the conclusion by using the Justify Formula:

• Premises + Answer choice = Conclusion

As with most Justify questions, there is a logical gap between the premises and the conclusion. To identify this gap easily, first connect the two premises using the contrapositive of the first:

• Premise (1) + (2): Reduce spending Increase enrollment Marketing

Now compare the additive inference to the conclusion. The premises suggest that to avoid having to reduce spending next year, the university needs to market its programs more aggressively. The conclusion, however, claims that aggressive marketing is necessary for maintaining the quality of education. To justify the conclusion, we need to establish a connection between maintaining the quality of education and not having to reduce spending next year:

• Premise (1) + (2): Reduce spending Marketing
  
  Justify Formula: Maintain quality Reduce spending
  
  Conclusion: Maintain quality Marketing

In other words, we are looking for a statement suggesting that the quality of education will be maintained only if the university does not reduce spending next year. This prephrase is the contrapositive of answer choice (D), which is the correct answer choice.

The correct answer choice can also be arrived at by the process of elimination. First, given that the conclusion introduces a new, “rogue” element into the argument (“maintain quality of education”), the correct answer choice must connect that element to the rest of the argument. This eliminates answer choices (B), (C), and (E). Second, “increasing enrollment” is a term common to both of the premises but not to the conclusion of the argument. Therefore, the correct answer choice need not restate it, which eliminates answer choices (A), (B), and (C).

Answer choice (A): The contrapositive form of this answer choice suggests that the quality of education will be maintained only if the university does not increase its enrollment:

• Maintain quality Increase enrollment

This is markedly different from our prephrase, as it justifies a different conclusion. When combined with the premises, answer choice (A) only proves that maintaining the quality of education requires reducing spending next year:

• Maintain quality Increase enrollment Reduce spending

Not only is this a different conclusion from the one we need to justify, but it is also the logical opposite of our Justify Formula.

It is also worth noting that “increasing enrollment” is a term common to both of the premises but not to the conclusion of the argument. Therefore, the correct answer choice need not restate it, making answer choice (A) relatively easy to eliminate.

Answer choice (B): This answer choice can be immediately eliminated because it does not specify a requirement necessary for the quality of education to be maintained. In other words, it does not connect the rogue element in the conclusion to the rest of the argument. It is also worth noting that this is the Mistaken Negation form of the first premise.

• Answer choice (B): Increase enrollment Reduce spending
  
  Premise (1): Increase enrollment Reduce spending

Answer choice (C): Like incorrect answer choice (B), this answer choice can be eliminated because it does not connect “maintain quality of education” to the rest of the argument. Also, this is a Mistaken Reversal of the second premise.

• Answer choice (C): Marketing Increase enrollment
  
  Premise (2): Increase enrollment Marketing

Answer choice (D): This is the correct answer choice, as it is identical to our prephrase:

• Justify Formula: Maintain quality Reduce spending
  Contrapositive: Reduce spending Maintain quality

When combined with the premises, this statement forms a logical chain sufficient to prove the conclusion. Note that there are many ways to introduce this conditional relationship:

• The university cannot both reduce spending and maintain the quality of education it provides.
  
  Unless the university avoids having to reduce spending next year, the quality of education it provides will not be maintained.
  
  The university will maintain the quality of education it provides only if it avoids having to reduce spending next year.

Answer choice (E): Like incorrect answer choices (B) and (C), this answer choice can be eliminated because it does not connect “maintain quality of education” to the rest of the argument. Also, it is the Mistaken Reversal form of the two premises, when combined:

• Answer choice (E): Marketing Reduce spending
  
  Premise (1) + (2): Reduce spending Marketing

[ylikate]

can someone help to diagram this out? is the conclusion "if we are to maintain the quality of ed, we must market our prog more aggressively?"

i saw someone else has posted the same problem, but the response was not helpful for me.

thanks. Kate

[David Boyle]

can someone help to diagram this out? is the conclusion "if we are to maintain the quality of ed, we must market our prog more aggressively?"

i saw someone else has posted the same problem, but the response was not helpful for me.

thanks. Kate

Hello Kate,

Yes, I suspect that is the right conclusion.
As for diagramming: "We will be forced to reduce spending next year if we do not increase our enrollment" could be diagrammed "slash ie arrow slash s". (No increase of enrollment means less spending) "Without such marketing we will be unable to increase our enrollment" can be diagrammed "ie arrow m". "if we are to maintain the quality of ed, we must market our prog more aggressively" can be diagrammed "qe arrow m".
So, mashing that all up, and using contrapositives, we get "s arrow ie arrow m". So how do we link that to "qe arrow m"?
Answer choice D can be phrased, "slash s arrow slash qe", which in contrapositive form is "qe arrow s". That lets us make a huge chain, "qe arrow s arrow ie arrow m". So all is linked together nicely.

Hope that helps,
David

[prep88]

Hello,

Can anyone please explain how answer choice (D) justifies the conclusion in conditional terms?

Thank you!

[Jon Denning]

Hey prep,

Sure thing! Let's set up the argument as given and see if we can figure out what's needed to justify it.

Premise: NOT Increase Enrollment Reduce Spending

Premise: NOT Aggressive Marketing NOT Increase Enrollment

Conclusion: Maintain Quality Education Aggressive Marketing
Conclusion (contrapositive): NOT Aggressive Marketing NOT Maintain Quality Ed.

The two premises can be combined to form a chain:

NOT Aggressive Marketing NOT Increase Enrollment Reduce Spending

And from the contrapositive of the conclusion, we see that the author believes:

NOT Aggressive Marketing NOT Maintain Quality Education

Can you see how we could attach "NOT Maintain Quality Education" (the new term in the conclusion) to the premise chain, so that starting the chain at "NOT Aggressive Marketing" would take us to it? All we have to do is make "Reduce Spending" point to it!

And that's exactly what answer choice (D) does:

Reduce Spending NOT Maintain Quality Education

The key here, as often happens with conditional reasoning, was considering both the original statements and their contrapositives, particularly the contrapositive of the conclusion. At that point all you need to do is note the new term in the conclusion and make sure you find an answer choice that properly attaches it to the other premises.

I hope that helps!

[EL16]

Hello,

I am having a difficult time understanding how get from my diagram for this stimulus to the correct answer choice. In the original post by the Administrator above, it seems that some nots/slashes are missing in the diagram, so I think it's confusing me more. I tried to use the diagramming in Jon's post above instead, so I just want to type out what I am thinking here to see if I'm understanding this correctly, and ask a couple clarification questions:

P1: NOT Increase enrollment reduce spending
P2: NOT aggressive marketing NOT increase enrollment
C: maintain quality aggressive marketing
and the contrapositive of the Conclusion is: NOT aggressive marketing NOT maintain quality

The premises form the following conditional chain: NOT aggressive marketing NOT increase enrollment reduce spending

In order to then justify the conclusion, we want to link "reduce spending" to "maintain quality". But how do we know which way to make this chain/connect these two terms? In other words, how do we know which of these 2 conditions is the sufficient and which is the necessary?
Would it be diagrammed as:
reduce spending NOT maintain quality
or
NOT maintain quality reduce spending

Obviously answer choice D aligns with my first diagram (reduce spending NOT maintain quality), so I know that must be correct, but I'm not sure how to have known which of those 2 ways was the proper way to diagram it, and therefore could have easily taken answer choice D as a mistaken negation if I used the 2nd way of diagramming it.
Any clarification would be much appreciated!

Thanks,
Elana

[Francis O'Rourke]

Hi EL, It does look like the original administrator's post has lost some negations. However, I believe that Jon Denning's above post answers your question as ready. As Jon wrote above:

The two premises can be combined to form a chain:

NOT Aggressive Marketing NOT Increase Enrollment Reduce Spending

And from the contrapositive of the conclusion, we see that the author believes:

NOT Aggressive Marketing NOT Maintain Quality Education

Can you see how we could attach "NOT Maintain Quality Education" (the new term in the conclusion) to the premise chain, so that starting the chain at "NOT Aggressive Marketing" would take us to it? All we have to do is make "Reduce Spending" point to it!

And that's exactly what answer choice (D) does:

Reduce Spending NOT Maintain Quality Education

Your diagrams look good to me. You may not know which of those two relationships would justify the conclusion in advance, so you need to try both out. Only one of them aligns the information in a way that will prove the conclusion. Let me know if you still need help understanding how this addresses the issue at hand.

When you write "therefore could have easily taken answer choice D as a mistaken negation if I used the 2nd way of diagramming it" do you mean that you are not sure how to diagram answer choice (D)?

[EL16]

Hi Francis,

Thanks for your help. I saw Jon's post above, but I am still confused about how meshed the 2 conditional chains together. I understand that answer choice D (the correct answer) has the conditional chain of: reduce spending NOT maintain quality and that this aligns perfectly if you meshed the 2 conditional chains in the stimulus as reduce spending NOT maintain quality.

But what if you had instead meshed the 2 chains in the stimulus the other way around, as follows:
NOT maintain quality reduce spending ?
Then answer choice D (which says reduce spending NOT maintain quality) would seem to be a mistaken reversal, and therefore I would cross of answer choice D and mark it as a loser, and would miss the correct answer choice.

How can I avoid this situation? This is not the first time this has happened to me. Is there some secret to knowing which condition is the necessary versus which is the sufficient when you're meshing 2 separate chains together to fill a gap, as we did here?

[Adam Tyson]

Hey there EL16, first things first - I believe the original post here at some point was the victim of a glitch that removed all the negations. We've put those back in, so now the original thread should be an accurate representation of the argument and of each answer choice. Look that over and see if it helps answer your question.

Your question seems to be asking how to avoid mistaken reversals, as that is what you would be guilty of if you had diagrammed the combined premises as:

maintain quality reduce spending

There are a few ways to avoid that, and the main one is to pay close attention to your diagram to see how it is built. Put together a chain and ask yourself what effect that relationship would have, if added to the argument as a new premise. Would it get you where you need to be? Mistaken reversals and mistaken negations won't make the required connections to justify your conclusion, and so you should see that it it isn't working.

To avoid this, be mechanical - connect the conditions as they are given to you.

Here's another technique you can use on Justify questions that are conditional: go clockwise. Here's what I mean:

Premise: Reduce spending Marketing

Conclusion: Maintain quality Marketing

Notice that we have a conditional premise and a conditional conclusion, with two different sufficient conditions, each of which leads to the same necessary condition. To justify this conclusion, connect the two different terms with a conditional arrow that goes clockwise. That is, make Maintain Quality (the sufficient condition in the conclusion) sufficient for the not reducing spending (the sufficient condition in the premise). With the premise on top of the conclusion like this, that means you will draw an arrow going up from Maintain Quality, pointing at Reduce Spending, Like so:

Reduce spending Marketing
^
|
Maintain quality Marketing

That's it! Go clockwise! Something similar happens when you have a conditional premise and conditional conclusion, and the sufficient conditions are the same but the necessary conditions differ. There, make the necessary condition in the premise sufficient for the necessary condition in the conclusion. Again, you would connect the two different conditions with an arrow that points in a clockwise direction, down from the top right to the bottom right. Hard to draw here, but give it a try and you'll see what I mean.

I hope that, and correcting the glitch in the official explanation, helps!

[EL16]

Thanks so much for clearing that up Adam! That's a great trick--thanks!