#13 - If the natural history museum stays within this year’s budget, it will

[Administrator]

Complete Question Explanation

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

Answer choice (A):

Answer choice (B):

Answer choice (C):

Answer choice (D): This is the correct answer choice.

Answer choice (E):

This explanation is still in progress. Please post any questions below!

[zoezoe6021]

I don't understand why D is correct.

D= renovate this year→/ stay with this year B

Stimulus:
stay with this year B→/ stay within next year B
/renovate this year→renovate next year→/ stay within next year B

If D is correct, then it seems like
A→B
A→C
========
B→C

[Jeff Wren]

Hi Zoe,

The first step to solving this Justify question is correctly identifying the conclusion and the premises of the argument. The conclusion is the first half of the first sentence.

You diagrammed this as:

stay with this year B→/ stay within next year B

One way to identify that this is the conclusion is the word "for" after the comma is a premise indicator, so the clause before the comma is the conclusion.

The other two conditional premises are:

P: /renovate this year→renovate next year
P: renovate next year→/ stay within next year B

You correctly realized that these premises can be linked into a conditional chain.

Our conclusion again is:

C: stay with this year B→/ stay within next year B

Now what we want in our answer is a conditional statement that gets us from the sufficient condition of our conclusion (stay with this year B) all the way to our necessary condition (/ stay within next year B) most likely by linking to our conditional chain in our premises.

A good prephrase for our correct answer would be:

stay with this year B →/renovate this year

Then we'd be able to link everything together:

stay with this year B →/renovate this year →renovate next year→/ stay within next year B

which would allow us to 100% prove our conclusion.

Now the tricky part is that any conditional answer can always be in the form of the contrapositive, which is what Answer D gives us.

renovate this year →/ stay with this year B (i.e. exceeding this year's budget)

is the contrapositive of what we were looking for to link everything together.

If you want to think of this argument using letters, the premises would be:

P: B → C
P: C → D

And our conclusion would be:

C: A → D

So what we need in our correct answer to link everything together is:

A → B

[oliviab97]

I'm still having trouble with this one - can you please explain why E is wrong?

[Jeff Wren]

Hi olivia,

The short answer is that Answer E is a Mistaken Reversal of what we are looking for.

Using letters to (hopefully) simplify the form of the argument,

We have two premises.

P: B → C
P: C → D

And our conclusion would be:

C: A → D

So what we need in our correct answer to link everything together is:

A → B

In this argument "A" would be "stay within this year's budget" and "B" would be "not renovate this year."

In other words, we're looking for an answer that states,

"If the museum stays within this year's budget, then they will not renovate this year."

This would allow us to link all of the terms together (A to B to C to D) and justify the argument.

Answer E is backwards, stating "if the museum doesn't renovate, then they will stay within this year's budget."

This would be the equivalent to "B -> A" when we need "A -> B."

Answer D however, is the contrapositive of what we are looking for, which is logically equivalent to our prephrase and does justify the argument.

[lsatlies]

With E, you can link the argument together just fine.
P: museum renovates next year => museum won't make next year's budget
P from E: museum stays within budget this year => it will not renovate this year
P: museum does not renovate this year => museum must renovate next year

C: museum stays within budget this year => museum won't make next year's budget

The premise connects museum stays within budget => won't renovate this year => must renovate next year => will miss next year's budget.

[Jeff Wren]

Hi lsatlies,

Unfortunately, Answer E doesn't say what you think it says.

You have it backwards.

The correct diagram is Not

museum stays within budget this year => it will not renovate this year

as you've diagrammed.

Instead, the correct diagram is

it will not renovate this year => museum stays within budget this year

Notice the word "if" in the middle of the sentence, which is a sufficient indicator, is modifying "not renovate." In other words, the sentence is saying "if it does not renovate this year, then the museum will stay within this year’s budget."

[kristinajohnson@berkeley.edu]

If the natural history museum stays within this year’s budget, it will be unable to stay within next year’s budget,

for renovating next year will make the museum’s expenditures exceed next year’s very tight budget.

After all, the museum will have to renovate next year if it does not do so this year, because work from previous renovations is deteriorating rapidly.


Conclusion: IF stays within this year’s budget THEN NOT stay within next year’s budget (stay within next year’s budget then NOT stays within this year’s budget ) TYB then NOT NYB

IF renovating next year THEN NOT stay within next year’s budget (stay within next year’s budget then NOT renovating next year) RNY then NOT NYB

IF NOT renovate this year THEN renovate next year (NOT renovate next year then renovate this year) NOT RTY then RNY

Combined: IF NOT renovate this year THEN renovating next year THEN NOT stay within next year’s budget (stay within next year’s budget then NOT renovating next year then renovate this year) NOT RTY then RNY then NOT NYB


Conclusion: TYB then NOT NYB (A then NOT B) (B then NOT A)
RNY then NOT NYB (D then NOT B) (B then NOT D)
NOT RTY then RNY (NOT C then D) (NOT D then C)
Combined: NOT RTY then RNY then NOT NYB (NOT C then D then NOT B) (B then NOT D then C)
Key: TYB=A, NYB=B, RTY=C, RNY=D


D: The museum will exceed this year’s budget if it renovates this year. (if renovates this year then NOT stays within this year’s budget) (stays within this year’s budget then NOT renovates this year) (RTY then NOT TYB) (C then NOT A) (TYB then NOT RTY) (A then NOT C)

If the conclusion is if A then NOT B, and we have premises that, when combined, say if NOT C then D then NOT B, and we need to get from A to NOT B then the missing link is if A then NOT C. That is what answer choice D says.

This is cool when I'm checking my work, in this case after I missed this problem, and I couldn't understand it another way, but I don't have an hour to break this down during a test. Any suggestions on how to identify the correct answer using a more practical approach to a difficult conditional justify problem?

Thank you.