Q22 - Economist: Real wages in this country

[LSAT-Chang]

Hello!
Could someone look over my diagram and tell me if this is the right way to do it?
I tried to do this timed, but as I am still not very comfortable with conditional logic, it took me over 5 minutes to figure out what I was supposed to "link" and how I should do that.. but here is my diagram! I would also love to hear any simpler/easier suggestions or tricks on how to "spot" these links quicker than 5 minutes.. Also, please let me know if I should add any other elements which you might think would be more helpful (I am getting myself in the habit of writing these all out and not using abbreviations as I find myself spending way more time figuring out what those stand for -- but I do shorten some of the wordings -- for example, instead of "real wages increase significantly" I would just ignore the significantly part of it -- please let me know if this is something important that I should have considered or if in the future, I should write those as well)!

Step 1 (just diagrammed the argument):

real wages increase --> productivity increases
----------------------------------------------------
investing very little in new tech --> real wages NOT increase

Step 2 (pondering for 5 minutes and thinking "hmm let me try the contrapositive and see if that leads to anything"):

real wages increase --> productivity increases
----------------------------------------------------
real wages increase --> NOT investing very little in new tech

Step 3 (finally found the missing link! -- something to do with productivity increases and NOT investing very little in new tech):

If we had..

productivity increases --> NOT investing very little in new tech

Then we would get..

real wages increase --> productivity increases
productivity increases --> NOT investing very little in new tech
----------------------------------------------------------------------
real wages increase --> NOT investing very little in new tech

NOW the argument works! So we have to assume:

productivity increases --> NOT investing very little in new tech

OR contrapositive would be:

investing very little in new tech --> productivity NOT increases

which is literally what (D) says!! I was confused at first since I am so used to having the "if, then" but (D) has "then, if" which I first thought was the reverse and almost eliminated it, until I saw the "if" in the middle of the statement and noticed that that is a sufficient indicator, so "if businesses do not make a substantial investment in new technology (which basically means investing very little in new tech) then productivity will not increase". I was also almost tripped up by the "substantial investment" since we never got any of that wording in the argument -- but thought that we could possibly equate that if we are investing very little in something, then it means that we are not investing a substantial amount in it.

So, what do you guys think? Is this the right way to go? How could I possibly NOT take over 5 minutes solving these conditional problems? It seems to take so long for this type of "link" to click on my mind. Is it just all about practice?

[timmydoeslsat]

Just practice and simply recognizing patterns will help you so quickly on these kinds of questions.

I will give you my stream of consciousness on this question:

"Oh OK, a sufficient assumption question.

Real wages will increase signif. ---> Productivity increases notably

I can't wait to diagram the next sentence!

Oh, it starts with a thus, I bet this is going to be the main conclusion of this argument, let me continue to read before I put my pencil to paper on this one.

Let's see, thus, it is unlikely that wages will increase significantly in the near future, since...

Ok, I know that the since is going to give me another premise on top of the other premise given in the first sentence. The thus part was indeed my conclusion.

Let me go ahead and put down everything in structure.


Real wages will increase signif. ---> Productivity increases notably

This country's businesses are currently investing very little in new technology and this pattern is likely to continue for at least several more years.

--------------------------

~ Real wages will increase signif.


I see that the reason I was given why real wages will not increase is simply bogus! I have no evidence as to why "the country's investing very little in tech and will do so for at least a several more years" has any impact on the idea of productivity and real wages.

Let me run through the answer choices that gives me SOMETHING about technology that can link me to a lack of it being really bad productivity. Because I know that denying the necessary condition for the sufficient condition of "real wages will increase signif" would allow me to get a necessary condition of "~real wages will increase signif."

Choice D states:

Productivity will not increase if businesses do not make a substantial investment in new technology.

~Substantial invest. in new tech. ---> ~Productivity increase


Plugging this into my argument, I can then use the contrapositive of the first statement to allow me to get to a conclusion of ~real wages will increase signif."

Let me know if you would like to talk about this more. Or about sufficient assumption questions in general.

[LSAT-Chang]

But do you agree with my way of diagramming it? I was still able to get the correct answer though it was more formulaic since I combined the sentence below into a diagram:

Thus, it is unlikely that real wages will increase significantly...investing very little in new technology"

investing very little in new tech --> unlikely that real wages will increase

and as you can see, I ignored the last sentence about "this pattern likely continue for several more years" as I didn't think it was important.

On the other hand, you seemed to have just diagrammed the conclusion only and not the part about "investing very little in new tech" with it. The way you did it was:

Premise 1 (diagram this in a conditional statement)
Premise 2 (not diagram this)
-----------
Conclusion (diagram just this one sentence)

Whereas what I did was:

Premise 1 (diagram this in conditional statement)
Premise 2 --> Conclusion

As with the second sentence, you can see that I combined the "Thus" and "Since" and put it as a conditional statement.. could I not do that?

[timmydoeslsat]

I believe I understand what you are getting at here.

The issue I saw was that it took you a long time to see what could be done to attack this question, a sufficient assumption question.

You stated that I did not diagram the second sentence, and you are correct. You cannot diagram since and thus as sufficient and necessary. You cannot know for sure that it is simply that premise alone that allows you to conclude with thus.

Example, from a problem I remember doing the other day.

Hypothetical Argument

Causing harm to a person is immoral. Thus, to threaten a person is immoral, since threatening a person is causing harm.


If you were to diagram that since-thus relationship into a conditional relationship you would have done this:

Threatening a person causes harm ---> Threatening a person is immoral

There are so many issues with this and I am going to go over these with you and how to correct this type of thinking and how to succeed on sufficient assumption questions.

The hypothetical argument I gave is a valid one. However, the conditional statement that was drawn from the since-thus relationship is NOT CORRECT. I was able to say my thus statement because of the TWO PREMISES that I had, which enabled me to make such a conclusion.

When you see thus in an argument, you know it is a conclusion. We just do not know if it is a main one or a subsidiary/intermediate one.

It was obvious to see in this argument that it was indeed the main one.

So I recommend placing that main conclusion at the bottom of our structure, and placing all of the available premises we have above it.

Premise 1
Premise 2
__________
Conclusion

[LSAT-Chang]

Ohhhhh..
So in the actual problem we were discussing above, I need the two premises combined to get the conclusion. I basically had the wrong "core" since I only had half of it, right? I had A --> C when it actually is A + B --> C and the helpful tip you are giving me is that in sufficient assumption questions, first look for the conclusion and place it way below all of the supporting premises. Right?

[timmydoeslsat]

Exactly!

Here is your thought process on EVERY LR problem.

"What is my question stem?"

Read the stimulus.

Determine the conclusion.

Identify the evidence for this.

Create a core in your head. Actually "see" the premises with the "+" combining them...and ask yourself if those premises guarantee or entail that conclusion.

On a sufficient assumption question, once you see it is one, read the argument, determine the conclusion, put that at the bottom, and place all premises above the line. Almost all, if not all, sufficient assumption questions have a variable that needs linking and once you identify what that term is, finding an answer choice will be much simpler.

For example:

Premise A: bland statement
Premise B: bland statement
_________________________
Conclusion, out of nowhere, brings up the movie "Office Space"

You need to tie the premises with Office Space for us to conclude something with Office Space.

[maryadkins]

Nice work and conversation here! A couple of things to add:

I actually also used CL on this problem. And it works the way you diagrammed it:

- Prod Increase --> - RW Increase (If productivity doesn't increase, real wages won't--this, as you properly identified, is the contrapositive of the first statement)

Conclusion:

- Biz invest much in tech --> - RW increase (If businesses aren't investing much in tech, real wages won't increase)

We need to link "- Biz invest much in tech" to "- Prod Increase," which (D) does. ("Much" is like "substantial.")

(A) is about the past; this argument is about the future.
(B) is out of scope. Skills?
(C) is the opposite of what the argument is saying.
(E) is about the present. Our conclusion is about what is happening in the future.

In the hypo below:

Causing harm to a person is immoral. Thus, to threaten a person is immoral, since threatening a person is causing harm.

You can actually diagram this. It would be:

Harm --> Immoral
Threaten --> Harm

Therefore:

Threaten --> Immoral

Your point about not conditionally diagramming the premise and the conclusion as if they're one giant "if... then" statement is a good warning. We definitely want to be careful of that. But I think your key point, which is spot on, is that IDing the conclusion and separating the premises from the conclusion is critical--not that diagramming them doesn't work. Sometimes an "if" can appear in the conclusion.

I think the final lesson from this question is that there are multiple approaches to solving this problem. Nice job.

[LSAT-Chang]

- Prod Increase --> - RW Increase (If productivity doesn't increase, real wages won't--this, as you properly identified, is the contrapositive of the first statement)

Conclusion:

- Biz invest much in tech --> - RW increase (If businesses aren't investing much in tech, real wages won't increase)

Hi Mary! So you did diagram the way I diagrammed it! Right? Looking at your conclusion diagram, I had it exactly how you had it (just minor word changes -- I just put: Invest litle in tech -> - RW increase). So my question is, was I not wrong to put the statement "Thus..since" part in conditional? Because just like how you did it, I read that as a "A -> B" thing, but after the discussion with timmydoeslsat above, I thought my approach was wrong since I can't diagram "Thus..since" in a conditional statement because of the other presmises that leads to the "thus" conclusion. So when exactly can I diagram "thus since" and when can I NOT? I am just a little confused after this discussion since you had it the way I first had it and got the correct answer but the discussion we had above talks about how the diagramming of "thus..since" isn't quite right.

We need to link "- Biz invest much in tech" to "- Prod Increase," which (D) does. ("Much" is like "substantial.")

Wow, this approach looks so much easier compared to what I did above. It's like we have:

NOT A -> NOT B
______________
NOT C -> NOT B

So we just have to connect NOT C -> NOT A since that will give us "NOT C -> NOT A -> NOT B" and THEN we have the conclusion of : NOT C -> NOT B.

My other question is.. how do you know which ones to use as contrapositives? Like if you see in my approach above, I just decided to try the contrapositive of the conclusion to see if that helped me get any link, and it did although it took over 5 minutes just figuring out how I could link it. Do you normally get the contrapositive of the premise?? Any tips on this?

[timmydoeslsat]

Conclusion:

- Biz invest much in tech --> - RW increase (If businesses aren't investing much in tech, real wages won't increase)

I would disagree that the conclusion is conditional in this problem.

I would also disagree that you could validly create a conditional relationship with a since-thus relationship when you have OTHER premises in support of the conclusion.

The author was not concluding with thus on the basis of fulfilling a sufficient condition of "since." The author used thus to conclude on the basis of both premises.

It is like:

Since statement 1
Since statement 2
____________________
Conclusion

You cannot say that statement 2 was used to entail a conclusion, it was both premises used together.

[LSAT-Chang]

Now I'm really confuzzled.. I wish Maryadkins or any other instructor could jump in on this wonderful discussion! But I have to agree with you timmydoeslsat, although I did diagram it, I feel like your logic is sound in that the diagram I drew does seem to say that it is just one premise about the "businesses investing little in new tech" that leads to the conclusion of "unlikely that real wages will increase significantly" when the first part about "real wages increase --> productivity increase" is crucial for the conclusion. I guess we'll just have to wait and see!

[ManhattanPrepLSAT1]

This is a really good discussion and I totally see the confusion. This all depends on your level of exactitude.

timmydoeslsat is actually correct on this. Take a look at the following example:

____A_____, since ____B________ .

that would set up an argument

B
----
A

it rests on an implicit premise B ---> A, and remember an implicit premise is an assumption (or a gap in the reasoning).

For this argument, the structure is

RW increase ---> P increases
~Bus Inv
---------------------------------
~RW increase

The assumption being ~Bus Inv ---> ~P increase, best expressed in answer choice (D). This bridges the gap between the second premise and the negation of the necessary condition in the conditional statement, thereby allowing us to use the contrapositive and get to the conclusion that real wages will not increase.

Hope that helps!

[LSAT-Chang]

Thanks for chiming in Matt! I think I got into a bad habit of thinking of the argument core as : "A therefore B" as equivalent to the conditional statement "If A then B"..........

[zainrizvi]

(E) is wrong because of scope shift. The argument states the country's businesses are investing very little in new technology. (E) says that the new technology in which businesses are currently investing is not contributing to productivity.

There are two problems with this:
1) There is no indication that the new technology in which businesses are currently investing will remain the new technology that they will invest in, meaning that the answer choice gets too specific on focusing "THE new technology". For all we know, there could be lots of new technologies being invested in (as long as overall, it would be "very little")

2) Currently is the bigger issue I think. They are currently investing little amounts is what the stimulus says. And this pattern of LITTLE investing will continue. Answer choice (E) extends that to saying CURRENTLY those businesses are not contributing to an increase in productivity. For all we know these businesses that are currently being invested in and currently sucking (e.g Microsoft in the 1970s) will become mammoths in the near future. It gets tricky because you have to realize the stimulus is talking about the pattern of investing, and doesn't extend to the pattern of their productivity.
Phew, analyzed the hell out of that, lol

[ManhattanPrepLSAT1]

Great points zainrizvi! Can I add one more to your discussion of answer choice (E)?

We need an answer that will help us determine that productivity is not increasing. While answer choice (E) suggests that productivity is not increasing from the current investments being made, it does not rule out the possibility that productivity is increasing as a result of some other factor. Answer choice (D) on the other hand, in conjunction with the fact that we know that major investments are not being made in technology would guarantee that productivity is not increasing.

[dandrew]

Could you attack this problem with conditional logic using the below method?

I = Investing
RW = Real wages
P = Productivity

Conclusion: ~I -> ~RW
Contrapositive of conclusion: RW -> I

Then link the sufficient and necessary conditions using information in premises:

RW -> P -> ? -> I

The question mark is what must be assumed. (D) fills this gap with the following logic: ~I -> ~P (or contrapositive, P -> I).

(E), on the other hand, makes illegal reversals and negations of the logic: I -> ~P

I understand the other previously stated reasons for why (E) is wrong, including the the temporal issues and the "currently" red flag. I'm also aware of the risks inherent in turning the conclusion into a conditional statement. However, I'd just like to know if my approach to the problem is sound.

Thank you!

[josh.randall52]

I was down to D/E here, and chose E, but I am missing how the "currently" part in the AC E rules it out? Doesn't the stimulus say that this current trend is likely to continue for several more years (the near future)? So the current investments (in AC E) would also include the near future, correct?

Is it because of the word "likely"?

I chose E running out of time because I saw it was a SA question and I was thinking that it was fully bridging the gap and had more info than D. Being more "precise", I thought it fit better as a SA answer.

I understand completely why it is D, though.

[roflcoptersoisoi]

I got why (D) is the correct answer, but am having a bit of trouble eliminating E.
Wouldn't E be incorrect because it's necessary, but not sufficient.


Premise(s):
Real wages will increase only if productivity increases.
Country's businesses are currently investing little in new technology.
Conclusion: Real wages won't increase

If the technologies in which businesses are investing are yielding an increase in productivity, this would seemingly destroy the conclusion.

Thoughts?