Q20 - On some hot days

[gregory.mortenson]

I narrowed the 5 choices down to A and E. I ultimately went with E. But according to the book, the correct answer is B.



what does this even MEAN and how does it apply to the question prompt??

[dan]

Hey Gregory. Hope you don't mind that I edited your post. We can't reproduce questions in our forums, so I took out the direct quotes from the question.

So, this question gives us three sets:

hot days (we'll call this "hot")
unsafe smog levels (we'll call this "smoggy")
wind blows from the east (we'll call this "windy")

Essentially, the argument tells us two things about how these sets overlap:

1. some hot are also smoggy
2. some hot are also windy

From this, the argument concludes that some smoggy are also windy.

Do you see the problem with this logic? If not, take the following example:

Assume we have 10 boys in a room, and we know two things about this group of boys:

3 of the boys wear hats ("some of the boys wear hats")
4 of the boys are in the 3rd grade ("some of the boys are in the 3rd grade")

Can we conclude that some of the boys that wear hats are also in the 3rd grade? It's possible that this is true, but we don't know for sure, right? Maybe the three boys who wear hats don't overlap at all with the 4 boys who are in the 3rd grade.

The same issue holds true for the original argument. If we have 10 hot days, and some of them are smoggy and some of them are windy, it does NOT necessarily mean that some of the smoggy days overlap with some of the windy days. Maybe 3 of the days are smoggy, and a different set of 4 days out of the 10 are windy.

So, the conclusion is flawed because it assumes an overlap between smoggy and windy. We want to choose and answer that expresses this flaw.

Answer (B) does this. The argument fails to consider that the hot set might overlap with each of smoggy and windy (some hot days are smoggy, some hot days are windy) even though those two other sets (smoggy and windy) might not have any members in common (maybe none of the smoggy days overlap with any of the windy days).

The key word in all of this is "some." Some boys wear hats. Some boys are in the 3rd grade. Do they overlap? Maybe, but not for certain.

What if we change "some" to "most"? Most boys wear hats. Most boys are in the 3rd grade. Do they overlap? Yes!! At least some do. If you're not sure why, take a sample of 10 boys and play out a few scenarios.

Hope that helps!

dan

[gregory.mortenson]

Thanks Dan, that was a very helpful explanation.

Two things really threw me off with this question:

1) I failed to recognize that the question does NOT imply causation, merely two things coincidentally happen at once. My initial reading of this question led me to believe that "hot" -> "smoggy"... with that in mind I went to answer choices with causation on the brain and was led further off the trail.

2) The wording of the correct answer choice is pretty tricky!


Cheers,
G

[deanmx]

Had the question listed the 2 relationships in the premise as "most" instead of "some" then the conclusion would have been correct right?

[dan]

Yes, that's exactly right. If the two statements had been "most" statements instead of "some," then the conclusion would hold.

dan

[b91302310]

I was wondering why answer choice B is better than A ? The author mistakes a condition that sometimes ( some hot days) accompanies unsafe levels of smog for a condition that necessarily (some days) accompanies unsafe levels of smog.

Could someone explain why answer choice A is wrong? Thanks !

[giladedelman]

Thanks for the question!

So, we know that on SOME hot days, smog reaches unsafe levels, and that on SOME hot days, the wind blows in from the east. Those are the two premises. From those, the author concludes that there must be some days during which the smog reaches unsafe levels and the wind blows in from the east.

In other words, the author is erroneously concluding that there must be some overlap here.

Answer (B) expresses that flaw. The author fails to recognize that the two sets -- smoggy days and easterly wind days -- may share some members with hot days without sharing members with each other. In other words, they may not overlap!

(A) is tempting, but I don't like your gloss of it; "necessarily" couldn't equal "some days"! It would have to mean "all" of something. Anyway, this answer is no good because the argument absolutely does not claim that anything necessarily accompanies anything else; all it says is that smog sometimes accompanies wind blowing from the east (and that it sometimes occurs on hot days).

(C) is silly. The argument doesn't use that word in two different ways.

(D) is not true. The premises are certainly plausible; it's the conclusion that's messed up!

(E) is out of scope. There is no causal component to this argument.

Does that answer your question? Let me know if you're still not seeing why (A) is no good.

[b91302310]

Thanks for your explanation and I now understand why A is not good.

Also, when I first read the stimulus, I once considered that the flaw could be mistaken the correlation (reaches unsafe levles vs. wind blows from the east) for the causal relationship. However, I also think that the flaw may also lie in the wording "some hot days" and "some days". So, I think the most difficult part is to get what the test maker intends to test.

[jamiejames]

The thing that threw me off about B was where it said one set may have some in common with two others, which implies there are 3 sets involved, where only the last two may not share anything in common, but what about the third set? Sorry, terribly wored, but I knew the other 4 choices were wrong and this wording really annoyed my brain.

[timmydoeslsat]

Let's break down answer choice B.

We realize that the stimulus is this:

HD some SUL
HD some WBE
______________
SUL some WBE

We know for a fact that SUL and WBE are members of the HD group. They have each occurred with a HD. However, just because one member has these two groups occur with it, does not mean that these two specified groups have members in common with each other. We know that SUL and WBE are members of the HD group. We just don't know if they ever occur at the same time.

[Daniella.owusu]

I would like to throw in my two cents on this explanation, although all of the other explanations have been very helpful. Before I begin, I would just like to explain a few terms that helped me in the Strategy book

Some=1 to 100
Many= 1 to 100
Few= 1 to 100
Several= 51 to 100
Most= 51 to 100

So, when one sees some, one needs to assume that the relationship works both ways. I will provide an example.
Some people who study will score a 180 on the LSAT. Hopefully, this will be all of us

When diagramming this statement, it becomes:
Study<<----some---->>score 180 LSAT

The reason why I made the arrows both ways is because when the word some, or any of its synonyms are used, the statement can go both ways. The same way that some people who study for the LSAT score a 180, it can be read in the reversed order that some people who score a 180 study for the test.

NOW, if the statement had said, MOST people who study will score a 180 on the LSAT, we would not be able to see it as going both ways. It would only be
Study----most-->>score 180 LSAT

If SOME cars are blue, then you know that some blue things (at least) are cars. But if MOST cars are blue, this does not necessarily mean that most blue things are cars.


Sorry for the long prerequisite, but I found it helpful to see the reasoning like this when I began studying these key terms. So,without further ado, let's take the same reasoning of the some mentality NOW TO THE QUESTION!!

HD<<---some--->>UL
HD<<---some--->>WBE

Conclusion:
WBE<<---some--->>UL

The flaw, as previously discussed, is that it combines two statements that do not necessarily have to be apart of the same "family." If I have ten shirts, and four of them are blue and six of them are green, I do not necessarily have to be picking up both when I say some shirts. I could mean four of the same color or just one. The flaw is trying to combine two different things because they stem from the same set.

B) correctly addresses this issue because the one set (hot days) has members with unsafe levels and wind blowing from the east, but that doesn't necessarily mean that wind blowing and unsafe levels share anything in common.

Wrong Answers
A) This isn't a sufficient/necessary condition so this is incorrect.
C) There was no term shift for unsafe
D) Doesn't happen
E) There is no causal relation here so this is incorrect.

Hope this helps. I apologize for the lengthy post.

[timsportschuetz]

Honestly, if you are anything like myself, looking at the above examples and illustrations using numbers does absolutely NOTHING for my long-term understanding on the LSAT.

Below are KEY inferences that are simply NOT POSSIBLE! Memorize these, and you will never miss a problem such as this one:
1) If you have TWO SOME statements with connecting terms, you CANNOT make ANY valid inferences! No exceptions; this is a concrete rule! Example: Some A's are B's. Some A's are C's. You CANNOT make any inferences between B and C.
2) If you have a SOME statement and a MOST statement with connecting terms you CANNOT make ANY valid inferences! No exceptions; this is a concrete rule!
3) If you have two MOST statements or two ALL statements, you can make valid inferences on some occasions! This depends on the direction of the arrows of these connecting statements. Below is a comprehensive method that enables you to make inferences with MOST-MOST relationships and ALL-ALL relationships:
Premises:
Bankers --> Athletes
Lawyers --> [NOT] Bankers

Step 1: Rearrange the premises in order to have the only similar term (Bankers) on the same side of the conditional logic diagram. It is very important to ensure that the similar term (Bankers) is on the LEFT and/or SUFFICIENT side of the conditional diagrams. If you choose to place the similar term on the RIGHT and/or NECESSARY side of the conditional diagrams, you are UNABLE to make any inferences (I need to qualify the previous statement - you can make inferences, albeit with MUCH MORE and unnecessary effort):

Bankers --> Athletes
Bankers --> [NOT] Lawyers

Step 2: Connect the above rearrangements in a slightly different way. Keep in mind that this method is fully valid and does not break any of the conditional logic rules. It simply visualizes the arrows in a different direction:

[NOT] Lawyers <-- Bankers --> Athletes

From this logic chain, you can ALWAYS infer the following (in formulaic terms):

SOME [NOT] Lawyers are Athletes
-AND-
SOME Athletes are [NOT] Lawyers

This holds true for all scenarios with the same structure - IE:

Premises:
B --> C
B --> A

Therefore:
A <-- B --> C

Thus, you can infer the following:
SOME A's are C's
-AND-
SOME C's are A's

For the people that would like to understand WHY you can make these inferences, please review the following rule: Any conditional statement that has an ALL and/or MOST relationship can be reversed (ie: "go against the direction of the arrow"). However, reversing the direction of the conditional logic arrow REQUIRES the addition of a "SOME" relationship. For example:
A --> B ("All A's are B's")

Inference:
SOME B's are A's

If you have: MOST A --> B, you can infer: Some B's are A's. (This works with both, "ALL" and "MOST" Conditional Logic Statements).

PLEASE NOTE THE FOLLOWING: If you have statements such as the following:
A --> B <-- C
YOU CANNOT make inferences! You MUST have the conditional arrows pointing AWAY from the middle term!

TO WRAP THINGS UP, STUDY THE FOLLOWING:
1) SOME-SOME: NO VALID INFERENCES
2) SOME-MOST: NO VALID INFERENCES
3) MOST-MOST & ALL-ALL: SOMETIMES there are valid inferences! Pay attention to the direction of the logical arrows!