Quantifiers Questions - - Question 2

Nearly all mail that is correctly addressed arrives at its destination within two business days of being sent. In fac...

Bluebell7612 May 2, 2019

My diagram led me to A

I diagramed the problem as follows: MCA-most-AW2BD not AW2BD==> D However for the part that states most mail arrives three business days or more after being sent, I understood that to mean that most mail DOES NOT arrive within 2 business days. Therefore, I diagramed it like this: M-most- not AW2BD And this can be chained with the conditional M-most- not AW2BD===> D Answer choice A seemed to match this most closely Someone please explain why this is wrong.

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Victoria May 20, 2019

Hello @Bluebell7612

Your initial diagram of the question was correct.

MCA-most-AW2BD

We can write the contrapositive as:

AW2BD-some-MCA

Not AW2BD - > damaged in transit

The contrapositive of this is that:

Not damaged in transit - > AW2BD

The question goes on to say that most mail arrives three business days or more after being sent. You are correct in identifying that most mail does not arrive within 2 business days, as we can diagram this statement:

Mail-most-not AW2BD

The key difference between the mapping of the third statement and the mapping of the first statement is that, unlike the first statement, the third statement is NOT discussing mail that is correctly addressed. Rather, it is discussing mail in general. Therefore, you cannot apply the transitive property here because the statements are not the same.

The first statement mapped is:

MCA-most-AW2BD

The third statement mapped is:

Mail-most-not AW2BD

A is incorrect because we know that nearly all mail that is correctly addressed arrives at its destination within two business days. Correctly addressed mail only takes longer than this when it is damaged in transit. Since nearly all mail that is correctly addressed arrives within this time period, it is clearly not damaged in transit. As nearly all mail that is correctly addressed is not damaged in transit, then it is not possible that a large proportion of the mail that is correctly addressed is damaged in transit, making this answer choice incorrect.

D is the correct answer. Of the mail that is correctly addressed, the majority arrives within two business days of being sent. Some mail that is correctly addressed takes longer than this because it is damaged in transit. As only some of the mail that is correctly addressed is damaged in transit, we cannot conclude that most of the mail has been damaged in transit. Therefore, the only other option is that the mail has been incorrectly addressed. Therefore, we can conclude that, if most mail arrives three business days or more after being sent, then most mail must be incorrectly addressed.

Hope this was helpful! Please don't hesitate to reach out if you have any further questions.

mprezzy January 20, 2020

This helps but isn't being incorrectly addressed just one possibility of what could have happened to the mail that doesn't arrive within 2 days or greater than or equal to 3 days? For example the mail could have been stolen but arrived in more than 3 days. If we use the possibility of it being incorrectly addressed, why is it only narrowed down to that particular possibility? Please help. Thank you.

Skylar March 1, 2020

@mprezzy, maybe I can help.

Our possibilities are limited by the second sentence, which states that "correctly addressed mail takes longer than this only when it is damaged in transit." The phrase "only when" is key here.

This gives us the following options: either the mail was correctly addressed and arrived within two business days, the mail was correctly addressed and arrived after two business days because it was damaged in transit, or the mail was incorrectly addressed.

You give the example of mail being stolen and arriving past two business days. Since we know that the only way correctly addressed mail arrives past two business days is if it was damaged in transit, the stolen hypothetical can only refer to incorrectly addressed mail. Perhaps the mail was stolen and incorrectly addressed, but all we can say definitively is that it is incorrectly addressed.

Does that make sense? Please let us know if you have any other questions!

Ashley123 August 6, 2021

I had the same train of thought and ended up with A. This helps a lot but I still wish LSAC had included something about incorrectly addressed mail. Since it was not explicitly stated, it makes it difficult to graph this scenario. It is easy to fear the risk of being out-of-scope for stimulus that is not included. This is definitely a tough one. Thank you!

Ravi February 7, 2022

@Ashley123, A doesn't because we know about the breakdown overall of mail that's late, but not between correctly and incorrectly addressed mail (this can be seen in Victoria's diagram above). Also, we don't even know whether all correctly addressed mail that's damaged in transit actually ends up late. Thus, we can get rid of A.