Quantifiers Questions - - Question 2

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

Kylechase June 2, 2020

Why must this be true?

there is nothing in the prompt that rules out the possibility that even 99% of mail is damaged in transit. so how can i conclude that most mail is incorrectly addressed when it could just as well be that most mail being damaged?

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shunhe June 2, 2020

Hi @Kylechase,

Thanks for the question! So let’s take a look at what the stimulus is telling us. First, we’re told that nearly all mail that’s correctly addressed arrives at its destination within two business days of being sent. To diagram this,

Mail correctly addressed —Most—> Arrives at destination within two business days

Then we’re told that correctly addressed mail takes longer only when it’s damaged in transit. Remember that X only if Y is diagrammed X —> Y. So we diagram this

Correctly addressed mail takes longer —> Damaged in transit

Then, we’re told that most mail arrives three business days or more after being sent. In other words

Mail —Most—> Arrives three business days or more.

Now notice that the second statement is diagrammed with “damaged in transit” as a necessary condition. Also notice that the first statement applies to “all mail,” not just “all undamaged mail.” In other words, almost all mail that’s correctly addressed arrives within two days. We can even ignore the second sentence. If we’re then told that most mail arrives after that time, that means that a large proportion of mail is incorrectly addressed, since that is the only explanation for all this late mail. Nearly all correctly addressed mail arrives within two days, but most overall mail arrives three days or later. That means there’s a lot of incorrectly addressed mail, and this is what (D) tells us. This has to be the case, whereas a lot of mail being damaged in transit is only a possibility, not something that logically must follow from the stimulus.

Hope this helps! Feel free to ask any other questions that you might have.

Kylechase June 3, 2020

But the prompt says "must be true", and nothing in the prompt rules out the possibility that most mail is damaged, so how can I say for sure that most mail is incorrectly addressed when no wording in the prompt eliminates the possibility that potentially most mail is damaged, which would also yield the same conclusion. The question does not ask me to logically follow, it asks me to identify which statement must be true, and D is not necessarily true.

Does the information about the damaged mail not cast doubt that a lot of mail must be mislabeled?

christinea303 June 20, 2020

I second this. This question is extremely frustrating. Every time I think I am beginning to figure out this exam, there's another question that completely counters what I have learned so far and is seemingly illogical.

Brett-Lindsay July 14, 2020

I don't think that the damaged part is that important - the incorrectly addressed part is more important.

As the final premise states, most mail arrives in greater than three days. This means that most (of all the) mail isn't correctly addressed. It's irrelevant what happens to the incorrectly addressed mail - ANYTHING could happen to it, including it being damaged, stolen, misplaced, refused delivery, etc.

The only time that damaged is inherently relevant is when we're discussing correctly addressed mail.

prisv February 20, 2021

When reading the stimulus, I noticed I did the first sentence wrong. Is it because "ALL" would be considered as "most"? Could you help me clarify this?


I diagrammed it like this:
MCA __> ADW2BS
Not ADW2BS ___> Not MCA

When it should be like this:

Mail correctly addressed —Most—> Arrives at destination within two business days