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#19- Nearly all mail that is correctly addressed arrives at

Johnclem
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Hello,
For the love of God ... How is A wrong ?
This is what I did .

1) mail is correctly addressed --> arrives within 2 business days
2) correctly addresses Mail would take longer (than 2 business days --> damaged
3) most mail arrives 3 or more business days

My prephrase was that either Most mail is getting damaged or else most mail is not correctly addressed .



Thanks
John
David Boyle
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Johnclem wrote:Hello,
For the love of God ... How is A wrong ?
This is what I did .

1) mail is correctly addressed --> arrives within 2 business days
2) correctly addresses Mail would take longer (than 2 business days --> damaged
3) most mail arrives 3 or more business days

My prephrase was that either Most mail is getting damaged or else most mail is not correctly addressed .



Thanks
John



Hello John,

Your prephrase may be somewhat accurate, and indeed, the second part of it, "most mail is not correctly addressed", is the right answer, D. Therefore, answer A doesn't have to be true.

Hope this helps,
David
ivan
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hello! could you please help me. The diagrams of the stimulus:

1) correctly addressed :arrow: 2 days
2) correcctly addressed AND 2 days :arrow: damaged
3) we know that most mail 3 or more days after being sent - 2 days

I choose answer D which is a contrapositive of the 1st giagram
2 days :arrow: correctly addressed

but I do not understand why A is incorrect. this is a repeat of the 2nd diagram:
correcctly addressed AND 2 days :arrow: damaged

Thank you!
Claire Horan
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Hello all,

As a sidenote, please be aware that when statements are limited by words like "some," "most," etc., you may not simply write the formal logic as if these words are not there. If you do, you are likely to get the problem wrong.

Mail correctly addressed :most: arrives within two business days
It follows that...
Of mail that is correctly addressed, most (more than half) does not take three or more business days.

But most mail (more than half) arrives three or more business days after being sent.

That means there must be a lot of mail that is incorrectly addressed. The "damaged in transit" part is a red herring because that we still have the fact that "nearly all mail (damaged or not) that is correctly addressed arrives at its destination within two business days of being sent. That means only a small amount of the mail that arrives late does so due to being damaged.
nikki.brar
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Hi, please help!

Diagram:

1)correctly addressed---> 2 business days
2)correctly addressed mail take longer than 2 business days ----> damaged
3) most mail arrives 3 + business days after being sent ( mail--(most)--> 3+days after being sent)

Ok so my thought process.. if mail is taking 3 or more days to arrive then its either damaged in transit or maybe its not correctly addressed.. I see this in answers A and D so i eliminate B,C,E..
Now to choose between A and D.

A) says a 'large proportion' of the correctly addressed mail is damaged.. where as the stimulus says NEARLY ALL correctly addressed mail arrives within 2 days and the only case that it correctly addressed mail doesnt come in 2 days is because it got damaged. so NEARLY ALL constitutes a majority.... so if a majority of correctly addressed mail arrives within 2 days, i think that less than a majority or some of the correctly addressed mail is damaged in transit. i dont know if this makes sense, but I eliminate on that basis.

D) i go with this answer because I eliminated A. but I don't really understand the reasoning.


Does this look right? Could someone help with why D is correct?

Nikki
Luke Haqq
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Hi Nikki!

Happy to try to help with seeing why (D) is correct (glad to hear you chose the right answer!).

As I understand this one, that answer comes from what you roughly have in your first diagram--

    correct address :most: 2 days

    contrapositive: ~(2 days) :most: ~(correct address)

The last sentence of the stimulus states, "Overall, however, most mail arrives three business days or more after being sent." In other words, we know its the case that ~(2 days). In most cases where mail doesn't arrive in 2 days, we know from the contrapositive, it's because it's incorrectly addressed. And that's another way of saying (D) "A large proportion of mail is incorrectly addressed."

Hope that helps!
bk1111
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Luke Haqq wrote:Hi Nikki!

Happy to try to help with seeing why (D) is correct (glad to hear you chose the right answer!).

As I understand this one, that answer comes from what you roughly have in your first diagram--

    correct address :most: 2 days

    contrapositive: ~(2 days) :most: ~(correct address)

The last sentence of the stimulus states, "Overall, however, most mail arrives three business days or more after being sent." In other words, we know its the case that ~(2 days). In most cases where mail doesn't arrive in 2 days, we know from the contrapositive, it's because it's incorrectly addressed. And that's another way of saying (D) "A large proportion of mail is incorrectly addressed."

Hope that helps!

Hi,

I thought we could not take a contrapositive of "most" or "some" statements. How can we use the reasoning above to logically conclude the answer as D?
LSAT2018
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To clarify, the correct answer (D) is a contrapositive of the first sentence?

Correctly Addressed (Most) → 2 Days
Not 2 Days (Most) → Not Correctly Addressed
3 Days or More (Most) → Not Correctly Addressed

So I take that with modifiers some/most remain unchanged in the contrapositive?
Jonathan Evans
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Hey, BK and LSAT2018,

I've got a short answer and a long answer.

The short answer is that you are correct, BK: you cannot make contrapositives of "some" and "most" statements (Luke has this one wrong unfortunately). There is a rather interesting exception to this rule in formal logic, but it has no bearing on this problem or on the LSAT.

If you wish to read a complete discussion of the rules of making inferences, there is an excellent in depth discussion in Chapter 13 of the Logical Reasoning Bible that helpfully covers what you need to know for the LSAT and omits extraneous information.

For the long answer, let's do a thorough analysis of this problem. I'm going to use a couple shortcuts, substituting "most" for "nearly all" for simplicity sake.

  1. MailCorrectly Addressed :most: Arrive in 2 days
  2. MailCorrectly Addressed not Arrive in 2 days :arrow: Damaged
  3. Mail :most: not Arrive in 2 days

Let's start by listing some safe assumptions:

    Mail :arrow: MailCorrectly Addressed OR Mailnot Correctly Addressed
    Mail :arrow: Arrive in 2 days OR not Arrive in 2 days

Let's now make whatever immediate inferences we can from each statement. In other words, let's see whether we know anything else from each statement by itself.

  1. MailCorrectly Addressed :most: Arrive in 2 days

      from this we know that 1'. MailCorrectly Addressed not most not Arrive in 2 days.
  2. MailCorrectly Addressed not Arrive in 2 days :arrow: Damaged

      from this we know that 2'. MailCorrectly Addressed not Damaged :arrow: Arrive in 2 days
      This is a conditional statement and thus has a valid contrapositive.
  3. Mail :most: not Arrive in 2 days

      from this we know that 3'. Mail not most Arrive in 2 days.

Now let's make any possible additive inferences (inferences that are possible by combining more than one statement).

  • Can we combine 1 and 2 to make any additive inferences? Not really anything useful. Do we know that a minority of correctly addressed mail is damaged? No, we do not. We know that MailCorrectly Addressed not Arrive in 2 days :arrow: Damaged but we do not know *MailCorrectly Addressed Damaged :arrow: not Arrive in 2 days. Notice this is a Mistaken Reversal™ of this conditional statement.
  • Can we combine 2 and 3 to make any inferences? Clearly we cannot. The variables in these two statements are completely different, and we are unable to make any useful chains here.
  • Can we combine 1 and 3 to make any inferences? Yes! We can do a couple different things here.
      Mail :some: MailCorrectly Addressed :most: Arrive in 2 days
      but Mail :most: not Arrive in 2 days
    Thus, we know that Mail :some: MailnotCorrectly Addressed
    Can we conclude that Mail :most: MailnotCorrectly Addressed? Almost. Not quite. We can make a pretty compelling case here that since "almost all" correctly addressed mail is delivered in two days and that most mail is not delivered in two days, then the vast majority of this mail not delivered in two days is incorrectly addressed (not just damaged). Thus, as the vast majority of this group is incorrectly addressed, that would likely represent more than half of all the mail. However, there is some uncertainty because some correctly addressed mail that is damaged arrives in longer than two days.
Fortunately, the LSAT lets us off the hook here! We do know that there is some sizable quantity of mail that is incorrectly addressed. Whether this group is more than half ends up being irrelevant because that's exactly what Answer Choice (D) says! Hooray!
LSAT2018
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The most/large proportion is confusing! If the contrapositives for some/most do not work, how do we arrive at not correctly addressed? Can you comment on the diagrams below?

Correctly Addressed → Two Days
Not Two Days → Not Correctly Addressed

Mail (Most) → Not Two Days
Mail (Some) → Correctly Addressed (Most) → Two Days
Mail (Most) → Not Two Days → Not Correctly Addressed


Thanks in advance!