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

[Megan Rogers]

Hey, I have a problem with question 22 from p. 396 (from Oct, 96, LR 2, Q#19)

I got this question wrong at first time but got it right eventually. But I am not 100 % sure how I got this right so I'm gonna right my thinking process here so hope someone can confirm whether I'm on the right track.

First of all, I initially picked an answer choice (C) but I am not so sure why it's wrong. If I have to guess it's probably because of 'Most'. If it's changed to 'Some', then would it be right?

You know, so that we can diagram like this:
Mail that arrives within two business days of being sent correctly addressed

and I believe that this could be inferred from the stimulus because of the first sentence
(which states that: mail that is correctly addressed arrives at its destination within two business days of being sent
and I believe that from here we can infer relationship between these twos)


and the second question is about (D), which is the correct answer.
I still can't figure out why this one is the right one...

Can someone please help? I would really appreciate it!
Thanks in advance )

[David Boyle]

Hey, I have a problem with question 22 from p. 396 (from Oct, 96, LR 2, Q#19)

I got this question wrong at first time but got it right eventually. But I am not 100 % sure how I got this right so I'm gonna right my thinking process here so hope someone can confirm whether I'm on the right track.

First of all, I initially picked an answer choice (C) but I am not so sure why it's wrong. If I have to guess it's probably because of 'Most'. If it's changed to 'Some', then would it be right?

You know, so that we can diagram like this:
Mail that arrives within two business days of being sent correctly addressed

and I believe that this could be inferred from the stimulus because of the first sentence
(which states that: mail that is correctly addressed arrives at its destination within two business days of being sent
and I believe that from here we can infer relationship between these twos)


and the second question is about (D), which is the correct answer.
I still can't figure out why this one is the right one...

Can someone please help? I would really appreciate it!
Thanks in advance )

Hello Megan Rogers,

I am glad that you are so thorough that you ask to understand why you are right, not just being content to be right! Anyway: answer C is not too helpful, since it's about why things go right, whereas we are worrying about things gone wrong. I guess that, though, it would be correct if it said "some", rather than "most", as you said above.
Let's look at "In fact, correctly addressed mail takes longer than this only when it is damaged in transit." I.e., > 2 days damaged. So, prephrasing, one might wonder, "Is it correctly addressed?' and "how often is it damaged?"
Answer D plays into that, and is about why things go wrong, i.e., incorrect addressing. So it is a better answer than C. More specifically: "Overall, however, most mail arrives three business days or more after being sent." is explained by answer D, showing that a lot of mail isn't correctly addressed.

Hope this helps,
David

[Johnclem]

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]

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]

hello! could you please help me. The diagrams of the stimulus:

1) correctly addressed 2 days
2) correcctly addressed AND 2 days 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 correctly addressed

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

Thank you!

[Claire Horan]

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 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]

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

[LSAT2018]

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]

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 Arrive in 2 days
2. MailCorrectly Addressed not Arrive in 2 days Damaged
3. Mail not Arrive in 2 days

Let's start by listing some safe assumptions:

• Mail MailCorrectly Addressed OR Mailnot Correctly Addressed
  Mail 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 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 Damaged
   
   • from this we know that 2'. MailCorrectly Addressed not Damaged Arrive in 2 days
     This is a conditional statement and thus has a valid contrapositive.
3. Mail 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 Damaged but we do not know *MailCorrectly Addressed Damaged 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 MailCorrectly Addressed Arrive in 2 days
    but Mail not Arrive in 2 days
  Thus, we know that Mail MailnotCorrectly Addressed
  Can we conclude that Mail 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]

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!