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

[Adam Tyson]

I'm going to suggest an alternate approach from the formal logic diagramming used by my esteemed colleagues here. I'm going to suggest instead that we play with numbers, because that is my preferred method for dealing with "some" and especially "most" in LSAT questions.

I'm going to start with the total amount of mail, and to keep it simple I am going to say that there are 100 pieces of mail, total, in all of world history.

Most of those take 3 days or longer to be delivered. That meas 51 pieces of mail, at a minimum, take that long, because "most" means more than half.

"Nearly all" is harder to quantify, but it has to be more than just 50% plus 1, I think. Let's be a little conservative and say that "nearly all" is 85%. So, 85% of all correctly addressed mail gets there within 2 business days.

From the numbers we have so far, how much mail could have been correctly addressed? Only 49 pieces got there on time in two days, but that has to be at least 85% of all the correctly addressed mail. I whip out my handy calculator (the one in my head), and I determine that 49 is 85% of...let's say 58. (For those of you who don't like math, do it this way - 85% of 100 is 85, so 85% of half that total, or 50, would be half that subtotal, or 42.5. I need to add 6.5 to that number to get up to my 49, so I'll add that plus a little more to 50 to get my guesstimated total of 58. Yes, sometimes we have to do a little math on the LSAT, sorry.).

So, of the 100 total pieces of mail, the most that could have been correctly addressed is 58, which is, conveniently, 58% of the total. It could have been even less than that, if some of the incorrectly addressed mail also got there in two days or less, but I am trying to push things to their limits here in order to test my understanding. In order for nearly all of the correctly addressed mail to get there on time, and yet still have less than half of the mail get there on time, even accounting for the percentage that is correctly addressed but damaged in transit, there's still 42% of the mail that is incorrectly addressed. That's pretty substantial!

Don't like those figures? Try your own! Maybe "nearly all" is just 70%? I don't like that, it feels too low to me, but give that a go anyway and see what you come up with. I think no matter what numbers you use, if you are being honest with yourself about what "nearly all" indicates, you're going to find that a substantial percentage of mail must be incorrectly addressed.

Formal logic diagrams, which bear a striking similarity to conditional diagrams, are great, but they are not the only way to approach these problems. Since the folks at LSAC provide no scratch paper and do not require you to show your work, don't get hung up on exactly how to diagram a question, and focus instead on what method works best for you to answer the question. When the diagrams aren't working for you, try another way! Count on it!

[Jerrymakehabit]

I am worried about (D) that "A large proportion of mail is incorrectly addressed". I think it should be "A large proportion of mail is incorrectly addressed and/or damaged". I feel "damaged emails" also play a role here. Can someone please help with my concern?

Thanks
Jerry

[Robert Carroll]

Jerry,

Often, Must Be True answer choices are unappealing because they don't make the strongest or most relevant statement that could be made based on the stimulus. The only thing you should care about, though, is whether the answer choices makes a TRUE statement based on the stimulus. Answer choice (D) does that, as discussed above. If it said something else, we could evaluate what it said and consider whether that statement had to be true, but there's nothing bad about answer choice (D) from a logical perspective - it must be true, so it's correct.

Robert Carroll

[Amitjohn]

Hello,

I am also having a bit of trouble understanding why (D) is correct and not (C).

Percentages and diagrams aside, how do we know that a large proportion of mail is incorrectly addressed? Couldn't it be that nearly all of the mail is correctly addressed however it is damaged in transit, causing it to be ~(2 days)?

(C) seems right to me because the first sentence says "Nearly all mail that is correctly addressed arrives at its destination within two business days of being sent" ... Therefore, it must be true that most mail that arrives within two business days of being sent is correctly addressed?

(D) seems like it is possible but doesn't have to be true because a large proportion of mail could be correctly addressed but damaged in transit causing it to take longer than 2 days in transit.

Can someone please help me understand where I'm making a reasoning error?

Sincerely,
John

[Adam Tyson]

Happy to help, John!

First, let's deal with the idea that most mail is actually damaged in transit, and that is why most mail takes three or more days to arrive. The problem with that idea is that it directly contradicts the first sentence: nearly all mail that is correctly addressed does manage to arrive in two business days. That means that damaged or not, if it is correctly addressed it is almost always going to get there that quickly. If most mail was damaged in transit, but most of it was nonetheless correctly addressed, then it would still nearly all arrive within two business days. We know this is true because we have to accept that claim in the first statement. So the facts here cannot be said to show that most mail is damaged, and damage to most mail cannot by itself explain why most mail takes longer.

Second, the idea that because nearly all the correctly addressed mail arrives within two days, most mail that arrives within two days must be correctly addressed. This is a classic flaw of Formal Logic, and an analogous argument might help clarify why it is a problem. What if I were to tell you that nearly all of the people raised in the state of Wisconsin attended public school as children. Could I then correctly claim that most people who attended public school as children were raised in Wisconsin? Not at all! That "nearly all" idea, like the similar concept of "most," cannot be proven to run both ways. It is entirely possible that most mail that gets to its destination within two days is incorrectly addressed, just as most public school kids might not be from Wisconsin.

Finally, one last tactic to approach this question, and that is to supply numbers. Imagine that there are just 100 total pieces of mail, including the ones that are incorrectly addressed and the ones that are damaged in transit. Most of the mail - at least 51 pieces - arrive three or more days after being sent. But nearly all of the ones that are correctly addressed get there faster than that. How many could be correctly addressed and have these two statements still both be true? It's hard to say how much "nearly all" is, but out of 100 pieces of mail I think 80% is the bare minimum (it's subjective, of course, but I think less than 80% would not longer be "nearly all" in most people's estimation). At most 49 pieces are getting to their destination within two business days, and if those 49 are 80% of the ones correctly addressed, then we are looking at no more than 61 pieces of correctly addressed mail. That means at least 39 pieces of mail - a substantial proportion, to be sure - are incorrectly addressed! We have proof for answer D!

Supplying numbers to questions involving "most" and "some" and percentages and ratios and other numerical ideas can be slow and inefficient, if math is not your jam, but if you happen to love math like me they can be a fast and easy way to see these relationships in very simple terms. As soon as I see a claim about "most people who drive red cars are single," in my mind there are 10 such people driving those cars and 6 of them have to be single. When I see percentages come up, like "40% of all known bird species," in my head there are instantly 100 such species and we are talking about 40 of them. Try that and see if it is to your liking!

[vbkehs]

It took me a while to follow the numbers, but it certainly helped once I understood. Thank you!

Happy to help, John!

First, let's deal with the idea that most mail is actually damaged in transit, and that is why most mail takes three or more days to arrive. The problem with that idea is that it directly contradicts the first sentence: nearly all mail that is correctly addressed does manage to arrive in two business days. That means that damaged or not, if it is correctly addressed it is almost always going to get there that quickly. If most mail was damaged in transit, but most of it was nonetheless correctly addressed, then it would still nearly all arrive within two business days. We know this is true because we have to accept that claim in the first statement. So the facts here cannot be said to show that most mail is damaged, and damage to most mail cannot by itself explain why most mail takes longer.

Second, the idea that because nearly all the correctly addressed mail arrives within two days, most mail that arrives within two days must be correctly addressed. This is a classic flaw of Formal Logic, and an analogous argument might help clarify why it is a problem. What if I were to tell you that nearly all of the people raised in the state of Wisconsin attended public school as children. Could I then correctly claim that most people who attended public school as children were raised in Wisconsin? Not at all! That "nearly all" idea, like the similar concept of "most," cannot be proven to run both ways. It is entirely possible that most mail that gets to its destination within two days is incorrectly addressed, just as most public school kids might not be from Wisconsin.

Finally, one last tactic to approach this question, and that is to supply numbers. Imagine that there are just 100 total pieces of mail, including the ones that are incorrectly addressed and the ones that are damaged in transit. Most of the mail - at least 51 pieces - arrive three or more days after being sent. But nearly all of the ones that are correctly addressed get there faster than that. How many could be correctly addressed and have these two statements still both be true? It's hard to say how much "nearly all" is, but out of 100 pieces of mail I think 80% is the bare minimum (it's subjective, of course, but I think less than 80% would not longer be "nearly all" in most people's estimation). At most 49 pieces are getting to their destination within two business days, and if those 49 are 80% of the ones correctly addressed, then we are looking at no more than 61 pieces of correctly addressed mail. That means at least 39 pieces of mail - a substantial proportion, to be sure - are incorrectly addressed! We have proof for answer D!

Supplying numbers to questions involving "most" and "some" and percentages and ratios and other numerical ideas can be slow and inefficient, if math is not your jam, but if you happen to love math like me they can be a fast and easy way to see these relationships in very simple terms. As soon as I see a claim about "most people who drive red cars are single," in my mind there are 10 such people driving those cars and 6 of them have to be single. When I see percentages come up, like "40% of all known bird species," in my head there are instantly 100 such species and we are talking about 40 of them. Try that and see if it is to your liking!

[eleanorsavas]

Hi I am still a little confused about why answer choice (C) is wrong. I see why (D) is correct.

D is correct because even though correctly addressed but damaged mail could take longer than 2 days, the stimulus still says that nearly all correctly addressed mail arrives within two days. This would mean that the reason that most mail takes 3 or more days must be because of incorrectly addressed mail.

However, I still do not see why it is that answer choice C is wrong. I guess it is more of a "could be true" answer than a "must be true" answer but I am still a little confused about the reasoning behind it.

Thanks!

[KelseyWoods]

Hi Eleanor!

You are correct that answer choice (C) is something that is possible, but not something that we can be certain must be true.

From the first sentence, we know that nearly all mail that is correctly addressed arrives within 2 business days. But that relationship only goes in one direction. It doesn't necessarily mean that most mail that arrives within 2 business days is correctly addressed. That would be a Mistaken Reversal of the first sentence.

You can make up numbers to prove that answer choice (C) is not necessarily true based on the statements in the stimulus:

Total pieces of mail: 100
# of correctly addressed pieces of mail: 20
# of pieces of mail that arrive within 2 business days: 45
# of correctly addressed pieces of mail that arrive within 2 business days: 18
# of pieces of mail that arrive 3 or more days after being sent: 55

These numbers match the statements in the stimulus:
Most mail arrives 3 or more days after being sent (55/100).
Nearly all correctly addressed mail arrives within 2 business days (18/20).

So these numbers satisfy all the requirements that we've been given. But, based on these numbers, answer choice (C) is not necessarily true because in this instance, we have 45 pieces of mail that arrive within 2 business days, but only 18 out of those 45 pieces of mail are correctly addressed. Thus, it is not true that most mail that arrives within two business days of being sent is correctly addressed.

Hope this helps!

Best,
Kelsey

[queenbee]

HI
I didnt select D because, if the mail doesnt arrive in 2 days, why does that mean that most of them are incorrectly addressed? They could also be damaged, or there could be some other reason. Are we to assume that there are only 2 reasons that mail will not arrive on time? Meaning incorrectly addressed or damaged?

Thank you
Neeli

[Luke Haqq]

Hi Neeli!

Regarding your question, "if the mail doesn't arrive in 2 days, why does that mean that most of them are incorrectly addressed?"--the final sentence of the stimulus is a good place to start. We're told there that "most mail arrives three business days or more after being sent." This should seem perhaps odd, because the stimulus states earlier that nearly all correctly addressed mail arrives within 2 days. This raises a question: how is it that most mail arrives in 3+ days when correctly addressed mail nearly always arrives within 2? Damage can account for part of it--correctly addressed mail will arrive within 2 days, and the only exception to this is if it is damaged (this is the second sentence of the stimulus). But we're still left with all non-damaged, correctly addressed mail arriving within 2 days, this accounts for "nearly all" of correctly addressed mail, yet "most mail" actually arrives in 3 or more. The stimulus leaves being incorrectly addressed as what can account for most mail arriving not within 2 days but rather after 3+ days.

To your other questions--"Are we to assume that there are only 2 reasons that mail will not arrive on time? Meaning incorrectly addressed or damaged?"--the answer is contained in the first two sentences of the stimulus, which specifically pertain to correctly addressed mail. "Nearly all" correctly addressed mail will arrive within 2 days, and the rest of the correctly addressed mail that falls outside that "nearly all" and takes 3+ days to arrive takes longer because it is damaged.