PT106 · S2 · Q19 Nearly all mail that is correctly

Why this is right

At first we might think, "This doesn't have to be true. Yes, we know that most mail takes 3 or more days, but that doesn't have to be because it's incorrectly addressed. It could be that it's correctly addressed but damaged in transit." Here's the problem with that -- if we tell ourselves that "most correctly addressed mail is damaged in transit, and thus takes more than 2 days", then we'd be contradicting the first sentence, which says that "nearly all correctly addressed mail arrives within 2 days". If all mail were correctly addressed, then this paragraph would contradict itself. If there were 100 pieces of mail, all correctly addressed, we know that nearly all (we'll say 90 of them) get there within 2 days. That leaves 10 pieces of correctly addressed mail not getting there within 2 days. But we were told that "most pieces of mail" take more than 2 days. 10 is not most of 100. We'd have to keep adding incorrectly addressed mail in order to be able to every honor the idea that most total mail takes more than 2 days. ? pieces of mail 100 correctly addressed ? incorrect 90 arrive w/in 2 days 10 take more than 2 (damaged in transit) Let's say we added in 50 incorrectly addressed pieces of mail. 150 pieces of mail 100 correctly addressed 50 incorrect 90 arrive w/in 2 days 10 take more than 2 (damaged in transit) Even if all 50 of those took more than 2 days, and we added in the 10 correctly addressed ones that took more than 2 days, we'd still only be at 60 pieces that took more than 2 days. And 60 is not most of 150. It's less than half. So we'd have to add even more incorrectly addressed pieces of mail. 180 pieces of mail 100 correctly addressed 80 incorrect 90 arrive w/in 2 days 10 take more than 2 (damaged in transit) Now we could have a total of 90 pieces of mail that took more than 2 days (80 + 10). 90 out of 180 is exactly half, so we'd still need to go a little higher with our incorrectly addressed total to make the "most" fact work. No matter what number of mail pieces we make the correctly addressed mail, we'll always have the problem that 90% of it gets there within 2 days and only 10% or less takes more than 2 days. In order to comply with the fact that more than 50% of all mail takes more than 2 days, we need to add a lot of incorrectly addressed mail to make the math work. "Large proportion" doesn't have a specific numerical cut-off, but it looks like we'll always need more than 40% of the mail to be incorrectly addressed in order to make all this math work, and more than 40% is definitely "a large proportion".

Skill tested: Must be True · how this choice captures the argument's function is the move to repeat next time.