Nearly all mail that is correctly addressed arrives at its destination

hello,

if we consider total mail be 100( <2 days & >3 days =100) then ' most mail arrives 3 or more business days after being sent" with number= 51( as most can be 51-100) and
few mails arrive within 2 business days= 49 ( few range is 1-49). so, mails that arrive within 2 business days are correctly addressed without damage(total 49) and mails that arrive 3 or more days can be correctly addressed with damage and not correctly addressed( 50 can be not correctly addressed and one can be correctly addressed with damage or viceversa) . so, we cannot conclude that large proportion can be incorrectly addressed(D)

please explain if my logic is wrong. i have selected answer as C

How is D justified?
It is very much possible that addresses were correct in large proportion of mails but they got damaged in transit.

Nearly all mail that is correctly addressed arrives at its destination within two business days of being sent. In fact, correctly addressed mail takes longer than this only when it is damaged in transit. Overall, however, most mail arrives three business days or more after being sent.
If the statements above are true, which one of the following must be true?
(A) A large proportion of the mail that is correctly addressed is damaged in transit.
(B) No incorrectly addressed mail arrives within two business days of being sent.
(C) Most mail that arrives within two business days of being sent is correctly addressed.
(D) A large proportion of mail is incorrectly addressed.
(E) More mail arrives within two business days of being sent than arrives between two and three business days after being sent


Please answer with the reasoning

hey can you plz help me with this question how
If i negate option C then it would be ''for NONE OR UPTO 50% OR LESS THAN 50%'' if i take the possibilty of none then it would be like then it shatters the conclusion as if none is affected then our conclusion that drivers performing best will shattered but if i take the possibility of UPTO 50% OR LESS THAN 50% then our conclusion will be shattered as well as in the argument it is every driver will be affected but argument says ALL DRIVERS WILL BE AFFECTED as by this negation our argument get shattered then why this is wrong .
and if in option C i replace most with every then can it be a answer
i really need you guidance
THANK YOU

(C) Most mail that arrives within two business days of being sent is correctly addressed.

Apparently this is a practice LSAT Analytical Reasoning question, and it's an excellent question. I'm not sure whether MLSAT is the source, but it is discussed on this page:
https://www.manhattanlsat.com/forums/post407.html

OK, let's think in terms of categories.

Category P === correctly addressed mail
Category Q === incorrectly addressed mail

That's the big breakdown. At the outset, we have no idea of the relative breakdown of these two, but the whole "population" of mail falls into one of these two categories.

Category P has the further breakdown
Category P1 = correct addressed and not damaged ---- this is "nearly all" of Category P, and this arrives "within two business days of being sent"
Category P2 = correctly addressed by damaged in transit --- this is some very small fraction of Category P (whatever the opposite of "nearly all" is!), and it doesn't arrive quickly

We absolutely know that mail in Category P1 arrives within two days. How fast does mail in category Q arrive? We can draw absolutely no conclusion about this. We also have no idea what proportion arrives earlier and what proportion arrives late.

Given the last piece of information --- "most mail arrives three business days or more after being sent" --- from this, we absolutely know that P1 does not account for a majority of mail. If P1 is less than half of mail, we know P2 is going to account for such a small percentage that it doesn't matter, and this means Q must account for the majority of mail. This is precisely what (D) says. This is by far the best answer, the only possible right answer.

Why is (A) wrong? This directly contradicts the statement that NEARLY ALL correct addressed mail arrives within two days and therefore is not damaged.

Why is (C) wrong? Well, this one could be true, but it is not necessarily true --- it doesn't reach the standard of "must be true" for which the question is asking. Consider these two scenarios.

Scenario #1:
P1 = 39%
P2 = 1%
Q = 60%, and all of it arrives late
This scenario is consistent with all the statements in the argument, and this supports answer (C)

Scenario #2:
P1 = 19%
P2 = 1%
Q = 80%, and this consists of two sub-categories
Q1 = 25% --- arrive in two days days
Q2 = 55% --- arrives in three or more days
Now, all the statements in the argument are still true --- it's still true that the majority of mail --- 56% (P2 + Q2) arrives late --- but now if we look at the 44% that arrives on time, 25/44 comes from Q, the incorrectly addressed mail, and 19/44 comes P, the correctly addressed mail. Thus, the majority of mail that arrives on time, 25/44, comes from category Q, the incorrectly addressed mail. This is a scenario totally consistent with the argument in which (C) is false.

Thus, we can construct scenarios consistent with the argument that make (C) either true or false, so it is not a candidate for a "must be true" answer.

The only viable answer is (D), the OA.

Please let me know if anyone reading this has any further questions.

Mike

Apparently this is a practice LSAT Analytical Reasoning question, and it's an excellent question. I'm not sure whether MLSAT is the source, but it is discussed on this page:
https://www.manhattanlsat.com/forums/post407.html

OK, let's think in terms of categories.

Category P === correctly addressed mail
Category Q === incorrectly addressed mail

That's the big breakdown. At the outset, we have no idea of the relative breakdown of these two, but the whole "population" of mail falls into one of these two categories.

Category P has the further breakdown
Category P1 = correct addressed and not damaged ---- this is "nearly all" of Category P, and this arrives "within two business days of being sent"
Category P2 = correctly addressed by damaged in transit --- this is some very small fraction of Category P (whatever the opposite of "nearly all" is!), and it doesn't arrive quickly

We absolutely know that mail in Category P1 arrives within two days. How fast does mail in category Q arrive? We can draw absolutely no conclusion about this. We also have no idea what proportion arrives earlier and what proportion arrives late.

Given the last piece of information --- "most mail arrives three business days or more after being sent" --- from this, we absolutely know that P1 does not account for a majority of mail. If P1 is less than half of mail, we know P2 is going to account for such a small percentage that it doesn't matter, and this means Q must account for the majority of mail. This is precisely what (D) says. This is by far the best answer, the only possible right answer.

Why is (A) wrong? This directly contradicts the statement that NEARLY ALL correct addressed mail arrives within two days and therefore is not damaged.

Why is (C) wrong? Well, this one could be true, but it is not necessarily true --- it doesn't reach the standard of "must be true" for which the question is asking. Consider these two scenarios.

Scenario #1:
P1 = 39%
P2 = 1%
Q = 60%, and all of it arrives late
This scenario is consistent with all the statements in the argument, and this supports answer (C)

Scenario #2:
P1 = 19%
P2 = 1%
Q = 80%, and this consists of two sub-categories
Q1 = 25% --- arrive in two days days
Q2 = 55% --- arrives in three or more days
Now, all the statements in the argument are still true --- it's still true that the majority of mail --- 56% (P2 + Q2) arrives late --- but now if we look at the 44% that arrives on time, 25/44 comes from Q, the incorrectly addressed mail, and 19/44 comes P, the correctly addressed mail. Thus, the majority of mail that arrives on time, 25/44, comes from category Q, the incorrectly addressed mail. This is a scenario totally consistent with the argument in which (C) is false.

Thus, we can construct scenarios consistent with the argument that make (C) either true or false, so it is not a candidate for a "must be true" answer.

The only viable answer is (D), the OA.

Please let me know if anyone reading this has any further questions.

Mike

Nearly all mail that is correctly addressed arrives at its destination within two business days of being sent. In fact, correctly addressed mail takes longer than this only when it is damaged in transit. Overall, however, most mail arrives three business days or more after being sent.

If the statements above are true, which one of the following must be true?


(A) A large proportion of the mail that is correctly addressed is damaged in transit.

(B) No incorrectly addressed mail arrives within two business days of being sent.

(C) Most mail that arrives within two business days of being sent is correctly addressed.

(D) A large proportion of mail is incorrectly addressed.

(E) More mail arrives within two business days of being sent than arrives between two and three business days after being sent.

Source : LSAT PrepTest20 Q#19