Critical Reasoning

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.

Mechmeera wrote: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.

We're told that nearly all mail that is correctly addressed arrives within two business days of being sent. We're also told that most mail overall arrives three or more business days after being sent. The only way these two assertions can be compatible is if there's a lot of mail that is incorrectly addressed. We get that in option D.

DavidG@VeritasPrep wrote: We're told that nearly all mail that is correctly addressed arrives within two business days of being sent. We're also told that most mail overall arrives three or more business days after being sent. The only way these two assertions can be compatible is if there's a lot of mail that is incorrectly addressed. We get that in option D.

Here is my analysis

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.........may or may not be. cannot be inferred.

B. No incorrectly addressed mail arrives within two business days of being sent......we have no info regarding incorrectly addressed mails arrival.

E. More mail arrives within two business days of being sent than arrives between two and three business days after being sent........cannot be inferred. new info

Now between options C and D

C. Most mail that arrives within two business days of being sent is correctly addressed...........this must be true as there is no other way it can be false.

D. A large proportion of mail is incorrectly addressed........since most mail arrive late the reasons may vary. A large portion of mail can be either incorrectly addressed or damages during transit. I feel we cannot infer the this statement as this is must be true question.

David please explain?

C. Most mail that arrives within two business days of being sent is correctly addressed...........this must be true as there is no other way it can be false.

C is an instance of what's called faulty reversal. In other words, if it is true that x-->y, it's not necessarily true that y-->x. You can see this with a simple example: 'If you were admitted to HBS, then you scored above a 500 on the GMAT' is a valid statement. Now reverse them. "If you scored above a 500 on the GMAT then you were admitted to HBS" is clearly not necessarily true.

In this argument, it's true that if a letter were correctly addressed it is very likely to have been delivered within two days. But if a letter were delivered within two days it isn't necessarily the case that it is likely to have been correctly addressed.

D. A large proportion of mail is incorrectly addressed........since most mail arrive late the reasons may vary. A large portion of mail can be either incorrectly addressed or damages during transit. I feel we cannot infer the this statement as this is must be true question.

D, on the other hand, has to be true. Imagine that every letter were correctly addressed. Say there were 10 of them. We know that nearly all arrived within two days, so say that 9 of the 10 arrived within two days. This means that 1 letter arrived in 3 or more days, so we've got a 9:1 ratio in favor of letters that arrived within 2 days. But we're told that a majority of the letters arrived in 3 days or more. The only way that could be possible is if there's another category of letters, aside from those that were correctly addressed, and that a lot of letters are in this category. Thus, there must be a lot of incorrectly addressed letters.

It might also help to use some numbers to illustrate why C doesn't have to be true. Let's reuse the numbers I proposed earlier: 10 letters are correctly addressed and 9 of those arrive in two days or less. Now let's say that 100 letters were incorrectly addressed and 40 of them arrived within two days, and 60 arrived in 3 or more days. In a matrix, the info would look like this:




Looking at the table, of the 10 letters that were addressed correctly, 9 arrived within two days. But of the 49 letters that arrived within 2 days, 40 were incorrectly addressed! So you end up with the following statistics that feel paradoxical: Of the correctly addressed letters, 90% (9/10) arrived within two days. And yet of the letters that arrived with 2 days, over 80% (40/49) were incorrectly addressed.

DavidG@VeritasPrep wrote:It might also help to use some numbers to illustrate why C doesn't have to be true. Let's reuse the numbers I proposed earlier: 10 letters are correctly addressed and 9 of those arrive in two days or less. Now let's say that 100 letters were incorrectly addressed and 40 of them arrived within two days, and 60 arrived in 3 or more days. In a matrix, the info would look like this:




Looking at the table, of the 10 letters that were addressed correctly, 9 arrived within two days. But of the 49 letters that arrived within 2 days, 40 were incorrectly addressed! So you end up with the following statistics that feel paradoxical: Of the correctly addressed letters, 90% (9/10) arrived within two days. And yet of the letters that arrived with 2 days, over 80% (40/49) were incorrectly addressed.

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DavidG@VeritasPrep wrote:

Mechmeera wrote: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.

We're told that nearly all mail that is correctly addressed arrives within two business days of being sent. We're also told that most mail overall arrives three or more business days after being sent. The only way these two assertions can be compatible is if there's a lot of mail that is incorrectly addressed. We get that in option D.

Dear David ,
I am still not able to connect with the correct option. The question asks for something that must be true. How then are we able to derive that the only reason letters are delayed is due to incorrect address, there is no mention of incorrect address in the entire paragraph.
It may be because of bad weather or bad roads etc
How then are we able to make the conclusion that only incorrect address is the real culprit here.
Please tell me where am I thinking wrong.
Thanks
Teja

evs.teja wrote:

DavidG@VeritasPrep wrote:

Mechmeera wrote: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.

We're told that nearly all mail that is correctly addressed arrives within two business days of being sent. We're also told that most mail overall arrives three or more business days after being sent. The only way these two assertions can be compatible is if there's a lot of mail that is incorrectly addressed. We get that in option D.

Dear David ,
I am still not able to connect with the correct option. The question asks for something that must be true. How then are we able to derive that the only reason letters are delayed is due to incorrect address, there is no mention of incorrect address in the entire paragraph.
It may be because of bad weather or bad roads etc
How then are we able to make the conclusion that only incorrect address is the real culprit here.
Please tell me where am I thinking wrong.
Thanks
Teja

Think about a more general case. Imagine that we have a class of children. I tell you that within this class, nearly every girl has blond hair, but that the majority of all the kids in the class have brown hair. How can that be? Well, there must be another category - in this case, boys - that has enough brown haired members to create a brown-haired majority.

Same logic here, but instead of girls and boys we have correctly and incorrectly addressed letters.

We know that nearly all the correctly addressed letters arrive within two days. We know that the majority of all letters take three or more days to arrive. How can that be? There must be another category - in this case, incorrectly addressed letters - that has enough letters that arrived in 3 or more days to create a 3-or-more-day majority. (Just as there must have been many brown-haired boys to offset the numerical advantage of blond-haired girls.) Why the letters are late is irrelevant. We just need to know that the incorrectly addressed letters exist

DavidG@VeritasPrep wrote:

evs.teja wrote:

DavidG@VeritasPrep wrote:

Mechmeera wrote: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.

We're told that nearly all mail that is correctly addressed arrives within two business days of being sent. We're also told that most mail overall arrives three or more business days after being sent. The only way these two assertions can be compatible is if there's a lot of mail that is incorrectly addressed. We get that in option D.

Dear David ,
I am still not able to connect with the correct option. The question asks for something that must be true. How then are we able to derive that the only reason letters are delayed is due to incorrect address, there is no mention of incorrect address in the entire paragraph.
It may be because of bad weather or bad roads etc
How then are we able to make the conclusion that only incorrect address is the real culprit here.
Please tell me where am I thinking wrong.
Thanks
Teja

Think about a more general case. Imagine that we have a class of children. I tell you that within this class, nearly every girl has blond hair, but that the majority of all the kids in the class have brown hair. How can that be? Well, there must be another category - in this case, boys - that has enough brown haired members to create a brown-haired majority.

Same logic here, but instead of girls and boys we have correctly and incorrectly addressed letters.

We know that nearly all the correctly addressed letters arrive within two days. We know that the majority of all letters take three or more days to arrive. How can that be? There must be another category - in this case, incorrectly addressed letters - that has enough letters that arrived in 3 or more days to create a 3-or-more-day majority. (Just as there must have been many brown-haired boys to offset the numerical advantage of blond-haired girls.) Why the letters are late is irrelevant. We just need to know that the incorrectly addressed letters exist

David, sorry to bother you again but this question is getting on my nerves now.
If I believe about what you say is right i.e the only valid reason for delay is incorrect letters , then how are we eliminating option B, it is also on the same line.
Apart from that how are we eliminating A , May be the only reason the most mails got delayed is coz all of them were damaged in the transit.
Still stuck among A, B, D
Thanks
Teja