Nearly all mail that is correctly addressed arrives at its destination within two business days of being sent. In fac...

Irina September 25, 2019

@SeonAh-Lee,

This question requires you to apply rules of inference to a set of premises to determine a valid conclusion. Let's see what the argument is saying:

(1) Most mail that is correctly addressed arrives within two days.

Correctly addressed -> two days
We can infer that if mail does not arrive within two days, it must be incorrectly addressed.

(2) Correctly addressed mail takes more than two days only when it is damaged.

We can infer that if a correctly addressed mail + more that two days -> damaged
We can also infer that if mail is not damaged, it either must arrive within two days or it is incorrectly addressed.
~ damaged -> arrive within two days v incorrectly addressed

(3) Most mail arrives after 3 or more days.
Combined with premise (1), we know that if mail fails to arrive within two days, it must be incorrectly addressed.
This is the proper inference out of the answer choices.

Let's briefly look at the rest of the options:
(A) A large proportion of mail that is correctly addressed is damaged in transit.

Incorrect. This is in an invalid inference, the second premise only allows us to infer that if the mail is correctly addressed AND takes longer than two days, it must be damaged, but the third premise only tells us that one of these conditions is true - it takes longer than two days. Since we cannot tell whether the mail is correctly addressed is true or false, we cannot conclude that it is damaged in transit.

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

Incorrect. This is a mistaken reversal of premise (1). Premise (1) tells us that correctly addressed mail -> two business days. The only proper inference is that the mail that takes longer than that -> incorrectly addressed. We cannot make any inferences if we only know that mail is incorrectly addressed to be true as this answer choice suggests - incorrectly addressed -> ?

(C) Most mail that arrives within two days is correctly addressed.

Incorrect. This is again a mistaken reversal of premise (1). From the premise - correctly addressed -> arrives within two days, it is impossible to infer that arrives within two days -> correctly addressed because we must reverse and negate the original premise per the rules of inference.

(E) More mail arrives within 2 business days of being sent than arrives between two and three business days of being sent.

Invalid. There is not enough information in the stimulus to make this inference. The conclusion only tells us that most mail arrives three or more days after being sent, but we have no further detail to determine the proportion of mail that arrives within 2 days, 2-3 days, 3-4 days etc. This statement could be true but it is not a MUST be true as the question requires.

Let me know if this helps and if you need any further clarification.

Kath October 7, 2019

How can you diagram the "(1) Most mail that is correctly addressed arrives within two days" to be "Correctly addressed -> two days"? Wouldn't it be like "Correctly addressed ---most--- two days"?

Skylar March 1, 2020

@Kath, your logic is correct here. The sentence "Nearly all mail that is correctly addressed arrives at its destination within two business days of being sent" is diagrammed as a most statement, as the video shows. We can write this as: MCA - most - less than or equal to 2 days.

Please let us know if you have any other questions!