noboru 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.
fameatop wrote:
Hi Mike,
I am not able to understand why option C is incorrect & D is correct. Can you kindly throw some light on the same. Waiting eagerly for your detailed explanation.
Regards, Fame
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:
http://www.manhattanlsat.com/forums/post407.htmlOK, 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
Let the number of mails be 100.
Since 'most' means more than half, let us say 51 out of these 100 take more than 3 days to arrive.
Correctly addressed mails that do not get damaged = 0.95x ( This takes less than 2 days to get delivered)
Correctly addressed mails that get damaged in transit = 0.05x (This takes more than 2 days to get delivered)
49 mails get delivered on time, so 0.95x = 49 , X = 51.5 mails ( Lets say 51 or 52)
In this scenario, mails with incorrect delivery addresses do not make a larger proportion of the mails than those that were correctly addressed. So I don't see how D can be the right option. Moreover, large is a very vague word. I usually find LSAT questions exceptionally well structured, and this is definitely not one of them.