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# PT20 S4 Q19 - Good people of 7sage, I humply request your assistance once again.

Core Member
edited September 2022 233 karma

I was revisiting some old PTs and stumbled across this question. It's giving me quite the headache. JY's explanation doesn't help at all because he assumes that the amount of correctly addressed but damaged mail is a small subset of correctly addressed mail. But where does this inference come from? It could very well be that all correctly addressed mail is damaged. I don't believe there's any reasonable basis to assume that only a minority of correctly addressed mail is damaged.

I believe most other explanations for this question claim the existence of the binary of correctly addressed mail and incorrectly addressed mail as the main reason why there must be a significant amount of incorrectly addressed mail. However, I don't believe this binary is of any significance because the stimulus gives us a way for these two groups to overlap via correctly addressed mail that is damaged. Since we know nothing about the respective sizes of the two groups, this scenario should be plausible:
1000 total mail
700=damaged
Thus, most mail arrives three or more business days after being sent.

As shown above, I believe the existence of this overlap makes it such that D is a "could be true." Now, if there was no overlap, then D must be true. But as stated above, without any information about the respective sizes of each group, we can't conclude anything.

• Core Member
edited September 2022 330 karma

We actually can support the inference that damaged mail makes up only a small subset of correctly addressed mail!

Correctly addressed (CA) mail can fall into two categories: damaged in transit and not damaged. Damaged mail takes longer, and non-damaged mail absolutely always arrives within two business days.

The first sentence point-blank tells us: nearly all CA mail arrives within two business days. Since damaged CA mail arrives later than two business days, we can directly infer that nearly all CA mail is not damaged.

In your hypothetical scenario, nearly all (700/800) of the CA mail is damaged. But then nearly all of the CA mail will take a long time to arrive, and that directly contradicts the first sentence of the stimulus telling us that nearly all CA mail does arrive quickly- so it's not actually a valid hypothetical.

Having inferred that nearly all CA mail is not damaged, the only way to reconcile 'nearly all CA mail arrives quickly' with 'most mail does not arrive quickly' would be to conclude that 'most mail is not CA.' That's exactly what we get with AC D.

• Core Member
233 karma

Oh my goodness. LMAO I’m actually so shook right now. I can’t believe I missed that. My brain is doing weird things lately…thanks a lot for your help!