Logical reasoning PrepTest 106 · Section 2 · Question 19

NA

Must Be True Questions

Correctly addressed mail --most--> Arrives at destination within 2 business days Correctly addressed mail AND ~Arrives at destination within 2 business days → Damaged in transit Mail --most--> ~Arrives within 2 business days

This is a bit of a frustrating Must be True question. It has conditional logic and quantifiers, but it doesn’t seem to nicely work together. Let’s work through our diagram and then dig into what we can infer. The first line is a most quantified statement (“Nearly all”) about correctly addressed mail. The second is conditional (“only when” introducing a necessary condition). We rephrased “longer than this” as the negation of arriving within 2 business days in the hopes that we can combine these statements. Finally, the last statement is another most quantified statement (“most”), this time about mail - but note that all other instances of mail are about “correctly addressed mail,” so this is a new term. With all that noted, we can see that combinations of statements are hard to draw since terms shift around. The two most statements would need to share a first term for a traditional inference, but they don’t. And the conditional would need to share it’s sufficient condition with either term in the most statements to combine them, but the sufficient condition of that conditional includes two terms, and the most statements don’t have both, so there’s not a solid inference to be drawn from there, either. However, we can get a bit fancy here. ~Arrive within 2 business days is a shared term, between statements #2 and #3, so we should see if we can get them in a form that will let us combine them. We know we can’t change up a most statement, but there are some ways to rearrange a complex conditional. To draw an inference, we would need to get the ~Arrive within 2 business days as the sole sufficient condition in the conditional. Here, we know: Correctly addressed mail AND ~Arrives at destination within 2 business days → Damaged in transit Does that tell us anything about mail that doesn’t arrive at its destination within 2 days? It does - it was either correctly addressed but then damaged in transit, or it wasn’t correctly addressed: ~Arrives at destination within 2 business days → ~Correctly addressed OR Damaged in transit Now, the sufficient condition overlaps with the second term in statement #3, which allows us to draw a most inference: ~Arrives at destination within 2 business days --most--> ~Correctly addressed OR Damaged in transit Let’s find an answer reflecting this.