Logical reasoning PrepTest 124 · Section 2 · Question 25

Incorrect. Since overworked" is the necessary condition of the conditional, we only know about some overworked students and we'll never be able to draw an inference about most of them based on this set of facts. (Yes, the sufficient condition is about all of the noted group, and the necessary condition is about some of that gro

Correct. Argument or Facts:
Facts

Question Type:
Must be True

Stimulus Summary:
(1) Serious students—most—Happy students
(2) Serious students—most—Grad students
(3) Grad students → Overworked

Answer Anticipation:
Must be True question with a mix of quantified and conditional statements? Since there are only three statements, and two of them don't share a term (1 and 3), we'll only need to consider two combinations, so we should make those inferences up front.

First, can we combine 1 and 2? Yep. We can combine two most statements when they share a first term. It gives us a some inference:
1+2) Happy students—some—Grad students

Second, can we combine 2 and 3? Yep. When the sufficient condition of a conditional shows up in a most (or a some) statement, we can draw an inference. However, while most inferences involving quantifiers are some inferences, there's one exception—one combo of a conditional and a most statement leads to a most inference, and this is it. (To walk through it quickly, if there are 100 serious students, at least 51 are grad students, and all 51 of them are overworked, so 51/100 or most serious students are overworked):
2+3) Serious students—most—Overworked

Normally, we'd be done. However, we have a new most statement—the combo of 2 and 3. Can that be combined with another statement? Sure—it shares a term with statement 1, and they are two most statements with the same first term, so we can draw a similar inference to the combination of 1 and 2:
1+2+3) Happy students—some—Overworked

One of these three will almost certainly be the answer!

Answer Explanation:
This answer is the valid combination of all three conditionals, so it's the correct answer!

Key Takeaway:
Learn your quantifier inference rules. Love your quantifier inference rules. They're not intuitive, but you can memorize them for a few points on the exam!

Incorrect. Similar to (A), we know only about some overworked students, so this answer about all of them is too strong.

Incorrect. Happy students are a term in a most statement, and we can't contrapose those, so we can't learn anything about unhappy students. Most serious students being happy does not imply that some serious students are unhappy—quantifier statements are guarantees of a minimum, not a maximum. (E.g., it's true to say that most humans are born on Earth—even though all humans are.)

Incorrect. We learn only about most serious students, so this answer about all of them is too strong.