Most parents who are generous are good parents, but some self-centered parents are also good parents. ███ ███ ████ ███████ █████ ███ ███████████████ ████ ███ ████ ██████████
This question gives us a bunch of quantified facts about parents. They're not telling us a story or making an argument. They're just a set of rules about what proportion of parents have various qualities. That's a sign we should engage the formal logic side of our brain and diagram the statements.
Since all of the facts are about parents, we can mentally track "parents" as the domain.
Statement 1: generous -most-> good
Statement 2: self-centered <-some-> good
Statement 3: good → good listener
In English: over half of generous parents are good parents, at least one self-centered parent is a good parent, and all good parents are good listeners.
Do any of these facts, when connected with another fact, produce a valid inference?
Statement 1 + Statement 3
Most generous parents are good parents. All good parents are good listeners. So most generous parents are good listeners.
generous -most-> good → good listener
—
Thus, generous -most-> good listener
Statement 2 + Statement 3
Some self-centered parents are good parents. All good parents are good listeners. So some self-centered parents are good listeners.
self-centered <-some-> good → good listener
—
Thus, self-centered <-some-> good listener
Statement 1 + Statement 2
Is there a valid inference from combining the first two statements? No. There's never an intersecting-set style inference from "most" plus "some." The generous parents and self-centered parents might just be different groups within the set of good parents.
The correct answer almost certainly comes from one of these two inferences:
Statement 1 + Statement 3: Most generous parents are good listeners.
Statement 2 + Statement 3: Some self-centered parents are good listeners.
Keep in mind that "some" relationships are reversible. If at least one self-centered parent is a good listener, that also means at least one good listener is a self-centered parent.
If all of the statements ██ ███ ███████ ███ █████ █████ ███ ██ ███ █████████ ████ ████ ██ █████
All parents who ███ ████ █████████ ███ ████ ████████
We don't know anything about all parents who are good listeners. "Good listener" sits on the right side of the only universal statement:
good (parent) → good listener
This tells us all good parents are good listeners, not that all good listeners are good parents. If you like (A), you're reading the conditional backwards. It's possible that tons of good listeners still aren't good parents.
Some parents who ███ ████ █████████ ███ ███ ████ ████████
Based on the contrapositive of Statement 3, we can prove that all parents who are not good listeners are not good parents. But that doesn't prove there must be some good listeners who aren't good parents.
Think about it this way. We know good parents are a subset of parents who are good listeners. But it's possible that those two sets are exactly the same set. Weird and probably not true in real life, but logically possible based on what we're given. So even though there could be some good listeners who aren't good parents, we can't say there must be.
Most parents who ███ ████ █████████ ███ █████████
We don't know anything about most parents who are good listeners. Just like with (A), "good listener" sits on the right side of the conditional in Statement 3. We can't read that conditional backwards to reach a conclusion about all or most good listeners.
Some parents who ███ ████ █████████ ███ ██████████████
This is one of the inferences we anticipated. Some self-centered parents are good parents (Statement 2). All good parents are good listeners (Statement 3). Chain them together:
self-centered <-some-> good → good listener
—
Thus, self-centered <-some-> good listener
And since "some" is reversible:
good listener <-some-> self-centered
Some parents who are good listeners are self-centered.
Fewer self-centered parents ████ ████████ ███████ ███ ████ ██████████
If you like this answer, it's probably because "most parents who are generous" just sounds like it's about a greater number of parents than "some self-centered parents."
Two problems. First, "some" doesn't have to be a smaller proportion than "most." "Most" means over 50%. "Some" means at least one. It's completely silent on the upper limit.
Second, even setting that aside, "most" and "some" are proportions of their respective groups, not absolute numbers. What if there are 100 generous parents and 1 million self-centered parents? Over 50% of 100 is a much smaller number than even 1% of 1 million. Without knowing the size of each group, we can't compare the totals.