PrepTest 124, Section 2, Question 25
Most serious students are happy students, and most(16 more words not shown)
Which one of the following(8 more words not shown)
- AMost overworked students(3 more words not shown)
- BSome happy students(2 more words not shown)
- CAll overworked students(3 more words not shown)
- DSome unhappy students(4 more words not shown)
- EAll serious students(2 more words not shown)
Reading the argument
These two majorities have to overlap.
Start with the same group each time: serious students. More than half are happy, and more than half go to graduate school. You can't put two separate majorities inside that one group without sharing at least some people.
Imagine 100 serious students. If 51 are happy and 51 go to graduate school, that's 102 group memberships among 100 people. At least two people must belong to both groups. The actual figures needn't be 51 percent; the point is that each group exceeds half of the same total.
Now use the final sentence. Every graduate student is overworked. That includes the happy graduate students we've just established must exist. Those people are both happy and overworked.
What we’re looking for
For the inference question, we can look for that modest conclusion. We know there is some overlap; we don't know that happy students make up most of all overworked students.
Working the answers
- A
We haven't counted the whole overworked group. There might be thousands of other overworked students outside the small overlap we established. Knowing some are happy doesn't tell us that most are. The original majorities concern serious students, not overworked students as a whole.
- BCorrect
Some serious students must be both happy and in graduate school because both groups contain a majority of the serious students. All of those graduate students are overworked. Therefore, at least some happy students are overworked. We can follow that connection without making any claim about what percentage of overworked students are happy.
- C
Going to graduate school doesn't require being a serious student under these facts. An unserious graduate student would still be overworked, since the last sentence covers all graduate students. There might also be overworked students outside graduate school. C rules out possibilities the passage leaves open.
- D
This could happen, but we haven't established it. “Most serious students are happy” allows all serious students to be happy, and nothing requires a graduate student to be unhappy. Our guaranteed overlap is between happy students and graduate students, not unhappy students and graduate students.
- E
Most serious students go to graduate school, so those students must be overworked. But some serious students could remain outside graduate school and not be overworked. The passage doesn't rule that out. It also doesn't say students outside graduate school can never be overworked; it simply leaves their status unsettled.
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