PrepTest 155, Section 4, Question 21
All of the students at Harrison University live(56 more words not shown)
If the statements above are(10 more words not shown)
- AMore than 38(14 more words not shown)
- BMore than 50(13 more words not shown)
- CMore students at(8 more words not shown)
- DHarrison students living(17 more words not shown)
- ENight classes at(10 more words not shown)
Reading the argument
If one residence is below the university-wide percentage, the other has to pull that percentage up. Every Harrison student lives in either Pulham or Westerville. Across the whole university, 38 percent take at least one night class. In Westerville, only 29 percent do. So Pulham's percentage must be above 38.
Suppose Pulham were at 37 percent. Combining a group at 37 percent with a group at 29 percent cannot produce an overall figure of 38 percent. Both groups would be below the number we're trying to reach. Even putting Pulham at exactly 38 wouldn't work, because Westerville's lower rate would pull the combined result below 38.
What we’re looking for
We don't need to know how many students live in each complex to make that inference. The group sizes determine how far above 38 Pulham must be, but it must be above 38. For the must-be-true question, that is the firm conclusion to keep in mind. Don't turn it into a claim about which complex has more students.
Working the answers
- ACorrect
Pulham's percentage must exceed 38 to balance Westerville's 29 and produce the overall 38. This follows because the two complexes include all the students. There isn't a third group outside them that could raise the university's percentage while both known groups stayed below it.
- B
A higher percentage within Pulham doesn't mean Pulham supplies most of the night students. Its total population could be much smaller.
For example, imagine 800 Westerville students, 232 of whom take a night class. That's 29 percent. Now imagine 200 Pulham students, 148 of whom take one. Together, 380 out of 1,000 students take a night class, exactly the required 38 percent. Pulham's rate is much higher, yet it supplies only 148 of those 380 night students, less than half. B therefore need not be true.
- C
The percentages don't establish which complex is larger. Different population sizes could work with different Pulham percentages. We can establish the direction of Pulham's rate relative to 38 without establishing the relative sizes of the residences.
- D
'At least one' includes people taking one, two, or more night classes. The figures don't break those groups apart. We cannot compare how likely students in the two complexes are to take more than one night class from information that groups all night-class students together.
- E
A small share of classes being held at night and 38 percent of students taking at least one of them doesn't establish average class size. We don't know how many day classes each student takes or how students are distributed among individual classes. The passage counts students with at least one night class, not all enrollments in day and night courses.
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