PrepTest 119, Section 3, Question 11
In early 1990, Queenston instituted a tax increase(50 more words not shown)
If the statements above are(16 more words not shown)
- ANo classes in(12 more words not shown)
- BThe total number(12 more words not shown)
- CThe operating budget(13 more words not shown)
- DMost teachers who(15 more words not shown)
- EThe quality of(10 more words not shown)
Reading the argument
More teachers sounds like a way to give each student more attention. But before deciding whether this was a good use of the money, look at what happened to the numbers. The system added 30 percent more teachers, yet the average number of students per teacher stayed the same. How could that happen? The number of students must have risen too.
Use simple numbers. Suppose there were 100 teachers and 2,000 students: 20 students per teacher. After the increase, there would be 130 teachers. If enrollment stayed at 2,000, each teacher would have fewer students on average. To keep the average at 20, enrollment would have to rise to 2,600. We don't need the actual enrollment to see the relationship.
What we’re looking for
The question asks what must be true. Our prediction is the increase in students. Perhaps families moved into Queenston, or more children switched into its schools. We don't know why enrollment rose, and we don't have to. The unchanged ratio and increased teacher count establish that it did.
Working the answers
- A
We don't know what happened in any particular class. Enrollment in calculus could have risen while enrollment in another course fell. A statement about the whole system's average doesn't tell us that every class avoided an increase. In fact, the system's total student population increased.
- BCorrect
With more teachers and the same average number of students per teacher, the system must also have more students. Keeping the student count fixed would lower the ratio. B states the conclusion we can draw without guessing where those additional students came from.
- C
The 30 percent describes the increase in teachers, not the increase in the operating budget. A school budget pays for things besides teachers, and we aren't told what each additional teacher cost. We cannot transfer the percentage from one quantity to the other.
- D
A larger teaching staff doesn't establish that most of the original teachers stayed. The system could replace many departing teachers and hire enough additional people to increase its total. We know the final size relative to the initial size, not which individuals remained.
- E
More funding or more teachers might help education, but the passage doesn't establish better educational quality. It gives staffing and enrollment information. Whether students learned more, received better instruction, or otherwise benefited is a separate question.
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