abrakadabra21 wrote:

In the years 1971 to 1980, the population of the state prison system was on average about 82 percent of maximum occupancy. During those years, the average number of prisoners entering the system each year was equivalent to 9.1 percent of maximum occupancy. From the years 1981 to 1984, the average number of prisoners entering the system each year fell to 7.3 percent of maximum occupancy, yet the population of the state prison system rose to almost 89 percent of maximum occupancy.

Which of the following, if true, helps to resolve the apparent discrepancy?

(A) The average sentence of a prisoner in the state system increased from 1981 to 1984.

(B) Beginning in 1981, many of those entering the state prison system had been transferred from prisons in other states.

(C) Between 1981 and 1984, the percentage of prisoners incarcerated for violent crimes increased by 26 percent.

(D) In 1981, a legislative fact-finding committee proposed a revision of the state's parole and work release programs.

(E) Between 1971 and 1984, the proportion of active criminals actually caught and incarcerated in the state prison system has steadily increased.

KAPLAN OFFICIAL EXPLANATION:

Here we have a case in which an apparent paradox stems from a misunderstanding of statistics. Clear up the misunderstanding, and the paradox vanishes—that is, the rise described at the end no longer seems surprising.

An 800 test taker knows that numbers and statistics can be fertile ground for all sorts of questions. She knows these questions may ask her to find the choice that points out a flaw or weakness in an argument, or, as in this case, that resolves an apparent discrepancy. Either way, she recognizes that understanding the ways in which numbers and percentages are used—or misused—is the key to answering any question concocted out of a numerical or statistical situation.

Here are the facts: In the early years, the prisons were 82% full, and just over 9% of the total possible occupancy arrived each year in the form of new prisoners. Now that the latter figure is down to 7.3%, the author is surprised that the prisons are more full: 89% full. She evidently expects that as one figure drops, so should the other. The key is seeing that she is focusing on the trend in incoming prisoners only, when the totals take into account all prisoners. Consider the long-termers. If the average length of sentences of all prisoners is increasing, then it's small wonder that the prisons are more crowded now, even if a smaller percentage of the inmates are newcomers. That's what (A), the correct answer, is all about.

(B) Where the prisoners came from has no impact on how many are, or should be, here in this state.

(C) Nothing in the evidence concerns the nature of crime, so no information about what landed these people in jail in the first place can resolve the paradox.

(D) A "proposed revision" is way too weak. Was it instituted? And even if it was, what effect would it have? There's no way to know, so (D) is irrelevant and does nothing to clear up what the author considers to be a surprising result.

(E), even if true, begs the question of why the percentage of the prison total entering the system is lower than years ago, but the prisons are fuller. All (E) says is that fewer criminals are getting off scot free.

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