aaba wrote:

A study found that last year roughly 6,700 homeless people in the United States were admitted to hospitals due to malnutrition. In the same year, a little more than 7,200 nonhomeless people were admitted to hospitals for the same reason. These findings clearly show that the nonhomeless are more likely to suffer from malnutrition than are the homeless.

The answer to which of the following questions would be most likely to point out the illogical nature of the conclusion drawn above?

(A) What is the relative level of severity of the malnutrition suffered by each group cited in the study?

(B) To what extent, on average, are the nonhomeless better off financially than are the homeless?

(C) To what extent are the causes of malnutrition in the nonhomeless related to ignorance of proper dietary habits?

(D) What percentage of each group cited in the study suffered from malnutrition last year?

(E) What effect would a large increase in the number of homeless shelters have on the incidence of malnutrition among the homeless?

KAPLAN OFFICIAL EXPLANATION:

The GMAT test makers have an incredible knack for writing short, unassuming arguments that nonetheless pack a major wallop. This one's a good example. It's one of the shortest arguments you'll see, and it doesn't even contain any difficult words, but it sure gives people fits— and that's because of the statistics involved. It goes to show that it really doesn't take much more than a few well-placed statistics to, shall we say, liven things up. The first thing you might have noticed is that the argument contains both numbers and statistics. The 6,700 and 7,200 figures represent actual numbers of people, while the conclusion states what's "more likely" to happen— a clear reference to an element of probability. Knowing from the stem that the argument is fatally flawed, this should have already raised a red flag. Here's the specific lowdown: Since only 6,700 homeless people suffering from malnutrition were admitted to U.S. hospitals last year, compared to 7,200 nonhomeless people, the nonhomeless must be more likely to suffer from malnutrition. Perhaps the argument immediately struck you as a little wacky, as it well should have given the clues in the question stem.

An 800 test taker is suspicious whenever she sees raw numbers side by side in an argument with rates, percentages, or probabilities— especially in a Logical Flaw question.

We're asked to find a question whose answer would most effectively illuminate the problem with the argument, and, as strongly suggested above, this boils down to a numbers versus percentages game: We cannot figure the odds of suffering from malnutrition solely from the number of malnourished people in each group. We must also know the overall total of people in each group before we can create ratios and thus figure out the "likelihood" of suffering from this condition. The only way for this conclusion to be valid is if the total number of homeless people in the U.S. equals the total number of nonhomeless people—then the 7,200 hospitalized nonhomeless, as opposed to the 6,700 hospitalized homeless, would suggests that the nonhomeless are more likely to suffer from malnutrition. But this is clearly a ludicrous assumption (at least at the present time)—there's no way the number of homeless equals the number of nonhomeless people in the U.S. The answer to the question in the correct choice will somehow point this out, thus making the flaw in the reasoning (using raw numbers as the basis for a conclusion about likelihood) plain to see. Choice (D) provides the question whose answer would provide the information we need to correctly understand the odds. Since the U.S. has far fewer homeless people than it has people with homes, the 6,700 figure would form a far higher percentage of homeless people who suffer from malnutrition than the percentage of nonhomeless people based on the 7,200 cases of malnutrition among this group. The answer to this question would allow us to see how the raw numbers cited do not support the author's counterintuitive conclusion that the nonhomeless are more susceptible to malnutrition than are the homeless.

Go with (D).(A) goes beyond the scope of the argument. The argument involves the likelihood of suffering from malnutrition, not the relative levels of severity.

(B) also introduces a new issue—finances. No matter how much people with homes are better off financially than are the homeless, the fact remains that more nonhomeless were hospitalized for malnutrition than homeless, and the answer to this question would do nothing to reveal the illogical conclusion that's drawn from this data.

(C) introduces another new issue. The argument draws no conclusion about the causes of malnutrition within these groups, only about the likelihood of malnutrition. Nailing down the precise causes of malnutrition in one of the groups wouldn't change the numbers in the evidence nor point out the problem with the logic.

(D) is irrelevant to the argument as presented. The future possibility of remedying homelessness to some degree does not impact upon these numbers and this particular conclusion drawn from them. The reasoning still seems off, but the answer to the question in (E) will not show how the logic goes astray.

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