Bunuel wrote:

School official: The rate of childhood obesity in Paceville has decreased by 50% in the last five years, whereas the rate of childhood obesity in Aratown has increased by 50% in the same time period. Children in the town of Paceville are obviously much less likely to be obese than are children in Aratown.

This argument fails to consider which of the following questions?

A. How many children were obese in Paceville and Aratown five years ago?

B. Were rates of childhood obesity in Paceville higher than those in Aratown five years ago?

C. Has there been any migration between Paceville and Aratown in the last five years?

D. What were the rates of childhood obesity in Paceville and Aratown five years ago?

E. What percent of children are likely to remain obese for five years or more?

Consider the following case:

Over the past five years, Aratown's childhood obesity rate has increased from 2% to 3%, a 50% increase.

Over the past five years, Paceville's childhood obesity rate has decreased from 6% to 3%, a 50% decrease.

The result:

Each town currently has the SAME childhood obesity rate: 3%.

Implication:

If Paceville's rate five years ago was exactly three times Aratown's rate five years ago -- in the case above, 6% versus 2% -- then children in the two towns currently have the same likelihood of being obese.

For Paceville's likelihood to be much lower than Aratown's, it would have to be true that -- five years ago --

Paceville's childhood obesiity rate was MUCH LESS THAN THREE TIMES Aratown's childhood obesity rate.

Only the answer to D will enable us to determine whether the statement in blue is true.

Thus, the argument is flawed because it fails to consider D.

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