# Percentage vs. Absolute Number

We are prone to assume that if something occurs with a high percentage then there must be a large amount of it. The writers of the LSAT like to capitalize on this tendency. The following example will illustrate.Example

Nutritionists have recommended that people eat more fiber. Advertisements for a new fiber‑supplement pill state only that it contains "44 percent fiber."
The advertising claim is misleading in its selection of information on which to focus if which one of the following is true?

- There are other products on the market that are advertised as providing fiber as a dietary supplement.
- Nutritionists base their recommendation on medical findings that dietary fiber protects against some kinds of cancer.
- It is possible to become addicted to some kinds of advertised pills, such as sleeping pills and painkillers.
- The label of the advertised product recommends taking 3 pills every day.
- The recommended daily intake of fiber is 20 to 30 grams, and the pill contains one‑third gram.

Solution

Although a pill with 44 percent fiber sounds good, the more important issue is “How much of the fiber we need each day does the 44 percent represent?” If we need 100 grams of fiber daily and the pill though almost half fiber contains only one gram of fiber, then we would have to take 100 pills a day to get our daily intake. In this case, the fact that the pill is 44 percent fiber is insignificant, and it is therefore misleading for the advertisement to focus on the percentage of fiber instead of the absolute amount. The answer is (E).

Example

The number of North American children who are obese—that is, who have more body fat than do 85 percent of North American children their age—is steadily increasing, according to four major studies conducted over the past 15 years.
If the finding reported above is correct, it can be properly concluded that

- when four major studies all produce similar results, those studies must be accurate
- North American children have been progressively less physically active over the past 15 years
- the number of North American children who are not obese increased over the past 15 years
- over the past 15 years, the number of North American children who are underweight has declined
- the incidence of obesity in North American children tends to increase as the children grow older.

Solution

Notice that the percentage of children who are obese is by definition
For example, suppose in a particular population of 100 people, 15 are obese and 85 are not obese. Then the rate of obesity would be 15 percent. If 20 years later there are 200 people in the population, then for the obesity rate to remain 15 percent there would have to be 15
Most people who miss this question assume that the general population is not increasing. In this case, as the absolute number of obese children increases, the absolute number of non-obese children must decrease. But then, of course, the 15 percent figure would increase.

__always 15 percent__: Obese children are those “who have more body fat than do 85 percent of … children their age.” So if the absolute number of obese children increases, there must be a proportionate increase in the absolute number of children who are not obese. Otherwise, the 15 percent figure would change.*more*obese people and 85*more*non-obese people. The answer is (C).