A very common flaw on the GMAT, and in life, is the confusion of absolute numbers and percentages. For example, which is larger, one-third of x or one-half of y? Without any information to compare x and y, we cannot answer this question. It is true that one-half is larger than one-third when applied to the same quantity, but when applied to quantities of different sizes, one-third could be much larger than one-half. For example, one-third of the population of New York City is a greater quantity than one-half the population of Boise, Idaho.
How does this play out on the GMAT? Consider the following argument:
At any given time, approximately fifteen percent of all homes in Florida are on the market. In Texas, however, only seven percent of all homes are on the market at any given time. Therefore, one will have a wider selection of homes to choose from if one looks for a home in Florida rather than in Texas.
This argument falsely assumes that the number of homes for sale in Florida is greater than the number of homes for sale in Texas, based on the fact that a larger proportion of homes in Florida are for sale. Imagine, however, that there are only 100 homes in Florida, yielding an available housing stock of 15 homes. And imagine that there are 1000 homes in Texas, yielding an available housing stock of 70 homes. In this case, the conclusion of the argument would not hold true. (Bonus: At least what percentage of the number of homes in Texas would the number of homes in Florida have to be in order for the argument to hold true? Answer found at bottom of page.)
The relationship between number and percent can also go the other way. Consider the following argument:
More people in California own air conditioners than do people in Illinois, Indiana, and Ohio combined. Therefore, Californians are clearly more concerned with their physical comfort than are people in those other three states.
This argument falsely assumes that the percentage of people who own air conditioners is higher in California than it is in Illinois, Indiana, and Ohio together, based on the fact that the number of people who own air conditioners is greater in California. Imagine, for example, that the population of California were 10,000,000, of whom 1,000,000 owned air conditioners - representing 10%. Imagine as well that the combined population of Illinois, Indiana, and Ohio were 1,000,000, of whom 900,000 owned air conditioners. Now, it would indeed be true that more people owned air conditioners in California, but it would represent only 10% of the population, whereas 90% of the population of the other states owned air conditioners. In these circumstances, it would be difficult to maintain that Californians care more about their physical comfort. When dealing with arguments that involve comparisons of quantities and/or percents, be sure you determine whether the comparison is valid.
(Bonus answer: In order for the argument to be valid, it would have to be true that 15% of homes in Florida is greater than 7% of homes in Texas. We can represent this as an equation:
. If we isolate F, we get:
Therefore, the number of homes in Florida has to be greater than 47% of the number of homes in Texas.)
Next week, we will look at flaws in arguments involving claims of causation.
