Maths in Critical Reasoning

Consider the following official argument:

In the United States, of the people who moved from one state to another when they retired, the percentage who retired to Florida has decreased by three percentage points over the last ten years.  Since many local businesses in Florida cater to retirees, these declines are likely to have a noticeably negative economic effect on these businesses and therefore on the economy of Florida.

Which of the following, if true, most seriously weakens the argument given?

  1. People who moved from one state to another when they retired moved a greater distance, on average, last year than such people did ten years ago.
  2. People were more likely to retire to North Carolina from another state last year than people were ten years ago.
  3. The number of people who moved from one state to another when they retired has increased significantly over the past ten years.
  4. The number of people who left Florida when they retired to live in another state was greater last year than it was 10 years ago.
  5. Florida attracts more people who move form one state to another when they retired than does any other state.

The argument’s conclusion is that Florida’s economy will suffer negative consequences. The central premise is that of the people moving from one state to another, a smaller percentage are going to Florida now than were going to Florida ten years ago. The assumption is that a smaller percentage moving to Florida means fewer people moving to Florida.

This line of reasoning is no more valid than asserting that Lebron shooting a lower percentage in 2015 than in 2014 means he made fewer shots in 2015. Just as we needed to know if there was a change in the total number of shots Lebron was taking in order to evaluate whether the change in percentage was meaningful, we need to know if there was a change in the total number of people moving from one state to another in order to properly assess whether it’s meaningful that a smaller percentage are moving to Florida.

Let’s evaluate the answer choices one by one:

  1. The distance people moved doesn’t matter. Out of Scope. A is out.
  2. North Carolina isn’t relevant to what’s happening in Florida. Out of Scope. B is out.
  3. This is the logical equivalent of pointing out that Lebron took many more shots in 2015 than in 2014. If far more people are moving from one state to another now than were moving from one state to another ten years ago, it’s possible that more total people are moving to Florida, even if a smaller percentage of movers are going to Florida. This looks good.
  4. First, the number of people leaving Florida has no bearing on whether a smaller percentage of people moving to Florida will have an impact on Florida’s economy. Moreover, we’re trying to weaken the idea that Florida’s economy will suffer. If more people are leaving Florida, it would strengthen the notion that Florida’s economy will endure negative consequences. That’s the opposite of what we want. D is out.
  5. Tempting perhaps, but ultimately, irrelevant. Just because Lebron led the league in field goals made in both 2015 and 2014 (he didn’t, but play along), doesn’t mean he didn’t make fewer field goals in 2015. E is out.

The answer is C.  If more people are moving from state to state, a lower percentage moving to Florida may not mean that fewer people are coming to Florida, just as Lebron’s dip in field goal percentage does not mean he was making fewer field goals if he was taking more shots.

Takeaway: The “math” concepts tested in Critical Reasoning are, in fact, logic concepts. By connecting the prompt to a more concrete real-world example, we make this logic far more intuitive and easily graspable when we encounter it on the test.