NB: This is a modified version of a post from another forum that might be of interest to readers of this Blog.

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As part of my effort to explain the power and fallibility of System 1 thinking to my Professional Responsibility students, I provided them with the questions from Shane Frederick‘s Cognitive Reflection Test (CRT). For those not familiar with the CRT, it consists of three questions that help illuminate the errors that can occur through quick, intuitive thinking.

Here are the CRT questions [spoiler alert for those who haven’t seen the test, the answers with explanations are at the end of this post]:

(1) A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost?

(2) If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?

(3) In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?

I’ll be curious to see how my students respond and whether they exceed the performance of the approximately 3400 undergraduate students who took the test in Frederick’s original study, which was **1.24 out of 3** (although there was a wide divergence of results, depending on the school). Interestingly, the undergraduates averaged slightly better than 252 trial judges in Florida who took the CRT as part of a study by Chris Guthrie, Jeffrey Rachlinski, and Andrew Wistrich, entitled *Blinking on the Bench: How Judges Decide Cases*.

The CRT is one way I’m exploring the foundations of BLE with my students. I’ll share others in the future (for example, this short video provides a quick overview of fast v. slow thinking). And, if anyone has used the CRT or other methods to teach any aspect of BLE, I’d be interested to hear about your experiences.

[As some may have seen, the CRT has generated publicity in the last few years for its role in studies of whether performance on the test predicts religious belief — here’s a sample].

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Here are the answers and explanations for the CRT provided by the authors of the *Blinking at the Bench* study (pp. 10-11, footnotes omitted):

“Each of the three CRT items has a correct answer that is easy to discern upon reflection, yet each also has an intuitive—but incorrect—answer that almost immediately comes to mind. Consider the first question. For many people, the answer that immediately jumps to mind is ten cents. Though intuitive, this answer is wrong, as a bit of reflection shows. If the ball costs ten cents and the bat costs one dollar more, the bat must cost $1.10. Adding those two figures together, the total cost of the bat and ball would be $1.20, not $1.10. Therefore, the correct answer is five cents—the ball costs five cents, the bat costs $1.05, and together they cost $1.10.

For the second question, the answer that immediately jumps to mind is 100 minutes. Though intuitive, this answer is also wrong. If five machines make five widgets in five minutes, then each machine makes one widget in that five-minute time period. Thus, it would take only five minutes for 100 machines to produce 100 widgets, just as 200 machines would make 200 widgets during that same period.

The third question immediately invites an answer of twenty-four days, which is wrong. The correct answer—obvious upon reflection—is forty-seven days. If the patch of lily pads doubles each day and covers the entire lake on the forty-eighth day, it must cover half the lake the day before.”