# RE7 | anthropic/claude-opus-5 | run 2

## Prompt

A bat and a ball cost $1.10 together. The bat costs $1.00 more than the ball. How much does the ball cost?

## Response

The ball costs **$0.05** (5 cents), and the bat costs **$1.05**. The intuitive answer of 10 cents is wrong because it would make the bat only 90 cents more than the ball, not a full dollar.

## The Algebra

Let \( b \) be the ball's price:

\[ b + (b + 1.00) = 1.10 \]

\[ 2b = 0.10 \]

\[ b = 0.05 \]

## Verification

| Item | Cost |
|---|---|
| Ball | $0.05 |
| Bat | $1.05 |
| Total | $1.10 |
| Difference | $1.00 |

This is the best-known item from Shane Frederick's Cognitive Reflection Test, designed to measure whether people override a fast, wrong gut answer with deliberate reasoning. Most respondents — including a majority of students at elite universities — answer 10 cents on first pass.

Want the other two questions from the Cognitive Reflection Test?
