# RE7 | anthropic/claude-opus-5 | run 1

## 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** and the bat costs **$1.05**. The intuitive answer of $0.10 is wrong because it would make the bat $1.00 and the total only $1.10 — but the bat would then exceed the ball by just $0.90, not $1.00.

## The Algebra

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

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

\[ 2b = 0.10 \]

\[ b = 0.05 \]

**Check:** $1.05 + $0.05 = $1.10, and $1.05 - $0.05 = $1.00. Both conditions hold.

## Why It Trips People Up

This is the first item on Shane Frederick's Cognitive Reflection Test, designed to pit fast intuition against deliberate calculation. Most respondents subtract $1.00 from $1.10 and stop, ignoring that the difference between the two items must be $1.00 — which requires splitting the remaining $0.10 evenly.

Would you like the other two Cognitive Reflection Test questions?
