A shirt and a hat together cost $150. The shirt costs exactly $100 more than the hat. How much does the hat cost?
Most people answer $50 immediately. It feels right - the numbers split cleanly, the reasoning seems obvious. But $50 is wrong. If the hat were $50, the shirt would be $150, making the total $200. Setting the hat at x gives the shirt as x + 100, so 2x + 100 = 150, meaning x = 25. The hat costs $25. The shirt costs $125.
The answer that feels correct is not correct. And the interesting thing is that knowing this in advance - being told that your first answer will be wrong - does not reliably stop you from producing it.
What It Is
Simple logic is a cognitive bias in which fast, intuitive thinking produces an answer that feels correct but is wrong, on problems that actually require slower, more effortful reasoning to solve correctly.
The framework comes from dual-process cognition. System 1 thinking is fast, automatic, and heuristic - it produces good-enough answers quickly. System 2 thinking is slow, deliberate, and analytic - it checks the work and catches errors. Simple logic bias occurs when System 1 produces a confident, plausible-feeling answer on a problem that needs System 2, and System 2 is not triggered to intervene.
The CRT - Three Classic Illustrations
Shane Frederick's Cognitive Reflection Test consists of three questions, each designed to produce a strong intuitive answer that is wrong. They have been widely used in research on reasoning and decision-making.
Question 1 (Bat and Ball): A bat and a ball together cost $1.10. The bat costs $1.00 more than the ball. How much does the ball cost? Intuitive answer: $0.10. Correct answer: $0.05.
Question 2 (Machines and Widgets): If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets? Intuitive answer: 100 minutes. Correct answer: 5 minutes.
Question 3 (Lily Pad): A patch of lily pads doubles in size each day. It takes 48 days to cover the entire lake. How long to cover half the lake? Intuitive answer: 24 days. Correct answer: 47 days.
In Frederick's original research, average CRT scores across university populations varied substantially - from under 1 to over 2 out of 3 - reflecting differences in reflective thinking style rather than general intelligence. Low CRT scores are associated with greater susceptibility to framing effects and more impulsive decision-making in economic tasks.
A Decision in Context
The shirt-and-hat puzzle at the top of this article is the approved illustration: a problem where the intuitive answer ($50) is wrong, the correct answer ($25) requires only a moment's algebra, and yet the intuitive answer is produced with confidence by most people, including those who know they are supposed to slow down.
The approved example captures what makes simple logic bias consequential: it is not that people cannot do the reasoning. It is that the intuitive answer arrives with such conviction that the reasoning is not attempted.
Why It Matters
Simple logic bias matters whenever a real decision involves numbers, ratios, rates, or conditional logic - not just on academic puzzles. Investment decisions, probability assessments, risk evaluations, and strategic planning all involve relationships between numbers where the intuitive answer is often incorrect and the stakes of the error are high.
Failing to override intuitive answers can lead to poor judgments in financial choices, medical decisions, risk assessments, and strategic planning. The bias does not produce random errors - it produces consistent errors in predictable directions, which means the mistakes can be anticipated and guarded against.
The Common Misunderstanding
Simple logic bias reflects low intelligence or poor mathematical ability. Research is clear that it does not. Performance on the CRT correlates weakly with IQ. It primarily reflects thinking style - the extent to which a person tends to check their intuitions before accepting them. The same person who scores highly on the CRT in a calm setting can show the bias under time pressure or cognitive load.
A second misunderstanding: the bias only appears on mathematical problems. The same mechanism - System 1 producing a fluent, confident answer that System 2 would revise if engaged - shows up in verbal reasoning, causal inference, and many everyday judgment contexts that trigger intuitive responses.
See Simple Logic in everyday decisions
Pick a life context to see how this bias can show up outside the textbook.
Quick Pricing Call Leads to Overstock
A product lead trusts her gut feeling about a bundle price and orders too many units, only to discover the math was off after the launch.
Scenario
Maria, a product lead at a midsize electronics firm, reviews a new accessory bundle. Her gut tells her the bundle should sell for eighty dollars because the main item costs sixty dollars and the accessory seems like it should be twenty dollars. She places an order for five hundred units based on that price, expecting forty thousand dollars in revenue. After the launch she learns the accessory actually costs thirty dollars, making the true bundle cost ninety dollars. The revenue projection collapses and she faces excess inventory.
Where The Bias Enters
Maria's fast intuition (System 1) gave her a price that felt right because the numbers appeared to split evenly, and she did not engage the slower, effortful check (System 2) that would have revealed the true cost.
Decision Check
Before confirming the order she could write down the component costs, add them, and compare the sum to her intuitive price, or ask a teammate to verify the arithmetic.
This scenario is illustrative. It explains the pattern and does not claim a documented public case.
Sources
- Frederick, Shane. Cognitive reflection and decision making.
- Toplak, M. E., West, R. F., & Stanovich, K. E. Assessing miserly information processing: An expansion of the Cognitive Reflection Test.
- Dobelli, Rolf. The Art of Thinking Clearly.