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Considered to be among the most challenging and concise intelligence quotient (IQ) assessments globally, this brief, three-question exam stumps a vast majority, with over 80% of individuals unable to pass. Known as the Cognitive Reflection Test, this demanding brain teaser presented a significant challenge in a 2005 research paper by MIT Professor Shane Frederick, achieving a mere 17% success rate among test takers.
Despite diverse educational backgrounds and even among individuals from esteemed institutions like Harvard and Yale, test participants found the assessment remarkably difficult. Professor Frederick noted that while the solutions to the Cognitive Reflection Test questions are straightforward once clarified, the challenge lies in overcoming initial, intuitive—but incorrect—responses. Recently gaining renewed attention online, many are now trying their hand at this perplexing challenge to gauge their cognitive abilities.
The Cognitive Reflection Test Questions
Test your problem-solving skills with these three logic puzzles:
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Question 1:
A bat and a ball together cost $1.10. The bat is priced $1.00 higher than the ball. What is the cost of the ball?
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Question 2:
If 5 machines can produce 5 widgets in 5 minutes, how long would it take 100 machines to produce 100 widgets?
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Question 3:
In a lake, a patch of lily pads doubles in size daily. If it takes 48 days for the patch to cover the entire lake, how many days would it take to cover half of the lake?
Common Incorrect Responses
Many test-takers intuitively provide these incorrect answers:
- 10 cents
- 100 minutes
- 24 days
Professor Frederick highlighted that even a brief moment of contemplation reveals the flaw in the common, incorrect answer for the first question. He noted, “A moment’s reflection reveals that the price difference between $1.00 and 10 cents is only 90 cents, not the required $1.00 as stated in the problem.” He further explained that identifying this error is crucial to solving the puzzle, as almost everyone who avoids the “10 cents” trap typically arrives at the accurate solution.
Correct Answers to the Cognitive Reflection Test
Here are the accurate solutions to the brain teaser:
- Five cents
- Five minutes
- 47 days
Answer Explanations
Understanding the logic behind the correct answers is key to grasping the test’s principles:
Question 1 Explanation:
Let’s denote the ball’s cost as ‘X’. The bat costs $1.00 more than the ball, making its cost ‘X + 1’. The combined cost is $1.10, so we have the equation: X + (X + 1) = 1.10. Simplifying this, we get 2X + 1 = 1.10, then 2X = 0.10, and finally X = 0.05. Therefore, the ball costs five cents and the bat costs $1.05.
Question 2 Explanation:
If 5 machines produce 5 widgets in 5 minutes, it means each machine takes 5 minutes to produce one widget. Consequently, if you deploy 100 machines, each machine will still take 5 minutes to produce a widget. Thus, 100 machines will produce 100 widgets in just 5 minutes.
Question 3 Explanation:
Considering the lily pad patch doubles in size each day, to find out when it covered half the lake, we simply need to go back one day from when it covered the entire lake. If it takes 48 days to cover the entire lake, then on day 47, the patch would have covered half of the lake’s surface.