July 21, 2020

Cognitive Reflection Test

Last updated on August 13, 2021

The Cognitive Reflection Test (CRT) is described by some to be the world’s shortest intelligence test, consisting of only 3 questions. Due to its popularity and some people’s familiarity with the questions, other lesser-known items have been added to revised versions of the test.

Dr. Natalie’s rating: 5 stars for appropriate and respectful wording, 5 stars for clarity & lack of ambiguity, and 4 stars for testing accuracy.
The test is accurate, but there is a clear gender bias related to numeracy. If you are female or have dyscalculia, the test is a less accurate measure of intelligence.

Take the test here:

CRT

 

Note: Please take the test before reading through the information.

Additionally, if you have dyscalculia and/or dyslexia, this could result in a lower score (read more in the Scoring section).


Who the test is designed for

  • Adults (age 16+)

What it tests


Versions & translations

  • The CRT has been translated into different languages.

Taking the test

The original CRT consists of just 3 questions, which require logic and calculus to answer. Answers will consist of numbers. Take the test below!

(The correct answers to the questions can be found in the Answers section)


Embrace Autism | Cognitive Reflection Test | icon Test Filled

Cognitive Reflection Test

  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?
    _____ cents.
  2. If it takes 5 machines 5 minutes to make 5 widgets,
    how long would it take 100 machines to make 100 widgets?
    _____ minutes.
  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?
    _____ days.

Scoring

The CRT is only available as a self-scoring test.

In his book David and Goliath, Malcolm Gladwell says the following about the average scores on the CRT:

Frederick gave the CRT to students at nine American colleges, and the results track pretty closely with how students from those colleges would rank on more traditional intelligence tests. Students from the Massachusetts Institute of Technology—perhaps the brainiest college in the world—averaged 2.18 correct answers out of three. Students at Carnegie Mellon University in Pittsburgh, another extraordinarily elite institution, averaged 1.51 right answers out of three. Harvard students scored 1.43; the University of Michigan, Ann Arbor, 1.18; and the University of Toledo 0.57.


Validity

How reliable, accurate, valid, and up to date is the test?

Discussion

Natalie:

The things to keep in mind are:

  1. Has the person seen the test before (the ball/bat question is often shared on social media).
  2. Men score higher than women.
  3. A person with dyscalculia will be at a disadvantage with this test even if they are bright.
  4. The CRT was thought to measure the ability to recognize and override errors that are made on quick and effortless intuition and instead use a system that is more controlled and slow. However, CRT items require math ability to be answered correctly and research has shown that mathematical ability is more important than cognitive reflection.
Kendall:

On seeing three statements, each involving numbers, I knew the CRT would be a problem. A score of 0 would be disheartening if I were unaware of my dyscalculia. Thus it is highly relevant to understand this when you are considering the results.

Martin:

I imagine knowing what the CRT actually measures can greatly influence your performance on the test. I remember that when I first heard the bat-and-ball question, I got the answer wrong. So when I took the CRT, I was careful to think it through rather than offering an intuitive response. If you take the test thinking it’s an intelligence test, you will be more likely to give the intuitive and therefore incorrect answer.

On the other hand, not knowing what the test measures may give a more accurate measure of your propensity to override an intuitive—but incorrect—response with a more analytical correct response. I think it will give a fair indication of your intelligence irrespective of whether you understand what the test measures and correlates with though. But if you want to take this test as a measure of intelligence and you have challenges with numbers, do take the CRT-2 instead.


Answers

  1. Correct answer = 5 cents; intuitive answer = 10 cents.
  2. Correct answer = 5 minutes; intuitive answer = 100 minutes.
  3. Correct answer = 47 days; intuitive answer = 24 days.

Explanations

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? (Answer: 5 cents.)

Note that the bat costs $1.00 MORE than the ball—whatever the price of the ball may be. So the bat doesn’t cost $1.00, and the ball $1, as that would mean the bat costs $0.90 more than the ball. The ball should cost $0.05 in order for the bat to cost $1.00 more (= $1.05), for a total of $1.10.

If you are more mathematically inclined, let’s say the ball costs X. We know that the bat costs $1 more than X, meaning that its price is X + 1. The total price of the bat and ball, then, is X + 1 + X. That’s a total of 2X + 1, which we already know is 1.1 ($1.10). In that case, we know that 2X = 0.1, which means that X = 0.05.

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

Each machine makes a widget in 5 minutes. The number of machines has no effect on how long it takes, because it will always take 5 minutes. So 100 machines working together will produce 100 widgets in 5 minutes.

Note also that the question can be interpreted such that at least 5 machines are required to work in unison to produce 5 widgets, but this also has no bearing on the answer.

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? (Answer: 47 days)

Every day the patch doubles in size, so every PREVIOUS day the patch was half the size. So if the patch takes 48 days to cover the lake, then the before-last day, on day 47, the patch covers half the lake.


Recommended next steps

After the CRT, consider taking one of the tests below.

Autism Spectrum Quotient (AQ)

A simple screening test that is used as a basis for pursuing a formal autism evaluation

Empathy Quotient (EQ)

Measures Theory of Mind

Systemizing Quotient (SQ)

Measures systemizing and pattern-finding proclivities

Online autism tests can play an essential role in the process of self-discovery, and may inform your decision to pursue a formal diagnosis. For a formal assessment, please see a knowledgeable medical professional trained in assessing autism.


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This article
was written by:
dr-natalie-engelbrecht
I’m a dually licensed registered psychotherapist and naturopathic doctor, and a Canadian leader in trauma, PTSD, and integrative medicine strictly informed by scientific research.And not only do I happen to be autistic, but my autism plays a significant role in who I am as a doctor and how I interact with and care for my patients and clients.

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