The following questions are known as the Cognitive Reflection Test by Shane Frederick (2005).

Can you answer them correctly?

(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

In a survey of 3,428 people, an astonishing 33 percent missed all three questions. Most people–83 percent–missed at least one of the questions.

Even very educated people made mistakes. Only 48 percent of MIT students sampled were able to answer all the questions correctly.

Give it a try before reading the answers.

How did you do..

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(1) 5 cents (not 10)

(2) 5 minutes (not 100)

(3) 47 days (not 24)

**Extra explanation**

**(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**

Say the ball costs X. Then the bat costs $1 more, so it is X + 1. So we have bat + ball = X + (X + 1) = 1.1 because together they cost $1.10. This means 2X + 1 = 1.1, then 2X = 0.1, so X = 0.05. This means the ball costs 5 cents and the bat costs $1.05

**(2) If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets? _____ minutes**

If it takes 5 machines 5 minutes to make 5 widgets, then it takes 1 machine 5 minutes to make 1 widget (each machine is making a widget in 5 minutes). If we have 100 machines working together, then each can make a widget in 5 minutes. So there will be 100 widgets in 5 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**

Every day FORWARD the patch doubles in size. So every day BACKWARDS means the patch halves in size. So on day 47 the lake is half full.