None of these need mathematics beyond primary school. They are hard because arithmetic intuition is fast, confident and, in specific well-mapped situations, reliably wrong.
The bat-and-ball problem is the famous example — almost everyone's first answer is ten cents, and almost everyone is wrong. What makes these questions worth studying is that the mistake is not random. The same traps catch the same people in the same way, which is exactly what makes them good questions.
Every question below shows all four options, the keyed answer, and the one-line explanation. If you want to turn these into video, the OmniFrame Quiz Studio is free and this pack is built in.
Question 1
A price rises 50% then falls 50%. Are you back where you started?
Why: A 50% drop from the higher price leaves 75% of the original.
Question 2
Assume two independent, equally likely child sexes. Given at least one boy, what is the chance both are boys?
Why: Conditioning on at least one boy leaves BB, BG, and GB as equally likely possibilities; one is BB.
Question 3
Two fair coins are flipped. Given at least one head, what is the chance both are heads?
Why: The remaining equally likely outcomes are HH, HT, and TH; one of the three is HH.
Question 4
A car travels 60 miles at 30 mph. How fast must it return to average 60 mph overall?
Why: The entire allowed time is used on the first leg.
Question 5
What is more: 10% of 90 or 90% of 10?
Why: Both equal 9.
Question 6
What is 6 divided by 2 times 3?
Why: Division and multiplication are evaluated left to right.
Question 7
A bat and ball cost $1.10. The bat costs $1 more. How much is the ball?
Why: The tempting 10 cents makes the bat $1.10 and the total $1.20; only 5 cents leaves a gap of exactly $1.
Question 8
If a shirt is 50% off then 50% off again, what is the total discount?
Why: Half off twice leaves 25% of the price.
Question 9
What is the average of 10 and 20?
Why: Add them and divide by 2.
Question 10
What is half of two plus two?
Why: Half of two is one, plus two equals three.
Question 11
If three people split $30 equally, how much does each get?
Why: 30 divided by 3 equals 10.
Question 12
What is 0 times any huge number?
Why: Any number multiplied by zero is zero.
Question 13
Which is larger: 1/3 or 0.3?
Why: One third is about 0.333.
Question 14
You roll one die. What is the chance of getting a 7?
Why: A standard die only has 1 through 6.
Question 15
What comes next: 3, 6, 12, 24?
Why: The pattern doubles each time.
Question 16
A lily patch doubles daily and fills a lake on day 48. When was it half full?
Why: Halving day 48 tempts you to say day 24, but doubling means the lake was half covered the day before.
These questions are free to use — in a classroom, a pub quiz, a video, or anywhere else. No attribution required. If you think one is ambiguous or an explanation is wrong, tell us and we will fix the page.
For how questions like these are constructed, see what makes a quiz question hard.