Trainers & Games
Rapid-Fire Quiz
Random questions from the 300-question bank, on a timer. Read, think, reveal, self-mark. Build a streak across probability, brainteasers and more.
Rapid-Fire Quiz
A random question appears. Think it through, then reveal the full worked solution and mark yourself honestly. Build the longest streak you can. Great for warming up before an interview.
Learn how it works
Five worked examples. Read a couple before you dive in, try to answer first, then reveal the solution.
Probability, sum of two dice
Roll two fair dice. What is the probability the sum is 7? (Attempt it before revealing.)
Show solution
Try first, then reveal. There are 6 × 6 = 36 equally likely outcomes. The pairs that add to 7 are 1-6, 2-5, 3-4, 4-3, 5-2, 6-1 → 6 ways.
- P(sum = 7) = 6 ÷ 36 = 1/6 ≈ 16.7%
7 is the most likely sum precisely because it has the most combinations.
Brainteaser, 8 balls, one heavier
You have 8 identical-looking balls; one is slightly heavier. Using a balance scale, what is the fewest weighings guaranteed to find it? (Guess before revealing.)
Show solution
Answer: 2 weighings.
- Weigh 3 vs 3. If they balance, the heavy ball is in the 2 you set aside → weigh those 2 against each other → done.
- If one side of 3 is heavier, the heavy ball is in that group of 3 → weigh 1 vs 1 of them; if they balance it's the third → done.
Splitting into three groups (not two) is the trick, each weighing has three possible results.
Statistics, mean and spread
Find the mean and standard deviation of: 2, 4, 4, 4, 5, 5, 7, 9. (Work it out first.)
Show solution
Reveal after attempting.
- Mean = (2+4+4+4+5+5+7+9) ÷ 8 = 40 ÷ 8 = 5
- Squared gaps from 5: 9, 1, 1, 1, 0, 0, 4, 16 → sum = 32
- Variance = 32 ÷ 8 = 4
- Standard deviation = √4 = 2
So the numbers cluster around 5, typically about 2 away.
Mental math, difference of squares
Compute 17 × 23 in your head. (Try, then reveal.)
Show solution
Notice 17 and 23 are both 3 away from 20, so use (20 − 3)(20 + 3):
- = 20² − 3²
- = 400 − 9
- = 391
Whenever two numbers are equally spaced around a round middle, use middle² − gap².
Market-making, long or short?
Fair value is 50 and you quote 48 / 52. A trader lifts your offer (buys). Which price did you trade at, and are you now long or short? (Answer before revealing.)
Show solution
Reveal: lifting your offer means they buy at your ASK = 52, so you SELL at 52. Selling leaves you short 1 unit.
- You collected +2 versus fair value (52 vs 50), good, if 50 is really fair.
- But you now carry short inventory: if price rises you lose on it, so you may want to skew to buy it back.
What you'll learn
Recall and reasoning speed across every interview topic, practice thinking on the clock, then self-mark against a full worked solution.