Mental Math Sprint
Train your mental math speed. Start with 60 seconds, earn time for correct answers!
New to case math? Read our complete guide →
Difficulty
Operations
Select specific operations or use "All Mixed" for variety
What this mental math trainer does
The sprint above generates fresh arithmetic every run and puts it under a shrinking clock. You start with 60 seconds. A correct answer buys you 2 more; a wrong answer costs you 2. That scoring is the whole design: it makes hesitation expensive in the same way an interviewer's silence does, and it stops you from grinding slowly towards a perfect score.
Nothing is pre-written. Questions are generated on the fly from 15 operation types across three difficulty bands, so you cannot memorise the set, and repeating a difficulty never gives you the same run twice.
The three difficulty bands, and what is actually in them
The bands differ by number range and by which percentages and multipliers get drawn, not just by a label:
- Easy
- Operands between 2 and 20, divisors up to 10, and percentages drawn from 10, 20, 25 and 50. This is the warm-up band: the arithmetic is not the challenge, the clock is. Use it to get comfortable answering without hesitating.
- Medium
- Operands between 10 and 100, divisors up to 25, and percentages from 5, 10, 15, 20, 25, 30, 50 and 75. This is the band that matches a real case interview. Most candidates should spend most of their time here.
- Hard
- Operands between 50 and 500, divisors up to 50, and awkward percentages such as 7, 12, 17, 23, 33, 67 and 85. Multiplication pulls from 11, 12, 15, 25, 50 and 99. Harder than most interviews, deliberately — if you can hold 60% accuracy here, the real thing feels slow.
If you are unsure where to start, run one Medium sprint. If you clear 60% accuracy, stay there. If you do not, drop to Easy for a few days before coming back — practising above your level mostly trains you to guess.
The 15 operation types
You can select any combination, or leave it on All Mixed. Each type trains something a case interview will ask for:
- Addition & subtraction
- Chained sums where the win comes from rounding to a friendly number and correcting afterwards. 487 + 316 is 500 + 316 − 13.
- Multiplication
- Weighted towards the multipliers that actually appear in cases: 11, 12, 15, 25, 50 and 99. ×99 is ×100 minus one copy; ×15 is ×10 plus half of it.
- Division
- Divisors of 4, 5, 8, 12, 15, 25 and 50 at the hard band. Dividing by 5 is doubling then moving the decimal; dividing by 25 is ×4 then ÷100.
- Percentages
- The single most common operation in a case. Anchor on 10% and 1%, then build: 23% of 840 is 168 + 16.8 + 8.4.
- Percent changes
- Growth and decline expressed as a change rather than a level. The trap is compounding two changes by adding them — a 10% rise then a 10% fall leaves you at 99%, not 100%.
- Reverse percentages
- Working back to the original from the result. If a price after a 20% discount is $80, the original is 80 ÷ 0.8 = $100, not 80 × 1.2.
- Fractions
- Converting between fractions, decimals and percentages on sight. Knowing 1/8 = 12.5% and 3/8 = 37.5% saves whole seconds each time.
- Ratios
- Splitting a total in a given ratio, and converting a ratio to a share. A 3:5 split of 320 is 120 and 200, because the parts sum to 8.
- Powers
- Squares and small powers, used constantly in growth questions and in sanity-checking orders of magnitude.
- Multi-step chains
- Two or three operations in sequence, which is where accuracy actually breaks down. Interviews rarely ask a single operation.
- Estimation
- Deliberately approximate answers where being close fast beats being exact slow. This is the market-sizing muscle.
- Decimals & negatives
- Decimal placement and sign handling — the two most common sources of an answer that is right except by a factor of ten or a minus sign.
How to get faster, specifically
Anchor on 10% and 1%
Almost every percentage in a case can be assembled from those two. 10% is a decimal shift, 1% is two. 35% of 620 is 62 + 62 + 62/2 = 217. Candidates who try to compute 0.35 × 620 directly are slower and wrong more often.
Round, then correct
Work with the friendly number next door and repair the difference at the end. 48 × 25 is 50 × 25 minus 2 × 25 = 1,250 − 50 = 1,200. The correction step is nearly always easier than the original multiplication.
Learn the fraction equivalents cold
1/3 = 33.3%, 1/6 = 16.7%, 1/8 = 12.5%, 3/8 = 37.5%, 1/12 = 8.3%. These appear constantly in margin and share questions, and recognising them removes a division entirely.
Say the magnitude before the digits
Decide whether the answer is in the hundreds, thousands or millions before you compute the digits. The most damaging case interview error is not being slightly off, it is being off by a factor of ten and not noticing.
Practise the reverse direction on purpose
Going from a discounted price back to list, or from a margin back to cost, is the operation candidates get wrong most often. It is always a division by (1 ± rate), never a multiplication by it.
Where this sits in your preparation
Mental math is the foundation layer, not the whole skill. Once you are comfortable here, move to case math drills, where the same arithmetic arrives wrapped in a business scenario and you have to decide which calculation to run before you can run it. Add brain teasers for the logic and estimation questions that show up in first rounds, and follow a structured study plan if you would rather not decide what to practise each day.
Frequently asked questions
How long is a mental math sprint?
A sprint starts at 60 seconds. Every correct answer adds 2 seconds and every wrong answer subtracts 2, so a strong run stretches well past a minute and a weak one ends early. There is no fixed question count — you answer as many as the clock allows.
Is the mental math tool free, and do I need an account?
It is free and no account is required. You can start a sprint immediately. Creating a free account only adds cross-device history and skill tracking; the trainer itself is identical either way.
How fast should I be at case interview mental math?
A useful working target is roughly one answer every 4 to 5 seconds at Medium difficulty with 85% or better accuracy. Accuracy comes first: an interviewer will forgive a candidate who thinks for four seconds and is right far more readily than one who answers instantly and is wrong.
Which operations should I practise first?
Percentages, percent changes and reverse percentages, in that order. They appear in almost every profitability, growth and pricing case, and reverse percentages are the single most commonly botched operation because candidates multiply back up instead of dividing.
How often should I practise?
Two or three sprints a day, roughly 10 to 15 minutes total, beats one long session a week. Mental arithmetic speed is a recall skill and it responds to frequency far more than to duration.
Can I use a calculator in a real case interview?
No. Consulting firms expect the arithmetic to be done on paper or in your head. Pen and paper are normally allowed and you should use them — the point of practising mentally is not to avoid paper but to make each step fast enough that you stay in conversation with the interviewer.
Does this cover McKinsey, BCG and Bain equally?
The arithmetic is the same across firms. What differs is the wrapper: McKinsey's interviewer-led cases tend to hand you clean numbers in a defined question, while BCG and Bain more often expect you to structure the calculation yourself. The speed and accuracy this tool builds is the shared foundation for all three.