Case Interview Maths and Brainteasers

What the arithmetic actually involves

The range is narrow. Percentages and percentage change, multiplication and division with large round numbers, breakeven calculations, growth over several years, ratios and margins, and reading numbers off a chart correctly.

Nothing beyond school arithmetic appears. What makes it difficult is doing it aloud, under observation, while holding the thread of an argument, which is a different skill from doing it on paper alone.

The techniques worth drilling

• Work in round numbers and adjust at the end. 4,850 times 19 is 4,850 times 20 minus 4,850, which is easier and about as accurate as you need.
• Handle zeros separately. Turn every figure into a small number times a power of ten, do the small arithmetic, then reattach the magnitude. This removes the single most common error.
• Learn the fraction equivalents: a third is 33 per cent, an eighth is 12.5, a sixth is about 17, a seventh is about 14. Converting a percentage to a fraction often turns hard division into easy division.
• Use the rule of 72 for compounding: something growing at 8 per cent doubles in about nine years. It answers a surprising share of growth questions in one step.
• Percentage change of a product: if price rises 10 per cent and volume falls 5, revenue moves by roughly 5 per cent. Adding the percentages is close enough for small changes and far faster.
• Round at the start and say so. "I will call it 70 million" is acceptable; quietly rounding mid-calculation and producing an inconsistent answer is not.

How to do it out loud

Announce what you are about to calculate before you start, so the interviewer can redirect you if it is the wrong calculation. That alone saves more time than any arithmetic shortcut.

Then narrate in steps rather than in silence followed by an answer. Silence means an error surfaces at the end with no way to locate it, and it also means the interviewer cannot give you credit for correct reasoning if the final number is wrong.

When you reach the answer, say what it means before moving on. A number without an interpretation is an incomplete contribution, and interpretation is worth more marks than the calculation was.

Checking, which is the actual skill

Every answer gets a two-second check against something you already know. Is this plausible relative to the revenue figure we saw earlier? Is a margin above 100 per cent? Is a per-person figure larger than a plausible income?

If a number fails the check, say so out loud and go back. Finding your own error is close to neutral in scoring and occasionally positive, because it demonstrates exactly the habit a client relies on. Presenting an impossible number confidently is the single most damaging thing you can do in a case.

A three-week drill

Ten minutes a day beats an hour a week, because this is a reflex rather than knowledge.

• Week one: percentages and fractions. Convert between them until it is instant, and practise taking percentages of awkward numbers.
• Week two: multiplication and division with magnitudes. Large round numbers, powers of ten, and dividing to two significant figures.
• Week three: case-shaped calculations. Breakeven, margin, growth over five years, and reading a number off a chart and using it.
• Throughout: do it aloud and standing up if you can, because doing arithmetic while talking is the thing being trained.

Brainteasers, where they still appear

Classic brainteasers have largely disappeared from consulting interviews and have not disappeared entirely, particularly in later rounds with partners who enjoy them. They also remain common at trading firms, so the skill is not wasted.

The approach is the same as everything else in the interview. Clarify the question, state your assumptions, reason out loud, and give an answer. Whether you have heard the puzzle before matters far less than whether your reasoning is followable. If you genuinely cannot see it, say what you have established and what you would need, which is a better outcome than silence.

Where a brainteaser is really an estimation question in disguise, which is most of the time, treat it as one and use the sizing method.

If maths is your weak point

It is worth saying plainly that this is the most fixable weakness in the process and the one candidates most often decide is innate. It is not. Three weeks of ten-minute sessions moves nearly everyone from uncomfortable to adequate, and adequate is all that is required.

What does not work is avoiding it in practice cases because it is unpleasant, which is the most common pattern among candidates who fail on quantitative dimensions. Do the calculation in every practice case, out loud, even when your partner would let you skip it.