Case Math Drills: What Each of Our Four Weights Buys

The four weights our math rubric applies

These weights are ours. No consulting firm publishes a rubric for case arithmetic, and Bain, which comes closest, tells candidates that its feedback rests on "an objective scoring system" without saying what that system measures. What follows is the barème our code applies, read from src/lib/grading/rubrics.ts at the line where each maximum is declared.

How each of the four points is won

Our grader is deterministic and it tests for the presence of moves. That is worth knowing precisely, because it changes what a score means. How an answer is assessed states the same limit in the platform's own words.

A number that misses tolerance still collects 12 of 40, because an attempt with a figure in it differs from an attempt with no figure at all. An answer with no number at all scores zero there.

So the Interpretation dimension can be won with a single word. Two things follow. First, the score is cheap to game, and gaming it teaches you nothing, since the sentence you would have to write to game it is the sentence a real interviewer wants anyway. Second, a well-phrased answer resting on a false premise will score well here and fail in a room. Our method page says exactly that, and it is the honest boundary of any automated marker.

A published case interview break-even, recomputed twice

Bain publishes a coffee shop case with every input on the page. That makes it the rare exercise you can check rather than trust. The case gives a town of 100,000 people, one cup a day each, a price of three pounds, a setup cost of 245,610 pounds, annual operating costs of 163,740 pounds, and a variable cost of one pound a cup.

The firm prints the equation and the result. Contribution per cup is two pounds. Total fixed cost in year one is 163,740 plus 245,610, which is 409,350 pounds. Divide that by two and you get 204,675 cups. The published answer agrees. As a check on the other side, 204,675 cups at 3 pounds is 614,025 pounds of revenue, less 204,675 pounds of variable cost, which leaves 409,350 pounds. The loop closes.

Now the part the case leaves for you. Setup is a one-off, so 204,675 is a first-year break-even. The recurring break-even carries only the 163,740 of operating cost, which gives 81,870 cups. The ratio between the two is exactly 2.5. That single distinction is worth more in a room than the arithmetic: it turns one number into a statement about when the shop starts making money rather than merely covering its bills. Bain also writes that "When making assumptions about market size, there is no 'right' or 'wrong' answer", which is the same point aimed at the input side.

What the thirty-drill case interview math practice set contains

The practice set at case math practice is built by a seeded generator, so the same series comes back identically every time. It rotates through eight calculation families in turn.

Thirty drills across eight families is an uneven split, and the rotation makes it predictable: the first six families appear four times each, the last two appear three times, and six fours plus two threes is thirty. Accuracy is accepted within 1 percent of the expected value there, with a floor of 0.05. The open-ended drill is looser at 2 percent, because it grades a written answer rather than a typed figure.

Three math practice habits that lift the other sixty points

The open-ended version lives at the math drill. It grades in your browser, with no account, and its clock starts on your first keystroke rather than when the page opens. Three habits move the dimensions that speed alone leaves flat.

1. Say the chain before the total. Write contribution, then fixed cost, then the division. This is the one habit BCG names for you: its case preparation page lists Show Your Thinking among six behaviors it wants, alongside Clarify Assumptions.
2. Carry the unit on every line. Pounds, cups, cups per day, months. Converting 204,675 cups a year into roughly 561 cups a day is a sanity check disguised as a unit conversion, and 365 times 561 lands within a cup of the annual figure.
3. End on the consequence. One clause, starting with so or therefore. The shop needs about 561 cups a day in year one and about 224 a day after that, so the question for the client becomes whether the town's traffic supports the higher number for twelve months.

Announce your rounding when you round. Writing roughly 561 when the division gives 560.75 is a case skill. Writing 561 with no signal is an error, and a careful interviewer will treat it as one.

Where case interview math practice stops helping

Two limits are worth stating plainly. The grader checks whether the expected moves are present, and it cannot tell whether your premise was sound. It will reward a fluent, well-signposted answer built on a number you should never have assumed. A human reader catches that in one question, which is the part of preparation that a rubric does not replace, and it is also why our own comparison with a private coach concedes the point rather than arguing it.

The second limit is the shape of the exercise. Bain describes a case as "a structured conversation where you work through a real business problem", and adds that the firm is "not looking for a single right answer". A drill cannot reproduce a conversation. It can reproduce the arithmetic inside one, under a clock, with the four dimensions marked separately so you know which of them cost you the answer. Build the habits here, then spend a live rehearsal on the thing a drill cannot test.

If you want the same arithmetic without the grading, the break-even calculator takes fixed cost, price and variable cost and prints the chain. Feed it 409,350, three and one, and it returns the same 204,675 that Bain publishes, which is a quick way to convince yourself the tool is doing real work.