Case Interview Math 2026: Units, Checks, and Rounding

Say the unit before the number in every case interview

The habit is one sentence long and it prevents the most expensive class of error.

Before any multiplication, say what the unit is. Per household. Per flight leg. Per year. Per visit. Then multiply.

A firm's own careers blog supplies the canonical case. At lek.com, a first-year London associate describes sizing the wedding market as if each person married separately rather than two people per wedding. The interviewer credited the method while pointing out the error. He writes: "The key was not necessarily getting the right answer but demonstrating structured problem-solving skills." That is one person describing his own interview on his employer's platform, and it is not a statement about how the firm grades.

The factor there was two, and two is the usual size of a unit error. Four families produce it constantly.

1. Pairs and individuals. Weddings, couples, accounts with joint holders. Two people, one event.
2. Legs and round trips. One round trip is two legs. This one appears below.
3. Households and people. A US household averages about 2.5 people, so any product bought by the household is oversized by 2.5 when sized per person.
4. Bottles and gallons, cases and units. Same volume, different base. McKinsey's published Electro-Light case describes a 16 ounce bottle as one eighth of a gallon, so the two bases differ by eight.

None of these is detectable in the final number. A market sized at 20 billion dollars looks exactly as plausible as one sized at 10 billion, which is why the check has to happen before the multiplication rather than after it.

A worked route, and the factor of two waiting in it

Stated assumptions: an airline runs two daily round trips on a route, with 180 seats per aircraft, an 80 percent load factor, a 210 dollar average one-way fare, and a cost of 32,000 dollars per flight leg. Operating 365 days.

The unit decision comes first. Two round trips a day is four one-way legs a day. Get that wrong and every line below is half of what it should be.

Every line recomputed by hand on 30 September 2026. Four legs a day times 365 is 1,460. Times 180 seats is 262,800. Times 0.80 is 210,240 passengers. Times 210 dollars: 210,240 times 200 is 42,048,000, plus 210,240 times 10 which is 2,102,400, so 44,150,400 dollars. Cost is 1,460 times 32,000, which is 46,720,000 dollars. The difference is 2,569,600 dollars of annual loss.

Say the result with its unit and its sign. The route loses about 2.57 million dollars a year, which is 2,569,600 over 44,150,400, or 5.8 percent of revenue. Both figures are useful and the percentage is the one that travels: a 5.8 percent negative operating margin on a route is a different conversation than a large absolute number with no scale.

Two ways to close a gap, and the one that is cheaper

The loss can be closed from the volume side or the price side, and working both is what turns arithmetic into a recommendation.

Volume side. Revenue must reach 46,720,000 dollars. At 210 dollars a fare that needs 46,720,000 over 210, which is 222,476 passengers. Against 262,800 available seats that is 222,476 over 262,800, which is 84.7 percent, rounded from 84.66. So the breakeven load factor is 84.7 percent against 80 percent today, a gap of 4.7 percentage points.

Price side. At today's 210,240 passengers, the fare must reach 46,720,000 over 210,240, which is 222.22 dollars. Against 210 dollars that is 222.22 over 210, which is 1.0582, so 5.8 percent higher.

Recomputed by hand. Note that the 5.8 percent fare increase and the 5.8 percent revenue shortfall are the same quantity, which is a useful internal check: if revenue is short by 5.8 percent and volume is fixed, price has to rise by 5.8 percent.

Now the sentence that makes it a recommendation. Closing the gap needs either 4.7 more points of load factor or 5.8 percent more fare, and the two are not equally available: 4.7 points of load on a route already at 80 is a marketing and schedule problem, while 5.8 percent on fare is a single decision that competitors can match. Which one you recommend depends on the competitive position, and asking for it is the right next move.

A third lever exists and it is worth naming out loud even without data. Cost per leg is 32,000 dollars, and 2,569,600 over 1,460 legs is 1,760 dollars per leg, so a 5.5 percent cost reduction closes the same gap. Recomputed: 1,760 over 32,000 is 0.055.

Three levers, three percentages, all roughly the same size. That symmetry is a real finding rather than a coincidence: any gap expressed as a share of revenue shows up as a similar share on each lever that touches revenue.

Sanity checks for case interview math, four seconds each

A sanity check is a comparison against something whose bound you already know. Four of them catch most broken chains.

1. Is the share above 100 percent? A load factor of 112 percent, a market share of 140 percent, a penetration above one. Any of these means an error upstream, and the check is free.
2. Is the per-person figure above the population? If you compute 400 million users in a country of 330 million, you counted devices or accounts rather than people.
3. Is the magnitude plausible against something you know? A 50 billion dollar market for a niche product is a signal. Naming one reference point before you compute, such as a national population or a household count, makes this check possible.
4. Do the two routes agree? Compute the same profit as contribution minus fixed cost, and again as revenue minus total cost. Disagreement locates the error.

The fourth is the strongest and the least used. On the route above: revenue 44,150,400 minus cost 46,720,000 gives a loss of 2,569,600. The other route is per leg: revenue per leg is 44,150,400 over 1,460, which is 30,240 dollars, against 32,000 of cost, so a loss of 1,760 per leg, and 1,760 times 1,460 is 2,569,600 dollars. The two agree, which takes twenty seconds and buys certainty.

Oliver Wyman's own criterion for a data question, printed under it at oliverwyman.com, asks the candidate to lay the data out so it can be computed quickly. A page arranged for one route of calculation makes the second route harder, so leave space.

Announcing a rounding, and why it is a skill

Rounding is expected. Silent rounding is an error, and the difference is one word.

The rule: say roughly, about, or call it, whenever the figure you speak differs from the figure you computed.

Worked from this page. The load factor is 84.66 percent and we said 84.7. The fare is 222.22 dollars and 222 would be fine if announced. The loss is 2,569,600 dollars and about 2.6 million is fine, announced.

What makes this a skill rather than a courtesy is that a listener uses your precision to judge your confidence. A candidate who says exactly 84.7 percent has claimed a precision the assumptions do not support, since the 80 percent load factor and the 210 dollar fare were both round inputs. A candidate who says roughly 85 percent against 80 today has said something defensible.

Bain publishes the underlying point about assumptions on its coffee case at bain.com: "When making assumptions about market size, there is no 'right' or 'wrong' answer." The assumption is free. The arithmetic on top of it is not, and neither is the precision you claim for the result.

A related habit: round early rather than late, and say so. Rounding 262,800 to 263,000 at the start costs 0.08 percent and saves several operations. Rounding after four operations compounds whatever you did along the way.

The sentence after the number in a case interview

A named Kearney business analyst publishes the rule on her employer's blog, read at kearney.com: "When you're working through the quantitative part of the case, you should never end on a number." That is her own practice, published by her employer, and not a firm policy statement.

The sentence that follows a number has three possible shapes, and one of them always applies.

• It clears a bar. A 5.5 percent cost reduction closes the gap, and your operations team has delivered that twice, so this is the lever I would pull.
• It fails a bar. An 84.7 percent load factor is above anything this route has achieved, so volume alone will not fix it.
• It brackets a bar. The three levers are all about 5 to 6 percent, so the decision is which of the three the client can actually move.

Every one of those names a comparison. A number with nothing to be compared against has not been interpreted, and if the interviewer has given you no bar, ask for one or state the one you are assuming.

Bain's own tips include highlighting key numbers, and the corollary is that most numbers are not key. On the route above, seven figures were computed and three belong in speech: the 2.57 million dollar loss, the 4.7 point load gap, and the 5.8 percent fare gap. The other four are working.

Where the habits meet our weights

These four lines belong to us. They are read from the grading code in src/lib/grading, and no consulting firm publishes a marking scheme in our corpus.

A checklist for the case interview math itself

1. Write both inputs down before multiplying. Transcription is the commonest error under time.
2. Say the unit out loud first. Legs rather than round trips. Households rather than people.
3. Announce the magnitude you expect. Millions, tens of millions. This catches an exponent slip immediately.
4. Round early and say so. Then keep the rounding consistent through the chain.
5. Check the share against 100 percent and the count against the population. Four seconds, two checks.
6. Recompute by a second route. Per unit against total, or contribution against full cost.
7. Name the bar, then interpret. Against today, against the hurdle, against the competitor.
8. Speak three numbers at most. The rest stay on the page.

Our math drill reports Answer, Working, Units and Interpretation as separate lines and names the first correction, and the market size calculator will check a sizing chain once you have built it by hand. Both are free and neither needs an account. Neither one can tell you which bar a client applies, and that is the input that decides whether your number is good news.

To practice rather than read, case math drills sets out what each of our four math weights buys and what a session should look for. For the shortcuts that make the chain fast, see case interview mental math. For the equations behind the lines, see case interview formulas. For reading the exhibit that supplies the inputs, see reading case exhibits.