A correct number can still leave the interviewer doing the important work. “£23,040” gives them an answer. “About £23,000 of annual contribution, which leaves only £3,000 after the extra staffing cost” gives them a business judgment.
That is the standard I would practise towards. Set up the right calculation, work through it visibly, and finish with the decision it helps you make. Speed becomes useful once those three things are reliable.
Decide what the answer needs to tell you
Before multiplying anything, finish this sentence: “I need to find ___ so we can decide ___.”
For example: “I need the annual contribution from the extra appointments so we can decide whether longer opening hours cover their cost.” That tells you to calculate completed appointments, rather than available slots, and contribution, rather than revenue.
This takes a sentence. It prevents several minutes of confidently solving the wrong problem.
Then say your equation in words. You do not need to narrate every scratch on your paper. Let the interviewer hear the plan before you disappear into the arithmetic:
“I'll calculate the additional appointments we can complete each week, multiply by contribution per appointment and operating weeks, then subtract the additional annual cost.”
Train setup, calculation and interpretation separately. Getting stuck on the equation needs a different exercise from losing a zero in multiplication.
Work through one calculation from beginning to end
Here is an illustrative clinic considering longer opening hours. Assume there is enough demand to book every new slot.
| Input | Value |
|---|---|
| Clinicians adding hours | 2 |
| Additional scheduled hours per clinician | 4 each week |
| Share available for appointments after administration and breaks | 80% |
| Appointment length | 30 minutes |
| Attendance rate among booked appointments | 90% |
| Contribution per completed appointment | £40 |
| Operating weeks | 50 per year |
| Extra annual staffing and facility cost | £20,000 |
First, calculate appointment time: 2 × 4 × 80% = 6.4 hours per week. Convert 30 minutes to half an hour. Then 6.4 ÷ 0.5 gives 12.8 bookable slots per week on average across the schedule.
Attendance applies to those bookings: 12.8 × 90% = 11.52 expected completed appointments per week. An individual week will contain whole appointments; this is an average for planning across the year.
Annual contribution is 11.52 × £40 × 50 = £23,040. I would multiply £40 by 50 first to get £2,000, then multiply by 11.52. Finally, subtract the extra £20,000: £3,040 of annual operating profit improvement, under the stated cost assumptions.
Keep those labels on the page. If you write only 6.4, 12.8, 11.52 and 23,040, returning to the calculation after an interruption becomes much harder.
Quick Case Math Drill
A city-centre bicycle repair shop is considering Sunday opening. One extra mechanic would cover the new day, and repairs are booked in advance.
- Bookable Sunday slots
- 50 repair slots per month
- Share booked and completed
- 80% of bookable slots
- Contribution per repair
- £45, before the mechanic's cost
After the £1,500 monthly mechanic cost, what is the monthly profit change?
Turn the result into a recommendation
Would you recommend extending the hours? The base case is positive, but its cushion is thin. Work backwards to identify what must hold.
Covering £20,000 requires £20,000 ÷ £40 = 500 completed appointments a year, or 10 a week. With 12.8 booked appointments available weekly, the attendance threshold is 10 ÷ 12.8 = 78.125%.
The proposed 90% attendance clears that threshold. If only 80% of the slots can be booked, however, completed appointments become 12.8 × 80% × 90% = 9.216 per week. Annual contribution falls to £18,432, leaving a £1,568 shortfall.
Now your conclusion has a useful next step:
“The extra hours improve annual profit by about £3,000 if we fill the new slots and maintain 90% attendance. I would check demand for those specific appointment times before adding a permanent shift. At 80% booking fill, the plan loses money.”
The arithmetic has identified the risk worth investigating. You have not just added “consider risks” to the end of an answer.
Make difficult arithmetic easier on paper
Use a short route you can explain and check. Mental maths in a case does not require keeping the entire problem in your head.
| Calculation | A cleaner route |
|---|---|
| 48 × 25 | 48 × 100 ÷ 4 = 1,200 |
| 15% of £2.4m | 10% is £240k; 5% is £120k; total £360k |
| £72m ÷ 24,000 customers | 72,000 thousands ÷ 24 thousands = £3,000 per customer |
| £1.8m ÷ £75 per unit | 1.8m ÷ 3 ÷ 25 = 600,000 × 4 ÷ 100 = 24,000 units |
Choose thousands or millions deliberately and carry the scale through. Saying “I'll work in thousands” is useful only if you actually label the numbers that way.
Do the arithmetic quietly when necessary. Explain your setup and your conclusion clearly; constant commentary while dividing can make both the calculation and the explanation worse.
Estimate first, then use the precision the decision needs
Before the clinic calculation, you can establish an upper bound. Eight scheduled hours cannot produce more than 16 half-hour appointments a week. At £40 each and 50 weeks, contribution cannot exceed £32,000 before the attendance and productive-time adjustments. A £230,400 result should immediately look wrong.
Rounding is also a decision choice. Suppose you estimate £98,500 of annual savings against a £100,000 requirement. Rounding both to £100,000 erases the shortfall you were supposed to assess. Work more precisely near the threshold.
Conversely, a market estimate built from rough population and adoption assumptions rarely deserves six significant digits. Give a sensible rounded result, then show which assumption could change the conclusion. Check the result against a plausible upper bound and the threshold that would change the decision.
Quick Answer Repair Drill
A parcel depot will approve a sorting robot only if it saves at least £120,000 a year in warehouse labour.
- Labour hours saved
- 2,950 per year
- Cost per labour hour
- £40
- Candidate's estimate
- 3,000 hours × £40 = £120,000, approve
What is the most important flaw in the candidate's estimate?
Correct an error without abandoning the case
If the interviewer asks you to check a number, stop and locate the issue. Start with the equation, units and scale. Repeating the same multiplication faster is a poor recovery strategy.
Say: “I compared weekly contribution with annual cost. I'll annualise the contribution, then revisit the conclusion.” Make the correction and state whether it changes your recommendation.
Keep the scale visible throughout. Do not wait until the final number to rediscover whether you were working in people, thousands of people or millions.
Practise the part that actually breaks
For your next practice session, take three unfamiliar questions. Before solving each, write the requested output, its unit and the equation. Calculate, check through a second route, then give one sentence on the implication.
Mark the first point where your answer needed help: setup, arithmetic, checking or interpretation. Use your practice log to choose the next exercise. A page of percentage drills will not fix a habit of presenting revenue as profit.
When you are ready to apply the whole sequence, try the front-desk staffing maths drill. Explain the monthly profit effect to Casey, then inspect the feedback on your setup and reasoning.
Case math drill
Can you talk an MBB interviewer through the numbers?
Monthly Profit Impact from Added Front-Desk Staff
Solve a case calculation and explain your workings aloud. Get feedback on your method, arithmetic and what the result means.
Frequently asked questions
Setting up the calculation
What should I work out before I start multiplying?
Decide what the answer has to tell you. Complete the sentence: I need to find ___ so we can decide ___. For a clinic extending its hours, you need the annual contribution from extra appointments so you can judge whether longer opening covers its cost. One sentence of framing prevents minutes spent on the wrong quantity.
Why calculate contribution and completed appointments rather than revenue and slots?
Because the decision is whether the extra hours pay for themselves. Available slots overstate activity when some patients do not attend, and revenue ignores the costs each appointment carries. Framing the question first shows that completed appointments and contribution are the figures you can fairly compare with the added staffing cost.
How does the clinic example reach about £23,000?
Two clinicians each add four hours, giving eight scheduled hours weekly. At 80% available time that is 6.4 hours, or 12.8 half-hour bookings. The total of £23,040 assumes 90% attendance, £40 contribution per completed appointment, 50 weeks and enough demand to book every new slot.
Turning numbers into a recommendation
What is the difference between giving a number and giving a judgement?
A number leaves the interviewer to interpret it, while a judgement does that work for them. Saying £23,040 is correct but incomplete. Saying it is about £23,000 of annual contribution, leaving only about £3,000 after the extra staffing cost, tells them the case is positive but marginal.
Should I recommend extending the hours if the base case is positive?
Recommend it with conditions, because the cushion is thin. Work backwards: covering £20,000 needs 500 completed appointments a year, or 10 a week. With 12.8 weekly bookings, attendance must be at least 78.125%. The proposed 90% clears that, so your recommendation should name attendance as the assumption that must hold.
Doing and checking the arithmetic
How can I make awkward multiplication easier during a case?
Choose a shorter route you can explain and check. For 48 × 25, multiply by 100 and divide by four to get 1,200. For 15% of £2.4m, take 10% as £240k, add 5% as £120k and reach £360k. You do not need to hold the whole problem in your head, so write the steps down.
Why estimate an answer before calculating it properly?
An upper bound exposes scale errors straight away. In the clinic case, eight scheduled hours cannot produce more than 16 half-hour appointments a week, so contribution cannot exceed £32,000 at £40 each over 50 weeks. If your working produces £230,400, you know a decimal place has slipped before you say the figure aloud.
How precise should my numbers be?
As precise as the decision requires. Suppose annual savings are about £98,500 against a £100,000 requirement. Rounding both to £100,000 hides a shortfall that may decide the case. When a result sits far from any threshold, rounding is usually harmless. Near the threshold, keep the extra precision and say why.
Recovering from errors and practising
What should I do when the interviewer asks me to check a number?
Stop and look for the error in the equation, the units and the scale, rather than repeating the same multiplication faster. Then say what went wrong, for example: I compared weekly contribution with annual cost, so I will annualise the contribution. Make the correction and state whether it changes your recommendation.
How do I avoid unit and scale mistakes in the first place?
Keep the scale visible throughout the calculation instead of restoring thousands, millions or time periods at the end. Label each line as weekly or annual, and in pounds or thousands of pounds. That makes it far easier to spot a weekly figure being compared with an annual cost.
How should I structure a case maths practice session?
Take three unfamiliar questions. Before solving each, write down the requested output, its unit and the equation. Calculate, check the result through a second route, then give one sentence on the implication. Fresh questions matter because setting up the problem is part of what you are practising.
Will percentage drills fix my case maths?
Only if arithmetic is where you actually break down. In each attempt, mark the first point where you needed help: setup, arithmetic, checking or interpretation. If the setup failed, a page of percentage drills will not help. Use your practice log to choose the next exercise.