1
Break the percentage into pieces
Never multiply by an awkward percentage. Split it into tens, fives and ones.
12% of 450: 10% is 45, 1% is 4.5, so 2% is 9. Answer 54.
Practice
Free and no sign-up. Twelve calculation tricks, 50 mental maths drills, 8 full market sizing drills set in this region, and a 33-question quiz.
Twelve maths tricks worth knowing cold
Case maths is not hard, it is fast. These are the shortcuts that let you keep the arithmetic in your head while you are still thinking about the problem.
2
Percentages are reversible
a% of b is the same as b% of a. Pick whichever direction is easier.
8% of 25 is awkward. 25% of 8 is 2. Same answer.
3
Learn the fractions, not the percentages
Dividing is faster than multiplying by a decimal.
12.5% is divide by 8. 14.3% is divide by 7. 16.7% is divide by 6. 20% is divide by 5. 25% is divide by 4. 33.3% is divide by 3.
4
Dividing by 5, 25 and 50
Multiply instead, then move the decimal point.
Divide by 5 is times 2 then divide by 10: 340 becomes 68. Divide by 25 is times 4 then divide by 100: 900 becomes 36.
5
Doubling and halving
Halve one number and double the other until one of them becomes round.
16 times 25 becomes 8 times 50, becomes 4 times 100. Answer 400.
6
Round up, then take the difference back
Work with the round number, then correct.
45 times 9.8: take 45 times 10 which is 450, then subtract 2% of 450 which is 9. Answer 441.
7
Dividing by a decimal is multiplying by its reciprocal
Turn awkward division into easy multiplication.
Divide by 0.8 is multiply by 1.25, so 60 becomes 75. Divide by 0.5 is times 2. Divide by 0.25 is times 4.
8
Rule of 72
Years to double equals 72 divided by the growth rate. It works backwards too.
9% a year doubles in 8 years. Something that doubles in 5 years is growing at about 15% a year.
9
Compounding adds more than you think
Never just multiply the rate by the number of years.
10% a year for 3 years is 33%, not 30%. 5% for 4 years is about 21.5%, not 20%.
10
Percentage changes do not reverse
A rise and an equal fall do not return you to the start.
Up 20% then down 20% from 100 leaves you at 96. To undo a 25% rise you need a 20% fall.
11
Margin and markup are different numbers
Markup is on cost. Margin is on price. Say which one you mean.
A 50% markup on a cost of 100 gives a price of 150, which is a 33% margin. A 100% markup gives a 50% margin.
12
Separate the digits from the zeros
Do the arithmetic on the leading digits, count the zeros separately, then recombine.
19m times 450: 19 times 45 is 855, then handle the zeros. Answer 8.55bn. Check the order of magnitude before you say it aloud.
Why this matters more than it looks. Interviewers rarely reject a candidate for slow arithmetic alone. What they notice is a candidate whose attention is consumed by the numbers, who goes quiet, loses the thread of the case, or cannot sanity-check an answer that is out by a factor of ten. The point of drilling maths is to free up attention for the actual problem.
50 mental maths drills
Seven sets covering percentages, breakeven, market sizing arithmetic, compounding, weighted averages, unit economics and conversions. Answer in your head, reveal, then mark yourself. The timer is the point: aim for under 20 seconds a drill.
Eight market sizing drills
Full prompts of the kind interviewers actually give, set in this region. No data is supplied, which is the point. Every assumption in the worked answers is built from something you could reasonably know or observe in the room, never from a statistic you would have no way of knowing. Work each one on paper first, then open the answer.
The two approaches
Every market sizing question is solved from one of two directions, and one of them is always better than the other. Say which you are using and why before you start calculating.
Demand-side
Start from the population or the installed base, then narrow it with the drivers that actually determine demand: age, income, household size, urban or rural, preference. If the question is annual, finish with frequency or a replacement rate.
Population → income split → age → preference → purchases a year
Supply-side
Start from the capacity that physically exists or would need to exist, then adjust for how much of it gets used. Better whenever the constraint is physical: runways, courts, pumps, beds, charging points.
Units → throughput per unit → operating hours → utilisation
The rule that decides your score. Every number you use needs a reason attached to it, drawn from what you know or can observe. You will not be given annual passenger figures or market data in the room. You are expected to build the answer from things you can defend: how many runways an airport has, why a Gulf population skews adult, why delivery frequency rises in summer. The interviewer is testing the logic, not the final number.
1
Padel in Riyadh
Demand-side, converted into capacityYour client operates sports and leisure venues across the Gulf. Padel has grown rapidly in Saudi Arabia and they are considering entering the market in Riyadh. They will only proceed if they believe the city can support at least 500 courts. Estimate the number of padel courts Riyadh could sustain, and advise whether they should enter.
Show the worked answer
Why this approach
The client is asking how many courts the city can support, so start from how many people play and how often, then convert that demand into the court-hours needed to serve it. A pure supply-side count is impossible because the courts do not exist yet.
How to structure it
- Size the population of Riyadh from the population of Saudi Arabia.
- Narrow to the people plausibly playing padel: age, income, and whether they play regularly.
- Convert players into weekly sessions, since a player plays more than once.
- Work out what one court can serve in a week, then divide and apply a utilisation rate.
A worked answer
| Assumption | Value | Why it is defensible |
|---|---|---|
| Saudi population | About 35 million | Widely known, and the single anchor worth memorising for any Gulf case. |
| Riyadh share | 20%, so about 7 million | Capital and largest city. In most countries the primary city holds 10 to 25% of the population, and Saudi urbanisation is high. |
| Adults aged 20 to 45 | 40%, so 2.8 million | Padel skews young and working age. Saudi Arabia has a notably young population, so this share is higher than in Europe. |
| Play padel regularly | 5%, so 140,000 players | Padel is popular but still a minority sport. Compare with gym membership, which would be far higher. |
| Sessions per player a week | 1.5, so 210,000 sessions | Regular players average more than one but fewer than two. |
| Court capacity a week | 14 usable hours a day, 90-minute slots, 4 players: about 260 player-sessions | Courts realistically run from mid-morning to late evening. |
| Courts at full utilisation | About 800 | 210,000 divided by 260. |
| At 50% utilisation | About 1,600 courts | No venue fills every slot. Demand concentrates in evenings and weekends. |
Recommendation. Comfortably above the 500-court threshold, so enter. The binding question is location and peak-hour capacity, not whether total demand exists.
What separates a strong answer. This is a capacity question wearing the clothes of a market question. Weak answers estimate spending on padel. The real constraint is court-hours. The strongest answers also note that utilisation is seasonal: outdoor courts are barely usable in Riyadh summer, which is why covered courts command a premium and why an annual average understates peak-season demand.
2
Dubai departures
Supply-sideA ground-handling company is bidding for a contract at Dubai International. Their model only works if the airport handles more than 500 departures a day. Estimate daily departures from Dubai International.
Show the worked answer
Why this approach
You cannot know annual passenger numbers in a room, and you should not pretend to. What you can reason about is physical capacity: an airport can only move as many aircraft as its runways allow.
How to structure it
- Identify the binding constraint. For an airport it is runway capacity, not terminals or gates.
- Estimate movements per runway per hour from the spacing between aircraft.
- Apply realistic operating hours and a utilisation rate, since traffic comes in banks rather than evenly.
- Halve total movements to get departures, since every movement is either an arrival or a departure.
A worked answer
| Assumption | Value | Why it is defensible |
|---|---|---|
| Runways | 2 | Dubai International is a two-runway airport. This is the kind of fact you can reason about from having been there, or ask the interviewer. |
| Movements per runway per hour | 45 | Aircraft are separated by roughly 60 to 90 seconds on final approach, so 40 to 50 an hour is the practical ceiling. |
| Effective operating hours | 18 | The airport runs around the clock but traffic arrives in banks, with a deep lull in the early hours. |
| Utilisation | 80% | No airport runs at theoretical maximum all day. |
| Total movements a day | About 1,300 | 2 x 45 x 18 x 0.8. |
| Departures a day | About 650 | Half of all movements. |
Recommendation. Above the 500 threshold, so the contract is viable on volume.
What separates a strong answer. The trap is reaching for a passenger number you do not have. Supply-side reasoning gets you there from facts you can defend: runways, aircraft spacing, operating hours. The second trap is forgetting to halve movements into departures, which doubles the answer. Strong answers then flag that a ground handler is staffed for the peak bank, not the daily average, so the relevant number is movements per hour at peak.
3
School uniforms in the UAE
Demand-sideYour client is a schoolwear manufacturer considering entering the UAE. They need the market to exceed AED 500 million a year. Estimate annual UAE spend on school uniforms.
Show the worked answer
Why this approach
A consumer spending question with a clearly segmentable population. Work down from total population through the filters that actually determine whether someone buys a school uniform.
How to structure it
- Start from total population and justify it.
- Filter to school-age children, adjusting for the UAE's unusual age structure.
- Apply an enrolment rate and the share of schools that mandate uniform.
- Multiply by annual spend per pupil, allowing for more than one set a year.
A worked answer
| Assumption | Value | Why it is defensible |
|---|---|---|
| UAE population | About 10 million | Build it up: Dubai around 4 million, Abu Dhabi emirate around 4 million, the five northern emirates around 2 million. |
| Share of school age, 5 to 17 | 15%, so 1.5 million | Lower than a global norm of around 25%, because a large share of UAE residents are single adult workers rather than families. |
| Enrolment | 85%, so about 1.3 million pupils | Near-universal enrolment, with a small allowance for children schooled abroad. |
| Share in uniform-mandating schools | Nearly all | Public schools and the large majority of private curricula require uniform. |
| Annual spend per pupil | AED 600 | Two sets at roughly AED 200, plus sportswear, replaced annually as children grow. |
| Market size | About AED 750 to 800 million | 1.3 million multiplied by AED 600. |
Recommendation. Above the AED 500 million threshold, so proceed.
What separates a strong answer. The age structure is the whole question. Applying a global 25% school-age share overstates the market by two-thirds. The justification matters as much as the number: say out loud that the UAE population skews adult because so many residents are workers on employment visas without dependants. Strong answers then note the market is concentrated in Dubai and Abu Dhabi, which changes the distribution model.
4
Food delivery in Kuwait
Demand-sideA regional delivery platform is deciding whether to enter Kuwait. They will proceed only if gross order value exceeds $1 billion a year. Estimate the annual value of food delivery orders in Kuwait.
Show the worked answer
Why this approach
Consumer frequency question. Population, then who orders, then how often, then value per order.
How to structure it
- Size the population, placing Kuwait against Gulf states you know better.
- Narrow to people who actually order delivery.
- Estimate orders per user per month, and justify why the Gulf differs from a global average.
- Apply an average order value and multiply out.
A worked answer
| Assumption | Value | Why it is defensible |
|---|---|---|
| Kuwait population | About 5 million | Between Qatar at around 3 million and the UAE at around 10 million. |
| Share ordering delivery | 50%, so 2.5 million users | Smartphone penetration is near universal and the population is young and urban. Excludes young children and some older residents. |
| Orders per user a month | 3 | Pushed up by extreme summer heat, high incomes, long working hours and a strong restaurant culture. Below a daily habit but well above a monthly treat. |
| Annual orders | About 90 million | 2.5 million x 3 x 12. |
| Average order value | $15 | Orders are frequently for families rather than individuals, and incomes are high. |
| Gross order value | About $1.3 billion |
Recommendation. Above the $1 billion threshold, so enter, though the market is small in absolute terms and probably already contested.
What separates a strong answer. Frequency is the number to defend, and the environment justifies a high one: for several months of the year, leaving the house in the middle of the day is genuinely unpleasant. That reasoning is what the interviewer is listening for. Strong answers also separate gross order value from platform revenue, which is a commission on that figure and perhaps a tenth of it. Say which one you are estimating.
5
EV charging points in the UAE
Supply-sideA charging infrastructure operator is sizing the 2030 opportunity. They need at least 10,000 public charging points to justify the build. Estimate how many public charging points the UAE will need by 2030.
Show the worked answer
Why this approach
The question is how much charging capacity is needed, so build from charging sessions demanded and what one charger can deliver, rather than copying a ratio from another country.
How to structure it
- Size the vehicle fleet from population and car ownership.
- Apply an electric vehicle share for 2030 and justify it.
- Estimate public charging sessions per vehicle per week, separating drivers with home charging from those without.
- Work out how many sessions one charger can deliver a week, then divide.
A worked answer
| Assumption | Value | Why it is defensible |
|---|---|---|
| UAE population | About 10 million | |
| Cars per person | 1 per 3 people, so about 3.5 million vehicles | Car ownership is high: limited public transport outside Dubai, cheap fuel, long distances. |
| EV share of fleet by 2030 | 15%, so about 525,000 EVs | Policy support and new-vehicle share rising fast, but fleets turn over slowly, so the installed base lags new sales. |
| Public sessions per EV a week | 1.5 | Villa residents charge at home and rarely need public charging. Apartment residents depend on it almost entirely. This is the blended average. |
| Weekly session demand | About 790,000 | |
| Sessions per charger a week | About 39 | 14 usable hours a day, roughly one hour a session, at 40% utilisation. |
| Charging points needed | About 20,000 | |
| Sensitivity | 13,000 to 34,000 | At 1 session per EV a week you need 13,000; at 2.5 you need 34,000. |
Recommendation. Above the 10,000 threshold on every reasonable assumption, so proceed. The investment case rests on the home-charging share more than on EV adoption itself.
What separates a strong answer. This is a forecast, so the assumptions carry the answer and you should show the range rather than a single number. The insight that separates strong candidates is that public charging demand is driven by housing type, not by EV count: a city of villas with private parking needs far fewer public points than a city of apartment towers. In the UAE that split varies sharply between emirates and between neighbourhoods.
6
Nursery places in Doha
Demand-sideAn education group is considering opening nurseries in Qatar. They need the addressable market to exceed 25,000 children. Estimate the number of nursery places needed in Doha.
Show the worked answer
Why this approach
A straightforward population filter, but one where a global age structure gives badly wrong answers.
How to structure it
- Start from Qatar's population and the share living in and around Doha.
- Filter to the under-fives, adjusting hard for the age structure.
- Narrow to nursery age, roughly two to four.
- Apply a take-up rate, remembering who is in the country and why.
A worked answer
| Assumption | Value | Why it is defensible |
|---|---|---|
| Qatar population | About 3 million, roughly three-quarters non-Qatari | A small peninsula state whose population is dominated by expatriate workers. |
| Share in greater Doha | Over 80% | The country is effectively one city plus industrial areas. |
| Share under five | 5%, so about 150,000 | Far below a global norm of around 9%. A large share of residents are single male workers on employment visas, which flattens the age pyramid. |
| Share aged two to four | 60%, so about 90,000 | Three of the five single-year cohorts under five. |
| Take-up rate | 40%, so about 36,000 places | High among dual-income expatriate families who have no extended family nearby, lower among Qatari families where domestic help and relatives are common. |
Recommendation. Above the 25,000 threshold, so proceed.
What separates a strong answer. Age structure decides this answer, and the justification is specific rather than generic: a large share of Qatar's residents are workers without dependants in the country. Applying a global under-five share would nearly double the market. Strong answers then split Qatari from expatriate families, because take-up, willingness to pay and curriculum preference all differ, and the two groups are effectively separate markets.
7
Hotel rooms for the 2034 World Cup
Supply-side, driven by peak concurrencyYour client is a hotel developer assessing Saudi Arabia ahead of the 2034 FIFA World Cup. They want to know whether there is a genuine shortfall before committing capital. Estimate the hotel rooms needed to accommodate visitors during the tournament.
Show the worked answer
Why this approach
The constraint is beds on the busiest night, not visitors across the tournament. Build visitor numbers from stadium capacity, then convert to concurrent demand.
How to structure it
- Derive total attendance from the number of matches and average stadium capacity.
- Split attendance between international visitors and domestic or regional fans.
- Convert attendances into people by assuming how many matches each visitor attends.
- Convert total visitors into concurrent visitors, then into rooms.
A worked answer
| Assumption | Value | Why it is defensible |
|---|---|---|
| Matches | 104 | The tournament runs a 48-team format, which is public and reasonable to assume. |
| Average attendance | 45,000 | Typical World Cup stadium capacity. |
| Total attendances | About 4.7 million | |
| International share | 60%, about 2.8 million attendances | High, because the domestic population is smaller than at recent host nations, though regional fans travel easily. |
| Matches per visitor | 3 | Visitors come for a stretch of the tournament rather than a single game. |
| International visitors | About 940,000 | |
| Average stay | 10 nights | |
| Tournament length | 35 days | |
| Concurrent visitors | About 270,000 | 940,000 x 10 / 35. Visitors arrive and leave in waves. |
| Rooms needed | About 150,000 | At 2 guests a room and 90% occupancy. |
Recommendation. A real shortfall against today's supply in the host cities, but the investment case depends on what those rooms are worth in 2035, not in 2034.
What separates a strong answer. Concurrency is the step that separates answers. Dividing 940,000 visitors by two guests a room gives 470,000 rooms, wrong by a factor of three, because they are not all there at once. Strong answers go further and challenge the brief: demand concentrates in a few host cities, a World Cup is a four-week spike against a permanent asset, and the right answer may be modular or serviced capacity rather than conventional hotels.
8
Specialty coffee in Jeddah
Demand-sideA specialty coffee chain is considering expansion into Jeddah. They need the market to be worth more than SAR 1 billion a year. Estimate annual spend on specialty coffee in Jeddah.
Show the worked answer
Why this approach
Consumer consumption question: population, then buyers, then frequency, then price.
How to structure it
- Size Jeddah from the population of Saudi Arabia.
- Narrow to adults who buy coffee out rather than making it at home.
- Separate specialty from mass-market buyers.
- Apply frequency and price per cup.
A worked answer
| Assumption | Value | Why it is defensible |
|---|---|---|
| Saudi population | About 35 million | |
| Jeddah share | About 10%, so 4 million | The second city, materially smaller than Riyadh at around 7 million. |
| Adults | 60%, so 2.4 million | A young population, so the adult share is lower than in Europe. |
| Buy specialty coffee regularly | 30%, so about 720,000 | Specialty is a premium segment sitting above mass-market chains and home brewing, concentrated among younger urban consumers. |
| Purchases a week | 3 | Cafes carry a large share of social life in a market with no licensed bars, so visits are frequent and often social rather than purely functional. |
| Annual cups | About 112 million | |
| Average price | SAR 18 | Specialty pricing, above mass-market chains. |
| Market size | About SAR 2 billion |
Recommendation. Comfortably above the SAR 1 billion threshold, so proceed.
What separates a strong answer. Frequency is the number to defend, and the environment justifies a high one: with no licensed bars, cafes absorb social occasions that would sit elsewhere in other markets, and the population is young and urban. That reasoning is the answer the interviewer wants to hear, not the arithmetic. Strong answers separate the dine-in occasion from takeaway and drive-through, because the price points and property requirements differ completely.
Two things to remember. There is no correct answer, so do not chase one. And every prompt here ends in a decision with a threshold: a candidate who produces a number without a recommendation has done half the work.
The 33-question quiz
Three sets on business and case maths, consulting fundamentals and interview skills, and the Middle East consulting market. Pick an answer, see why it is right, and get a score at the end.
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