Investment Banking puzzles, solved step by step
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008How many taxis are operating in Hong Kong's Central district at a busy weekday lunchtime?HSBCCentral · 2026
Try it first
What should your first sentence be, before any number?
Show the worked solution
Roughly 2,000 to 2,500 taxis, inside a defensible range of about 1,000 to 4,000. Assume 300,000 people in Central at lunch, 2% of them taking a taxi trip that touches the district in the peak hour, and each trip spending 15 minutes inside it: 1,500 cabs occupied at any moment. Add half as many again cruising or queuing empty and you reach about 2,250.
Why count trips and minutes rather than cabs?
Picture a busy restaurant. If 60 diners arrive an hour and each stays half an hour, about 30 seats are taken at any moment, whatever is on the menu. That rule, known as Little's lawThe number of items in a system on average equals the rate they arrive multiplied by how long each one stays., turns a flow into a count. The taxis in Central at one moment equal the trips touching Central per hour multiplied by the hours each trip spends there, plus the cabs that are empty. You cannot see cabs from an interview room, but you can reason about people and journeys.
Three hundred thousand people at lunch, 2% taking a taxi trip in the hour and 15 minutes per trip inside the district give 1,500 occupied cabs; adding empty cabs gives about 2,250, inside a range of 1,050 to 4,200. Where do the numbers come from, and which one moves the answer most?
Every number is an assumption you state, not a fact you recall. Central is a dense office district, so assume 250,000 office workers plus 50,000 visitors and shoppers at lunch. Most walk or take the train; assume 2% take a taxi trip that starts or ends in Central in the busiest hour, which is 6,000 trips. A cab picking up, crawling through lunchtime traffic and dropping off spends perhaps 15 minutes in the district per trip. The minutes-per-trip assumption moves the answer as much as the head count does, so say it slowly and invite challenge on it. Empty cabs cruising or waiting at ranks add about half again.
Assumption Low Base High People in Central at lunch 250,000 300,000 350,000 Share taking a taxi trip that hour 1.5% 2% 2.5% Minutes inside Central per trip 12 15 18 Empty cab uplift x 1.4 x 1.5 x 1.6 Taxis in Central 1,050 2,250 4,200 Every input is an illustrative assumption; moving all four together gives the range. How do you sanity-check it from the supply side?
Come at it from the fleet. Suppose the city has about 18,000 licensed taxis, a number you would state as an assumption and check against the current licence count, and the busiest business district holds 10% to 15% of them at peak. That gives 1,800 to 2,700. Two methods landing in the same range is worth more than either number on its own. If they had disagreed by a factor of three, you would say which assumption you trust less and why.
Where candidates lose it
Candidates jump straight to a number, or try to recall the city's taxi count and multiply by a share they cannot defend. The interviewer is scoring the structure, so a remembered figure with no logic behind it earns very little.
The second loss is false precision. Saying 2,250 as if it were measured sounds naive; give the central figure, the range, and the one assumption that would move it most.
What the interviewer asks next
- How would your answer change at 3 am?
- How many taxi trips start in Central across a whole weekday?
- Which single assumption would you research first, and how would you check it?
Asked at HSBC, Sales and Trading, Central, 2026 (Wall Street Oasis):
How many taxis are in HK central How many beds in the nyc hotel
024Size the annual market for wedding catering in India, in Rs crore.Rothschild & CoNew York · 2026
Try it first
Which structure gives the most defensible answer?
Show the worked solution
Roughly Rs 2.3 lakh crore a year, on stated assumptions. Assume about 90 lakh weddings a year, from a population of about 140 crore. Split them into budget, mid-range and premium tiers, each with its own plate count and cost per plate. Budget weddings contribute about Rs 47,000 crore, mid-range Rs 81,000 crore and premium about Rs 1 lakh crore: 5% of weddings, 44% of the spend.
How many weddings happen a year?
Start from people, not from a remembered statistic. Assume a population of about 140 crore, a figure to confirm, and an average lifespan near 70 years, so roughly one seventieth of people, 2 crore, reach marrying age each year. Assume 90% marry: 1.8 crore people, or 90 lakh weddings. A count built from cohorts can be checked line by line, which is what makes it defensible in the room. One caveat is worth saying: a young population has larger cohorts than one seventieth, so this may undercount a little.
Why split by tier rather than use one average wedding?
Think of a school canteen and a five-star hotel both serving lunch. Averaging their prices and their customer counts separately, then multiplying, gives a number neither of them earns. Big weddings have both more guests and a higher cost per plate, so averaging guests and price separately understates the market. On the tiers below, the average-wedding shortcut, 435 plates at Rs 400, gives Rs 1.57 lakh crore, about 32% less than the tiered Rs 2.29 lakh crore. Plates here count every guest meal across all the functions of a wedding, and catering means food only, not venue or decoration.
About 90 lakh weddings a year, split into budget, mid-range and premium tiers with their own plate counts and prices, give about Rs 2,29,500 crore of catering, while one average wedding multiplied out gives only Rs 1,56,600 crore. Tier Share of weddings Weddings Plates Rs per plate Rs crore Budget 70% 63 lakh 300 250 47,250 Mid-range 25% 22.5 lakh 600 600 81,000 Premium 5% 4.5 lakh 1,500 1,500 1,01,250 Total 100% 90 lakh 2,29,500 Every input is an illustrative assumption stated for the estimate, not a measured figure. Which assumption moves the answer most?
The premium tier. It is 5% of weddings and 44% of the value, so a change in its plate count or price moves the total more than any change in the budget tier. When one segment dominates the value, spend your sanity checks there: is 1,500 plates across several functions at Rs 1,500 a plate plausible for the top twentieth of weddings? Halve the premium tier's value and the total falls to about Rs 1.8 lakh crore, which is the honest low end of the range to quote.
Where candidates lose it
The common loss is one average wedding: a few hundred guests at a few hundred rupees a plate, times the number of weddings. It sounds reasonable and quietly drops about a third of the market, because the weddings with the most guests also pay the most per plate.
The second loss is reciting a wedding-industry figure from an article. The interviewer wants a structure built from people, tiers and plates, with every number said as an assumption.
What the interviewer asks next
- How would you size the decoration market for the same weddings?
- How does the wedding season affect the capacity a caterer needs?
- How would you check the premium tier's assumptions with a few phone calls?
Asked at Rothschild & Co, Generalist, New York, 2026 (Wall Street Oasis):
1st round all technical focused mainly on DCF and Eq Val and Enterprise Value questions, mental math, and some market sizing
