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How many cars are in a Spanish city (top-down)

You run the case. Read the prompt, answer questions from the notes below, and share data only when the candidate asks for it or gets stuck. Score at the end.

Case timer

00:00

Target length:

1. Read the prompt aloud

Read it slowly, then pause. Let the candidate ask questions before they structure.

Estimate the number of passenger cars registered in a Spanish city of 2,000,000 people.

2. Answers to clarifying questions

Give these answers only if the candidate asks. If they ask something not listed, give a sensible answer or say it does not matter here.

If asked: Do you mean cars registered in the city, or cars on its roads at one moment?
Answer: Cars registered to people and businesses in the city.
If asked: Only private cars, or also taxis, company cars, and rental cars?
Answer: All passenger cars.

3. The hypothesis a strong candidate states

Listen for an early, testable guess like this one. It does not need to match word for word.

City households own fewer cars than rural ones, and many own none. My hypothesis is about one car per household, plus a small number of business cars.

4. A model structure

Compare the candidate's structure with this one. A different split can be just as good if it is clean and fits the problem.

Cars = household cars + business cars
- Households = population / people per household
- Household cars = households x cars per household
- Business cars (taxis, company, rental) as an add-on

5. The working, step by step

Each step shows how a strong candidate works it out. Share a new fact from it only when the candidate asks or is stuck, and let them do the math: the result in the dark box is what they should reach.

Step 1: Households
What a strong candidate does: Cars are owned by households more than by individuals. Spain averages about 2.5 people per household.
Households: 2,000,000 ÷ 2.5 = 800,000
Step 2: Household cars
What a strong candidate does: Assume about 1.0 car per household on average, blending households with none, one, and two cars.
Household cars: 800,000 × 1 = 800,000
Step 3: Add business cars
What a strong candidate does: Taxis, company cars, and rental cars add roughly 5 percent.
Total cars: 800,000 × 1.05 = 840,000
Step 4: Sanity-check against an outside anchor
What a strong candidate does: Convert to cars per 1,000 people and compare with Spain's national figure of roughly 500. Our answer is a little lower, which fits a large city with good public transport.
Cars per 1,000 people: 840,000 ÷ 2,000,000 × 1,000 = 420

The recommendation to listen for

At the end, say: "The CEO walks in. What is your recommendation?"

About 840,000 cars, or about 420 per 1,000 people. First, 2,000,000 people at about 2.5 per household make about 800,000 households. Second, about one car per household plus about 5 percent business cars gives about 840,000. Third, that is about 420 cars per 1,000 people, a little below Spain's national figure of roughly 500, as expected for a big city with good public transport. The same method for a city of 2,000,000 in India would need very different inputs (about 4.5 people per household and far fewer cars per household), which is why you always say which region an assumption is for.

Risks a strong answer names: Cars per household is the swing assumption; 0.8 instead of 1.0 would lower the answer by a fifth.

Next steps: Check the national figure for cars per 1,000 people and adjust the city discount.

Strong versus weak

A strong answer

Clarified what counts as a car, split households from businesses, and checked the answer against a national anchor rather than against its own assumptions.

A weak answer

Assumed "one car for every two people" without saying for which country, and called that a sanity check.

Score the candidate

Score each criterion from 1 to 5. A 2 or a 4 sits between the descriptions.

This case has no exhibit. Score Exhibit reading on how the candidate used the data you gave them: did they pick out the number that matters and say what it means?

Structuring

1: No clear structure, or a memorized framework that does not fit the problem.
3: A sensible structure, but with some overlap, a gap, or no clear priority.
5: A structure built for this problem, with no overlap and no gaps, a stated hypothesis, and a clear first step.

Math

1: Frequent errors, no units, or needed heavy help to finish.
3: Right answers but slow or messy working, or one error caught late.
5: Accurate and clearly narrated, with units, a sense check, and what the number means.

Exhibit reading

1: Read the chart aloud without finding the number that matters.
3: Found the key number but gave only part of the so-what.
5: Pulled the right number quickly and said what it means for the case.

Synthesis

1: Summarized what was done, with no clear answer.
3: Gave an answer, but with weak reasons or no next step.
5: Answer first, then two or three reasons with numbers, the main risk, and next steps.

Communication

1: Hard to follow: long silences, no signposting.
3: Clear most of the time, with some rambling.
5: Calm and concise, signposted each step, and checked in with the interviewer.

Total

0 out of 25

Score all five criteria to see the band and the feedback template.