Big-number questions don't test hard maths. They test set-up: which groups, which exclusions, which units. When the options sit close together, a small slip lands on a wrong option that looks perfectly reasonable.
The method, in 4 steps
Words first
Write the build: clients × average loan × change in rate, per group, then add.
Exclusions before multiplication
Take out what the brief excludes before you touch a number.
Estimate
Round everything and get the size of the answer. A factor of 10 or 100 shows up here.
Calculate if the options are close
Options a few percent apart need the exact figure. Count zeros separately.
Worked example
Union Commercial Bank, question 7
Example · practice contentPlay the free case first (40 min)
UCB's clients are grouped by size. The top 25 clients (in Group 1) are excluded. Every other client's rate rises by 0.11 percentage points on average, with no fall in loan volume.
| Group | Clients in scope | Average loan |
|---|---|---|
| Group 1 (excl. top 25) | 75 | $270M |
| Group 2 | 200 | $85M |
| Group 3 | 400 | $50M |
Client counts and average loans as the case's answer key works them from the exhibit.
What is the estimated change in annual interest revenue, to the nearest million dollars?
Show the workingTry it first. The method, step by step, then the answer.
- WordsΣ (clients × average loan) × 0.11%.
- ExclusionGroup 1 counts 75 clients, not 100: the top 25 are out.
- EstimateLoans in scope ≈ $20bn + $17bn + $20bn ≈ $57bn. × about 0.1% ≈ $57M. The answer is in the right part of the list, but the options are $2M apart, so calculate.
- Calculate75 × $270M = $20,250M. 200 × $85M = $17,000M. 400 × $50M = $20,000M. Total $57,250M × 0.11% = $62.975M.
- Round$63M.
Answer $63 Million.
Recap · Lesson 04
Pause here
- Words before numbers: If you can't write the build, you don't know which numbers to pull.
- Exclusions first: The brief's "except" is part of the formula.
- Estimate, then decide: Far-apart options: the estimate answers. Close ones: calculate.
Tonight · free20 min
A free percentage drill
Say the rough answer out loud before you type anything. Count the zeros separately.
Open it freeSources2 numbered sources, labeled by type
- DrillCase guide DrillCase: BCG Casey math, with six worked problems
- DrillCase guide DrillCase: Union Commercial Bank, the free Casey-style demo case: question text and answer key.
Independent practice. Not affiliated with BCG.