Investment Banking Brainteasers: Timed Set

An investment-banking brainteaser asks you to turn an unfamiliar prompt into a defensible answer. Restate the goal, choose a structure, state the assumptions that matter, work through the cases or calculation, and explain a check. The exact mix of tests depends on the employer, role, and invitation. Oxford Careers Service describes assessment centres with different combinations of tasks, while Cambridge's banking guide includes brainteasers as one possible part of some cognitive interviews. Use the invitation for the actual format and rules.

TL;DR

Restate the goal and define the output.
State assumptions before inserting numbers.
Enumerate cases or build a driver tree.
Give a result, uncertainty, and sanity check.

What types of banking brainteasers should you practise?

Type	First move	What a good answer shows
Probability	Define the event and condition	Dependence, calculation, and a bounds check
Estimation	Set scope and build a driver tree	Units, assumptions, range, and sanity check
Logic	Translate the prompt into constraints	Case coverage and contradiction checks
Arithmetic warmup	Write the relationship	Clean numeric fluency before open-ended reasoning

Use the numerical reasoning guide for tables, ratios, percentages, and statement decisions. Use the market-sizing framework for larger driver trees and the market-sizing questions for larger worked cases. For arithmetic fluency, use the mental math guide.

The short practice block below is an arithmetic warmup. It gives three local checks: a per-share percentage premium, a Rule of 72 doubling-time estimate, and an after-tax income calculation. After those checks, signup continues in Mental Math. Use the open-ended exercises in this article to practise probability, estimation, logic, and spoken reasoning.

Practice inside this guide

Numerical reasoning

Question 1 of 3

A target trades at $10.00. What offer price is a 20% premium?

Your answer

$/share

How do you solve a probability brainteaser?

Define the event and what it is conditional on. List the possible cases, then decide whether the events are independent. A complement is often faster for an "at least one" question. Calculate, check that the probability is between zero and one, and say what would change if the dependence assumption failed.

Try this fictional model-review puzzle before opening the answer

Assume a material error is already present in a fictional model review. Check A catches that error with probability three quarters. Check B catches it with probability two thirds. Assume the two detection events are independent, conditional on the material error being present. What is the probability that at least one check catches the error? State the condition before you calculate.

Reveal the worked probability answer

We are calculating the probability that at least one check catches the error, given that the error is present. The complement is that both checks miss it. The miss probabilities are one quarter and one third, so under the stated conditional independence assumption:

1 - (1/4 x 1/3) = 1 - 1/12 = 11/12, or approximately 91.7 percent.

The answer is within the zero to one range and is higher than either individual detection probability. This calculation says nothing about how likely an error was before the checks. That would require a separate base rate. If the checks are dependent, multiplying the miss probabilities is not justified. With only the two conditional detection probabilities and no dependence information, the probability that at least one catches the error can range from three quarters to one.

How do you handle an estimation brainteaser?

Clarify the geography, period, unit, and output. Choose a top-down or bottom-up driver tree. Put the assumptions beside each variable, calculate with round numbers, and finish with a range or a sanity check. Separate a mandate being won from a fee being earned in the period you are estimating.

Try this fictional advisory-fee estimate before opening the answer

Estimate the fee revenue recognized in one year by a fictional advisory team serving one region. Choose your own reasonable assumptions for the target-company pool, the share that becomes a serious prospect, the win rate, the average fee, and the share of won mandates that complete and are recognized in the same year. State your units and give a low and high scenario. This is a structure exercise, not a market fact.

Reveal one worked estimation model

Here is one illustrative model. Assume 60 target companies, 25 percent becoming serious prospects, a 40 percent win rate, and an average fee of USD 250,000. Also assume each won mandate completes and its fee is recognized in the same year. The calculation is:

60 companies x 25 percent x 40 percent = 6 won mandates

6 mandates x USD 250,000 = USD 1.5 million of recognized fee revenue

A won mandate is not automatically a fee earned in the same year. If completion lags, recognized revenue would be lower. For a simple scenario range, use 4 to 8 completed mandates and an average fee of USD 200,000 to USD 300,000. That gives a low case of USD 0.8 million and a high case of USD 2.4 million. This is a scenario range, not a confidence interval. In these scenarios, the mandate count changes more proportionally than the fee, so test the completion assumption first. As a sanity check, six completed mandates from 60 targets means converting 10 percent of the pool. The base revenue is USD 25,000 per target company, averaged across wins and non-wins. Ask whether the team has capacity to complete six mandates in the year; a sales estimate above delivery capacity needs revision.

For larger market-sizing cases, continue with the market-sizing framework.

How do you solve a logic brainteaser?

Write each rule as a constraint. Place the strongest relationship first, test every possible position or branch, and remove a case as soon as it breaks a rule. Finish by explaining why the surviving case satisfies every constraint.

Try this original review-order puzzle before opening the answer

Four review steps must each appear exactly once: assumptions (A), debt (D), revenue (R), and sensitivity (S). A must come before D. R must be immediately before S. D cannot be last. What is the only valid order?

Reveal the worked logic answer

Treat R and S as one adjacent block, RS. It can start in position one, two, or three.

If RS starts in position one, A and D occupy positions three and four. A must come before D, which puts D last and breaks the rule.
If RS starts in position two, A and D occupy positions one and four. A must come before D, which again puts D last and breaks the rule.
If RS starts in position three, A and D occupy positions one and two. A before D gives the only valid order: A, D, R, S.

The method is the important part: compress an immediate relationship, enumerate its possible positions, and eliminate contradictions before committing.

What should you say while solving?

Use a short spoken sequence that keeps the other person oriented:

Restate the goal. Say what you are estimating, counting, or proving.
Name the structure. Say whether you will use a complement, a driver tree, or constraint cases.
State the material assumptions. Invite a correction before doing the arithmetic.
Work one step at a time. Keep units, conditions, and branches visible.
Name uncertainty. Identify the input that could move the answer most.
Check and commit. Test the range or order of magnitude, then give the answer clearly.

If you catch a wrong branch, say what assumption failed, reset the structure, and continue. For example: "I treated the two checks as independent. If they tend to miss the same errors, I cannot multiply those miss probabilities. I would need their joint miss rate." Then explain which part of your answer still holds.

How should you practise a timed set?

Use the invitation for an employer's actual timing, calculator, and navigation rules. The routine below is an editorial practice suggestion for this page, not a universal assessment rule:

Give yourself three minutes per prompt to restate the goal, set the structure, attempt the work, and record the answer or range.
Stop when the attempt window ends. Mark the assumption or branch where you were least certain.
Review separately for five minutes per prompt. Open the worked answer only after your attempt and compare the structure, not just the final number.
Log the miss as interpretation, setup, assumption, case coverage, arithmetic, communication, or time management. Rework the weakest category aloud.

Oxford's psychometric guidance recommends practice that balances speed with accuracy, but it does not set a brainteaser timer for every employer. Match your practice rules to the format you are actually invited to complete.

Frequently Asked Questions

Are brainteasers common at every bank?

Formats vary by employer, role, and stage. Cambridge's banking guide describes brainteasers as one possible part of cognitive interviews, especially in quantitative roles. Oxford's assessment-centre guidance also lists several possible task combinations. Check the invitation and prepare the reasoning method that transfers across formats.

Should I memorize solutions?

No. Practise defining the event, stating assumptions, enumerating cases, and checking the result. Cambridge's example interview-question guide also presents reported questions as topic orientation rather than a list to memorize.

Can I use a calculator or take extra time?

Follow the employer's instructions. Calculator access, timing, and answer rules can vary. If you need an adjustment, ask the stated recruitment contact early. Oxford lists examples such as extra time, rest breaks, written instructions, and format information, but the employer decides what is available.

Sources

Oxford Careers Service: Assessment Centres (checked 5 September 2026)
Oxford Careers Service: Psychometric Tests (checked 5 September 2026)
Oxford Careers Service: Getting Workplace Adjustments (checked 5 September 2026)
University of Cambridge: Banking and Financial Markets Short Guide to Recruitment 2025 to 2026 (checked 5 September 2026)
University of Cambridge: Example Interview Questions for Banking and Financial Markets (checked 5 September 2026)