Investment Banking interview preparation
Every question below is either traced to a named firm from a public candidate report, or tagged at desk level when we could not trace it. Answers are written the way you would actually say them out loud — answer first, then the mechanism, then the limitation.
100 questions, mapped to the firms that asked them
- Questions
- 100
- Traced to a firm
- 100
- Firms
- 46
- Updated
- September 2026
092I paint the surface of a 10x10x10 cube green. How many of the small cubes have green on them, and how many do not?TD SecuritiesGeneralist · New York · 2024
Say this
488 have green on them and 512 do not. Solve the easy half first: the unpainted cubes form an inner 8x8x8 block, which is 512. Subtract that from 1,000 to get 488 painted.
Then walk it
- Total small cubes: 10 cubed is 1,000.
- Any cube not touching the surface is one layer in from every face. That leaves an 8 by 8 by 8 core, because you remove one layer from each of the two opposite sides in all three dimensions.
- 8 cubed is 512 unpainted.
- So painted is 1,000 minus 512, which is 488. Computing the painted faces directly is possible but far more error-prone.
- If they push further: 8 corner cubes have three painted faces, 96 edge cubes have two, and 384 face cubes have one. That sums to 488, which confirms the answer.
Where candidates lose it
Trying to count the painted cubes face by face and double-counting the edges and corners. Always solve for the interior and subtract. Saying 'I will do the easy side first' out loud is itself the signal they want.
Expect next
- How many have exactly two painted faces?
- Generalise it for an n-cube.
- Now do it for a 10x10x10 where I only paint the top and bottom.
Reported by candidates at TD Securities (Generalist, New York, 2024). Source: Wall Street Oasis.
Firm tags come from public, anonymous candidate reports on Wall Street Oasis: strong signal, not sworn testimony. Firms are named as the places a question was reported, not as partners of Fin Maverick. Answers are written for this page to show how to think out loud; they are not scripts to recite.