Quant Interview Back-of-Envelope Math
How to use back-of-envelope math, rounding, ranges, and sanity checks in quant interviews without pretending rough estimates are exact.
Candidates practicing estimation, expected value, and market making under time pressure.
Use round numbers deliberately
Back-of-envelope math is useful when exact precision is unnecessary or impossible. Round inputs to convenient numbers, but say what you rounded and whether the answer should be high, low, or roughly centered.
Work in ranges
Many estimation and market making prompts deserve a range, not a single fake-precise number. A range communicates uncertainty and gives you room to update when new information arrives.
Decompose arithmetic
Break calculations into reliable pieces: 17 percent as 10 + 5 + 2 percent, or 49 x 21 as 50 x 21 minus 21. The best shortcut is the one that reduces error risk.
Concrete example
To estimate 12 percent of 480, use 10 percent plus 2 percent: 48 + 9.6 = 57.6. If the interview only needs a rough value, saying about 58 may be better than spending time on unnecessary precision.
Check scale
Every rough answer needs a scale check. Is it within possible bounds? Does it have the right units? Would doubling an input roughly double the answer? These quick checks catch many errors.
Common mistakes
Candidates either avoid approximation entirely or approximate without saying so. Use approximate math openly: it is a tool for decision-making, not a trick to hide uncertainty.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.