These estimation questions always feel deceptively easy until you're actually doing the math out loud.
Break the problem into two parts: estimate the height of the Empire State Building and the thickness of a quarter, then divide. Clearly state your assumptions and round to make the math easy, focusing on demonstrating logical reasoning rather than getting the exact number.
Pro tip: Interviewers care more about your thought process than the final number. Verbalize your assumptions and sanity-check your answer (e.g., 'Does 3 million quarters seem reasonable?') to show you can handle ambiguity and validate your work.
Confirm what 'match the height' means (e.g., stack height equals building height) and whether to include the antenna. Ask if you should assume standard quarter thickness.
Recall or estimate the building's height. A common figure is about 1,250 feet to the roof, or 1,454 feet including the antenna. Choose one and state it.
A quarter is about 1.75 mm thick. Convert this to feet (approximately 0.00575 feet) or convert the building height to millimeters for easier division.
Divide the building height by the quarter thickness. For example, 1,250 feet / 0.00575 feet ≈ 217,000 quarters. Round to a sensible number.
Verify the answer makes sense: 217,000 quarters is about $54,250 in quarters, which seems plausible. State your final answer with the assumptions made.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.