Complements to 10/100: Fast Subtraction Trick (Case Math)
Complements to 10 and 100
What are complements in mental math? Complements are numbers that, when added to a given number, create a round figure (like 10 or 100). For example, the complement of 7 to 10 is 3. This technique is a powerful shortcut for fast subtraction and making change in case interviews.
What Are Complements?
Complements are a foundational mental math technique that can dramatically speed up your calculations during a case interview. They are particularly useful for subtraction and scenarios like calculating market gaps or making change in retail cases.
- The complement of 7 to 10 is 3 (because 7 + 3 = 10).
- The complement of 64 to 100 is 36 (because 64 + 36 = 100).
Mastering complements allows you to bypass slow, traditional subtraction and perform calculations instantly.
How to Use Complements for Quick Subtraction
Forget borrowing digits. Use this fast 3-step method.
Find the Complement
Identify the complement of the subtrahend to a round number (usually 100).
Add the Complement
Add this complement to the minuend (the number you’re subtracting from).
Subtract the Round Number
Subtract the round number used in step 1.
Example: 83 - 76
Complement of 76 to 100 is 24 → 83 + 24 = 107 → 107 - 100 = 7
✅ Answer: 7
Where You'll Use This in a Case Interview
Use complements when:
- Estimating market gaps (Total Market - Current Players)
- Calculating profit margins (Revenue - Costs)
- Making change in retail scenarios (e.g., $3.64 paid with $5.00 → change is $1.36)
This technique is often tested in first-round interviews and retail cases.
Ready to Drill This Skill?
Reading is not enough. To make complements second nature under pressure, you need timed, focused practice.
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