Grades 11-12 Video Solutions 2025-2025_11-12

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Video Summary

The problem involves calculating the largest possible percentage decrease, \(P\%\), when a two-digit number \(AB\) has its last digit erased, leaving \(A\). The original number is \(10A + B\), and the decrease is \(9A + B\) as a percent of \(10A + B\). The goal is to maximize \(P\), which simplifies to minimizing \(A/(10A+B)\). Setting \(B\) to the maximum digit 9 maximizes the decrease. Evaluating various \(A\) values shows \(A=1\) produces the greatest percentage decrease when the number is 19, leading \(P\) to approximately 95%, which is option D.

Keywords

largest percentage decrease

two-digit number

digit erased

maximize P

option D