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TOT 2004 Spring - Junior A-Level p3 increases or decreases by n %

Source:

February 25, 2020
combinatoricsalgebra

Problem Statement

Each day, the price of the shares of the corporation “Soap Bubble, Limited” either increases or decreases by nn percent, where nn is an integer such that 0<n<1000 < n < 100. The price is calculated with unlimited precision. Does there exist an nn for which the price can take the same value twice?
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