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Algebra Level 3

There are three kinds of liquids \(X, Y,\) and \(Z.\) Three jars \(J_1, J_2,\) and \(J_3\) contain 100 ml of liquids \(X,Y,\) and \(Z,\) respectively. By an operation we mean three steps in the following order:

stir the liquid in \(J_1\) and transfer 10 ml from \(J_1\) into \(J_2;\)
stir the liquid in \(J_2\) and transfer 10 ml from \(J_2\) into \(J_3;\)
stir the liquid in \(J_3\) and transfer 10 ml from \(J_3\) into \(J_1.\)

After performing the operation four times, let \(x,y,\) and \(z\) be the amounts of \(X,Y,\) and \(Z,\) respectively, in \(J_1.\) Which of the following is correct?

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