# Are you smarter than me? 10

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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