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The average of the three numbers $x, y$ and $z$ is $48. x$ is greater than the average of $y$ and $z$ by $9.$ The average of $y$ and $z$ is greater than $y$ by $2.$ Then the difference of $x$ and $z$ is :

1. $2$
2. $6$
3. $7$
4. $8$

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