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1. Which one of the following numbers can be removed from the set S = {0, 2, 4, 5, 9} without changing the average of set S?

Solution:
The average of the elements in the original set S is:
0+2+4+5+95=205=4
If we remove an element that equals the average, then the average of the new set will remain unchanged. The new set after removing 4 is {0, 2, 5, 9}.
The average of the elements is,
0+2+5+94=164=4

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