Determine the RANGE of the sum.
There are 10 fractions in total.
The smallest fraction is 1/100.
The greatest fraction is 1/91.
If all 10 fractions were 1/100, then S = 10(1/100) = 1/10.
Since 9 of the fractions are actually GREATER THAN 1/100, S must be GREATER THAN 1/10.
If all 10 fractions were 1/90, then S = 10(1/90) = 1/9.
Since all 10 fractions are actually LESS THAN 1/90, S must be LESS THAN 1/9.
Thus:
1/10 < S < 1/9.
Of the 3 options, only III is less than S.
The correct answer is C.
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