We are talking about 10 numbers from 91 to 100. What you can immediately notice is that, since 100 is the greatest of them, that means that 1/100 will be the smallest. So you have:
1/91 > 1/100
1/92 > 1/100
......
1/100 >= 1/100
Adding these babies (=equations for quant addicts like myself) up will give you that S > 10*1/10 = 1/10. So S is greater than 1/10. However, we don't konw the relationship between S and 1/8 and 1/9.
So here's part two: since 91 is the smallest number of the series 91 - 100, this means that 1/91 will be the biggest of them all, compared to 1/92 ... 1/100. So you get that:
1/91 >= 1/91
1/91 > 1/92
.....
1/91 > 1/100
Adding it all up leads us to the conclusion that 10*1/91 > S, or that 10/91 > S. Now all we have to do is compare 10/91 with 1/9. Since 1/9 = 10/90 and 91 < 90, this means that 10/91 < 1/9. But since 10/91 > S, this will definately mean that 1/9 > S. And again, since 1/8 > 1/9, 1/8 is obviously greater than S.
Conclusion: only 1/10 is smaller than S.
Answer: C.
