Reciprocals Question

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.

Thanks Dana, but i don´t understand your method. Can you explain it again?

Sure... My method relies on writing the equations described above and just adding them together... The first set of equations is smth like :
1/91 > 1/100
1/92 > 1/100
1/93 > 1/100
........ [meaning so on snd so forth]
1/99 > 1/100
1/100 >= 1/100

If you add all the numbers on the left side of the ">" you get S, if you add everything on the right side you get ten times 1/100 or 10*1/100.

The same goes for the other set of equations, just the other way around: on the left side you get 1/91 ten times or 10*1/91 and on the right side you get S.

Hope this makes it a bit more clear. IMO, just try to write the whole thing on paper and you'll be able to tell how I did it...

Answer is C

1/91, 1/92,......1/100

1/100 <1/99 <1/98 ..... <1/91

The sum will be greater than 10( total numbers) times the lowest value(1/100) and less than 10 times higher value(1/91).

10(1/100) < S < 10(1/91)


so 1/10 is the less than S

Thanks
Raama