IfS is the sum of the reciprocals of the consecutive integer

[AnitaX292]

[Problem text removed]

As 91 and 100 are the 2 extreme numbers, i thought the sum of the reciprocals must be between 10(1/91) and 10(1/10). Therefore, S is: 10/91 < S < 1/10

Then I compared the given fractions with this inequality and thought that the answer mus be "A. None" because 1/8 and 1/9 and 1/10 are bigger than the inequality. But the correct answer seems to be "C. III only."

I am not sure what am I doing wrong here. Can you please explain/clarify? Thanks

[Sage Pearce-Higgins]

Just to check that you've read the forum rules: where is this problem from? Unfortunately we're only allowed to post problems from GMAT Prep tests 1 and 2 as the others are paid-for resources.

Your working is excellent, S must be between the boundaries that you determined. However, you've got mixed up. Which is larger, 1/91 or 1/100? Hopefully you can see that 1/91 is larger. Therefore S is smaller than 10/91 and larger than 10/100.

[AnitaX292]

Thanks for the explanation and pointing out my error! Sorry, it is from GMAT prep 3. I will make sure I don't post any from Prep 3. thanks .

[Sage Pearce-Higgins]

No worries.