Estimation problem Number 80 from OG Math Problem Solving

[hoaska]

Hello all,
I started studying for the GMAT last week and realized that I forgot everything in Math. I am having hard time understanding the following question from the OG Math Problem Solving Practice Question number 80.
M is the sum of the reciprocals of the consecutive integers from 201 - 300, inclusive. Which of the following is true?
A. 1/3 <M < 1/2
B. 1/5 <M < 1/3
C. 1/7 <M < 1/5
D. 1/9 <M < 1/7
E. 1/12 <M < 1/9

The OG explains the solution process and says that the right answer is A. But after many times of reading the solution over and over again, I do not see reason why the right answer is A.

Please help!

Thank you

[Uva@90]

Hello all,
I started studying for the GMAT last week and realized that I forgot everything in Math. I am having hard time understanding the following question from the OG Math Problem Solving Practice Question number 80.
M is the sum of the reciprocals of the consecutive integers from 201 - 300, inclusive. Which of the following is true?
A. 1/3 <M < 1/2
B. 1/5 <M < 1/3
C. 1/7 <M < 1/5
D. 1/9 <M < 1/7
E. 1/12 <M < 1/9

The OG explains the solution process and says that the right answer is A. But after many times of reading the solution over and over again, I do not see reason why the right answer is A.

Please help!

Thank you

Hi Hoaska,
This question is already Discussed here, with Brent Reply too.
https://www.beatthegmat.com/gmat-question-t109408.html

Regards,
Uva.

[GMATGuruNY]

M is the sum of the reciprocals of the consecutive integers from 201 - 300, inclusive. Which of the following is true?
A. 1/3 <M < 1/2
B. 1/5 <M < 1/3
C. 1/7 <M < 1/5
D. 1/9 <M < 1/7
E. 1/12 <M < 1/9

M = 1/201 + 1/202....+ 1/299 + 1/300.

Consider the EXTREMES
All of the values in M are BETWEEN 1/300 and 1/200, inclusive.
If all 100 values were the lower extreme -- 1/300 -- the result would be the following sum:
100 * (1/300) = 1/3.
If all 100 values were the upper extreme -- 1/200 -- the result would be the following sum:
100 * (1/200) = 1/2.
Since all of the values in M are BETWEEN these two extremes, the sum must be BETWEEN 1/3 and 1/2.

The correct answer is A.