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OG - Problem Solving # 80

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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OG - Problem Solving # 80

by sjcl1526 » Sun Apr 14, 2013 8:39 am
Hi,
I did not understand how the sum of reciprocals is calculated. Could anyone please help me with this?
Thank you in advance.

Here is the question one more time.

M is the sum of reciprocals of the consecutive integers from 201 to 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

Thank you!
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by Anju@Gurome » Sun Apr 14, 2013 8:54 am
sjcl1526 wrote:M is the sum of reciprocals of the consecutive integers from 201 to 300 inclusive. which of the following is true?
We don't need to calculate sum of reciprocals.
Look at the options, we need an estimated value or a bound for M.

M = (1/201 + 1/202 + 1/203 + ... + 1/299 + 1/300)

Note that there are 100 terms in the sum.
Also note that each term in the sum is less than 1/200 and more than 1/300 (except 1/300 which is equal to 1/300).

So, (1/300 + 1/300 + ... 100 times) < M < (1/200 + 1/200 + ... 100 times)
--> 100/300 < M < 100/200
--> 1/3 < M < 1/2

The correct answer is A.
Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
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by sjcl1526 » Sun Apr 14, 2013 3:15 pm
Thank you Anju!!
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