OG 16 #100

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OG 16 #100

by Azizakaria » Sun Oct 11, 2015 4:30 am
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

I don't understand the solution, please help, thanks.[/spoiler]
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by GMATGuruNY » Sun Oct 11, 2015 4:44 am
Azizakaria wrote: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
If all of the 100 values were 1/300, the result would be the following sum:
100(1/300) = 1/3.
Since all but one of the values are actually GREATER THAN 1/300, the value of M must be GREATER THAN 1/3.

If all of the 100 values were 1/200, the result would be the following sum:
100(1/200) = 1/2.
Since all of the values are actually LESS THAN 1/200, the value of M must be LESS THAN 1/2.

Thus:
1/3 < M < 1/2.

The correct answer is A.
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by [email protected] » Sun Oct 11, 2015 9:38 am
Hi Azizakaria,

In this prompt, the answer choices are "ranges"; this usually means that there's a way to avoid doing lots of math and instead use patterns and logic to save you time.

Mitch's already pointed out the easiest way to figure out the minimum and maximum values of the sum of the reciprocals. You can actually stop working once you figure out the minimum though:

Since 1/300 < 1/201 and the sum of those 100 terms would be 1/3 AT THE MINIMUM, the only answer that's possible would be A. The extra work that Mitch did just confirms the maximum value of the sum, but it's unnecessary.

As you continue to study, be mindful of how the answer choices are written - they can sometimes provide a huge hint into the fastest way to answer the question.

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