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Which of the following is less than the sum of the

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Which of the following is less than the sum of the [#permalink] New post 20 Aug 2006, 01:16
Which of the following is less than the sum of the reciprocal of integers from 91 to 100?

I.1/8
II.1/9
III.1/10
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 [#permalink] New post 20 Aug 2006, 01:40
At a first glance ...the answer is none of them

Because to have a common deniminator for all of these fractions (it would result in a very big in value deniminator ).
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 [#permalink] New post 20 Aug 2006, 01:49
I think answer is III only.

Each of terms 1/91, 1/92........1/100 is less than 1/90 sum will be less than 10* 1/90 = 1/9.
Each of terms 1/91, 1/92........1/100 is greater than 1/100 sum will be greater than 10 * 1/100 = 1/10

Sum 1/10 < SUM < 1/9
Hence 1/10 is less than the sum.
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  [#permalink] 20 Aug 2006, 01:49
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