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If x is the sum of the reciprocals of the consecutive integers from 51 24 Jun 2022, 18:30
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C
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55% (hard)

Question Stats:

63% (02:21) correct 37% (02:16) wrong based on 353 sessions

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If x is the sum of the reciprocals of the consecutive integers from 51 to 60, inclusive and y is the sum of the reciprocals of the consecutive integers from 61 to 70, inclusive, which of the following is correct?

I. 1/x > 6
II. 1/y > 7
III. 1/y > 1/x

(A) Only I
(B) Only II
(C) Only III
(D) Only II and III
(E) I, II and III
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C
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If x is the sum of the reciprocals of the consecutive integers from 51 08 Oct 2022, 00:35
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average value of X = 1/55 , count =10
so, sum of x = 10/55
1/x = 55/10 = 5.5

average value of Y = 1/65, count = 10
so, sum of Y = 10/65
1/y = 6.5
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If x is the sum of the reciprocals of the consecutive integers from 51 24 Jun 2022, 18:47
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The question #156 of the gmat official guide 2022 you can solve exactly the same way that I solved this one.
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If x is the sum of the reciprocals of the consecutive integers from 51 08 Oct 2022, 02:37
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Asked: If x is the sum of the reciprocals of the consecutive integers from 51 to 60, inclusive and y is the sum of the reciprocals of the consecutive integers from 61 to 70, inclusive, which of the following is correct?

\(x = \frac{1}{51} + \frac{1}{52} + \frac{1}{53} +\frac{1}{54} + \frac{1}{55} + \frac{1}{56} +\frac{1}{57} + \frac{1}{58} + \frac{1}{59} +\frac{1}{60} \)

\(y = \frac{1}{61} + \frac{1}{62} + \frac{1}{63} +\frac{1}{64} + \frac{1}{65} + \frac{1}{66} +\frac{1}{67} + \frac{1}{68} + \frac{1}{69} +\frac{1}{70} \)

\(\frac{10}{60} = \frac{1}{6}<x = \frac{1}{51} + \frac{1}{52} + \frac{1}{53} +\frac{1}{54} + \frac{1}{55} + \frac{1}{56} +\frac{1}{57} + \frac{1}{58} + \frac{1}{59} +\frac{1}{60} < \frac{10}{50} = \frac{1}{5}\)

\(\frac{1}{6} < x < \frac{1}{5}\)
\(5< \frac{1}{x} < 6\)

\(\frac{10}{70} = \frac{1}{7}< y = \frac{1}{61} + \frac{1}{62} + \frac{1}{63} +\frac{1}{64} + \frac{1}{65} + \frac{1}{66} +\frac{1}{67} + \frac{1}{68} + \frac{1}{69} +\frac{1}{70} < \frac{10}{60} = \frac{1}{6}\)

\(\frac{1}{7} < y < \frac{1}{6}\)
\(6< \frac{1}{y}< 7\)

I. 1/x > 6: Incorrect
II. 1/y > 7: Incorrect
III. 1/y > 1/x : Correct

IMO C
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If x is the sum of the reciprocals of the consecutive integers from 51 15 Oct 2025, 04:30
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