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The data collected for 20 years of population surveys of a city C were

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gmatophobia
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The data collected for 20 years of population surveys of a city C were [#permalink] New post   23 Apr 2023, 23:41
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The data collected for 20 years of population surveys of a city C were analyzed. It was observed that population change follows a certain pattern such that \(\frac{a_n}{a_{(n-1)}} = r\) for n \(\geq 2\) where r is a positive constant and \(r \neq 1\) and \(a_n\) denotes the population in the nth year.

In how many of the first 13 years, the population of city C was lesser than 1000?

(1) \(a_{13} = 16900\)
(2) \(a_7 = 1000\)­
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Charlotte12345
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Re: The data collected for 20 years of population surveys of a city C were [#permalink] New post   24 Apr 2023, 03:58
IMO B is the correct solution.

1) We know that in the 13th year, the population is 16900, however we have no information whether the population is increasing or decreasing ( r could be <1 or > 1). Not sufficient.

2) We know that in year 7, the population is 1000. We also know, because r is /= 1, that the population never stays the same. Therefore, for r <1 we know that in the first 13 years the population was smaller than 1000 for 7 years and for r > 1 we know that the population is smaller for (13-7) = 6 years.

Please correct me if I'm wrong.
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Re: The data collected for 20 years of population surveys of a city C were [#permalink] New post   22 Apr 2024, 21:50
I think this question's answer is C.

You need to know if the population is increasing (K > 1) or decreasing (0 < K < 1). Without the knowledge in Statement 1, we don't know if it was 7 years (increasing) or 6 years (decreasing).
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Re: The data collected for 20 years of population surveys of a city C were [#permalink] New post   23 Apr 2024, 00:55
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wolfof6thstreet wrote:
The data collected for 20 years of population surveys of a city C were analyzed. It was observed that population change follows a certain pattern such that \(\frac{a_n}{a_{(n-1)}} = r\) for n \(\geq 2\) where r is a positive constant and \(r \neq 1\) and \(a_n\) denotes the population in the nth year.

In how many of the first 13 years, the population of city C was lesser than 1000?

(1) \(a_{13} = 16900\)
(2) \(a_7 = 1000\)­

I think this question's answer is C.

You need to know if the population is increasing (K > 1) or decreasing (0 < K < 1). Without the knowledge in Statement 1, we don't know if it was 7 years (increasing) or 6 years (decreasing).

­C is a trap answer. The point is, regardless of whether \(r < 1\) or \(r > 1\), whether we have an increasing sequence or a decreasing sequence, \(a_7 = 1000\) would be the median value, so 6 terms will be less than it and the remaining 6 terms will be greater than it. Hence, (2) is sufficient and the answer is B.

Check a very similar question from the old GMAT Prep:

https://gmatclub.com/forum/in-the-seque ... 26119.html

Hope this helps.
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gmatclubot
Re: The data collected for 20 years of population surveys of a city C were [#permalink]
23 Apr 2024, 00:55
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