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wolfof6thstreet
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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