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# Shouldn't n be defined as a non negative number is the stem

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Shouldn't n be defined as a non negative number is the stem [#permalink]  09 Oct 2010, 12:37
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If series A(n) is such that A(n) = \frac{A(n-1)}{n} , how many elements of the series are larger than \frac{1}{2} ?

1. A(2) = 5
2. A(1) - A(2) = 5

Shouldn't n be defined as a non negative number is the stem ???
because the question is to find an exact number, and if n can be negative than we have no idea about that number.
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Re: Series - m15 q3 [#permalink]  09 Oct 2010, 12:38
OE :

1) Explanation 1:

Statement (1) by itself is sufficient. Together with the information from the stem, S1 completely defines the series.

Statement (2) by itself is sufficient. A(1) - A(2) = 5 = A(1) - \frac{A(1)}{2} from where A(1) = 10 .

2) Alternative Explanation from GMAT Club member laxieqv:

Statement (1) by itself is sufficient. A(2)= 5 \rightarrow A(1) = 10 , A(3) = \frac{5}{3} , A(4)= \frac{5}{12} ( all are according to the provided formula). Notice that the larger n , the smaller A(n) . For n \ge 4 , A(n) \le \frac{5}{12} \lt \frac{1}{2} \rightarrow there are only A(1) , A(2) , A(3) which are larger than \frac{1}{2} .

Statement (2) by itself is sufficient. A(1)- A(2)= 5 , together with A(2)= \frac{A(1)}{2} \rightarrow A(1) = 10 and A(2)= 5 \rightarrow come back to S1.
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Re: Series - m15 q3 [#permalink]  09 Oct 2010, 12:49
Barkatis wrote:
If series A(n) is such that A(n) = \frac{A(n-1)}{n} , how many elements of the series are larger than \frac{1}{2} ?

1. A(2) = 5
2. A(1) - A(2) = 5

Shouldn't n be defined as a non negative number is the stem ???
because the question is to find an exact number, and if n can be negative than we have no idea about that number.

I think n here denotes the order number of an element a in the sequence, so it can not be negative. For example: a_1 means firs element in the sequence, a_2 - the second, a_n - n_{th} and so on. There can not be -4th element in the sequence.

Hope it's clear.
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Re: Series - m15 q3 [#permalink]  09 Oct 2010, 15:27
Barkatis wrote:
If series A(n) is such that A(n) = \frac{A(n-1)}{n} , how many elements of the series are larger than \frac{1}{2} ?

1. A(2) = 5
2. A(1) - A(2) = 5

Shouldn't n be defined as a non negative number is the stem ???
because the question is to find an exact number, and if n can be negative than we have no idea about that number.

n is an index, so by definition it can not take negative values. It is like defining a function f(x) where x can only take non-negative integral values.
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Re: Series - m15 q3   [#permalink] 09 Oct 2010, 15:27
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