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In the sequence of positive numbers \(x_1\), \(x_2\), \(x_3\), ..., what is the value of \(x_1\)?

(1) \(x_i=\frac{x_{(i-1)}}{2}\) for all integers \(i>1\) --> we have the general formula connecting two consecutive terms (basically we have geometric progression with common ratio 1/2), but without the value of any term this info is insufficient to find \(x_1\).

(2) \(x_5=\frac{x_4}{x_4+1}\) --> we have the relationship between \(x_5\) and \(x_4\), also insufficient to find \(x_1\) (we cannot extrapolate the relationship between \(x_5\) and \(x_4\) to all consecutive terms in the sequence).

\(x_i=\frac{x_{(i-1)}}{2}\), so every next term is preivious term times \(\frac{1}{2}\) --> \(x_4=x_3*\frac{1}{2}=x_2*\frac{1}{2}*\frac{1}{2}=x_1*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}=x_1*(\frac{1}{2})^3\).
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But how do you account for the fact that x4 could be equal to zero.

By taking both the statements together, one of the solutions is also x4 = 0. It nowhere mentions in the question that the sequence has all distinct numbers. Or may be I am unaware that sequence is meant to consist of distinct numbers only.

But how do you account for the fact that x4 could be equal to zero.

By taking both the statements together, one of the solutions is also x4 = 0. It nowhere mentions in the question that the sequence has all distinct numbers. Or may be I am unaware that sequence is meant to consist of distinct numbers only.

Stem says: "In the sequence of positive numbers ..."
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Re: In the sequence of positive numbers x1, x2, x3, ..., what [#permalink]

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05 Jun 2013, 03:38

1 st.) Does not tell us anything. It only tells us the sequence formula and how each term in the sequence are related, but no numbers.

2 st.) Again this statement tells us the relation of X5 and X4, no real numbers. Not sufficient.

Combining two statements we see that according to the first formula X4+1=2 which means that X4=1. Solving it for X3=X2/2, X4=X2/4--->1=X2/4---> X2=4. X2=X1/2--->X1=8

The answer is C.
_________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Note : you will find two values of X1 from above quadratic equation i.e X1 = 0 and X1 = 8, since it is given that X1 is positive so we cant take X1=0 hence sufficient

In the sequence of positive numbers \(x_1\), \(x_2\), \(x_3\), ..., what is the value of \(x_1\)?

(1) \(x_i=\frac{x_{(i-1)}}{2}\) for all integers \(i>1\) --> we have the general formula connecting two consecutive terms (basically we have geometric progression with common ratio 1/2), but without the value of any term this info is insufficient to find \(x_1\).

(2) \(x_5=\frac{x_4}{x_4+1}\) --> we have the relationship between \(x_5\) and \(x_4\), also insufficient to find \(x_1\) (we cannot extrapolate the relationship between \(x_5\) and \(x_4\) to all consecutive terms in the sequence).

In the sequence of positive numbers \(x_1\), \(x_2\), \(x_3\), ..., what is the value of \(x_1\)?

(1) \(x_i=\frac{x_{(i-1)}}{2}\) for all integers \(i>1\) --> we have the general formula connecting two consecutive terms (basically we have geometric progression with common ratio 1/2), but without the value of any term this info is insufficient to find \(x_1\).

(2) \(x_5=\frac{x_4}{x_4+1}\) --> we have the relationship between \(x_5\) and \(x_4\), also insufficient to find \(x_1\) (we cannot extrapolate the relationship between \(x_5\) and \(x_4\) to all consecutive terms in the sequence).

I tried to do this by plugging in numbers and after 3+ minutes, I chose "Neither Suff" b/c I wasn't seeing any trends.

A and B are both insufficient because we don't have a starting point. When I combined, I still didn't see a starting point and went through the calculations only to realize that I STILL didn't have a starting point.

In retrospect, if I was to plug in numbers, what would be the better approach? Should I pick a number for say X5 and work backwards on both A and B or does picking numbers in this problem fail? It seemed to me that I could get MULTIPLE values since I could assign ANY value to X5 etc.?

I tried to do this by plugging in numbers and after 3+ minutes, I chose "Neither Suff" b/c I wasn't seeing any trends.

A and B are both insufficient because we don't have a starting point. When I combined, I still didn't see a starting point and went through the calculations only to realize that I STILL didn't have a starting point.

In retrospect, if I was to plug in numbers, what would be the better approach? Should I pick a number for say X5 and work backwards on both A and B or does picking numbers in this problem fail? It seemed to me that I could get MULTIPLE values since I could assign ANY value to X5 etc.?

On DS questions when plugging numbers, goal is to prove that the statement is not sufficient. So we should try to get an YES answer with one chosen number(s) and a NO with another.

You can easily see that (1) and (2) are not sufficient alone: different numbers plugged there will lead to different values of x1. When you take the statements together you are able to find the value of x4, and then the value of x1, so no need to plug-in there.
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Re: In the sequence of positive numbers x1, x2, x3, ..., what [#permalink]

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06 Jul 2014, 08:51

Bunuel wrote:

In the sequence of positive numbers \(x_1\), \(x_2\), \(x_3\), ..., what is the value of \(x_1\)?

(1) \(x_i=\frac{x_{(i-1)}}{2}\) for all integers \(i>1\) --> we have the general formula connecting two consecutive terms (basically we have geometric progression with common ratio 1/2), but without the value of any term this info is insufficient to find \(x_1\).

(2) \(x_5=\frac{x_4}{x_4+1}\) --> we have the relationship between \(x_5\) and \(x_4\), also insufficient to find \(x_1\) (we cannot extrapolate the relationship between \(x_5\) and \(x_4\) to all consecutive terms in the sequence).

In the sequence of positive numbers \(x_1\), \(x_2\), \(x_3\), ..., what is the value of \(x_1\)?

(1) \(x_i=\frac{x_{(i-1)}}{2}\) for all integers \(i>1\) --> we have the general formula connecting two consecutive terms (basically we have geometric progression with common ratio 1/2), but without the value of any term this info is insufficient to find \(x_1\).

(2) \(x_5=\frac{x_4}{x_4+1}\) --> we have the relationship between \(x_5\) and \(x_4\), also insufficient to find \(x_1\) (we cannot extrapolate the relationship between \(x_5\) and \(x_4\) to all consecutive terms in the sequence).

Re: In the sequence of positive numbers x1, x2, x3, ..., what [#permalink]

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06 Jul 2014, 19:39

Bunnuel,

Are AP and GP formulas and concepts required for GMAT? Its obvious that knowing them can be helpful like it helped here, but does GMAT need you to know these thoroughly?

gmatclubot

Re: In the sequence of positive numbers x1, x2, x3, ..., what
[#permalink]
06 Jul 2014, 19:39

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