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In the sequence of positive numbers x1, x2, x3, ..., what

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In the sequence of positive numbers x1, x2, x3, ..., what [#permalink] New post 14 May 2006, 04:20
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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 \(i>1\).

(2) \(x_5=\frac{x_4}{x_4+1}\)

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-sequence-of-positive-numbers-x1-x2-x3-what-96206.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 20 Jan 2014, 09:40, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: DS: Sequence [#permalink] New post 14 May 2006, 06:49
M8 wrote:
In the sequence of positive numbers X1, X2, X3, ..., what is the value of X1?

1) X(i) = X(i-1)/2
2) X(5) = X(4)/X(4)+1


do you mean X(5) = X(4)/X(4)+1 ......... as .......... X(5) = [X(4)/X(4)] + 1
or as X(5) = X(4)/[X(4)+1] ?
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Re: DS: Sequence [#permalink] New post 14 May 2006, 09:57
M8 wrote:
In the sequence of positive numbers X1, X2, X3, ..., what is the value of X1?

1) X(i) = X(i-1)/2
2) X(5) = X(4)/X(4)+1


1) tells us nothing of the values of the terms
2) tells us nothing of the sequence

together:

from 1: Each term is half of the preceeding term.
from 2: the only way for this stmt to be true and to follow the seqyence is if x(4) = 1. Therefore, x(1) = 8.

C
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 [#permalink] New post 14 May 2006, 10:04
In the sequence of positive numbers X1, X2, X3, ..., what is the value of X1?

1) X(i) = X(i-1)/2
2) X(5) = X(4)/X(4)+1

From (1), X(1) = x(0)/2
Not Sufficient

From (2), X(1) = X(0)/{X(0) + 1}
Not Sufficient.

Taking both together, lets assume X(0) = a
Thus a/2 = a/(a+1)

Solving for a yields a=1

Hence C

What is OA?
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Re: DS: Sequence [#permalink] New post 14 May 2006, 10:25
M8 wrote:
In the sequence of positive numbers X1, X2, X3, ..., what is the value of X1?

1) X(i) = X(i-1)/2
2) X(5) = X(4)/X(4)+1




hm..interesting..

step1) from2), x(5)=2 cuz, X(4)/x(4) = 1
step2) from1) x(5)=x(4)/2 =2 so x(4)=4

... thus, C
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Re: DS: Sequence [#permalink] New post 14 May 2006, 11:11
Professor wrote:
do you mean X(5) = X(4)/X(4)+1 ......... as .......... X(5) = [X(4)/X(4)] + 1
or as X(5) = X(4)/[X(4)+1] ?


Sorry Prof, of course X(4)/[X(4)+1]. I do not know how to depict small digits in the sequence in this forum so I just depicted them in parentheses.
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Re: In the sequence of positive numbers X1, X2, X3, ..., what is [#permalink] New post 20 Jan 2014, 09:35
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M8 wrote:
In the sequence of positive numbers X1, X2, X3, ..., what is the value of X1?

1) X(i) = X(i-1)/2
2) X(5) = X(4)/X(4)+1


Solve it this way

Statement 1

xi = x (i-1) /2 ....(1)

Clearly insuff

Statement 2

x5 = x4/(x4+1)

Clearly Insuff

Both statements

From (1) x5 = x4/2

From 2 x5 = x4/(x4+1)

Combine both x4 = 1

Work down till X1, or simply know that having the ratio and a value in the sequence then X1 can be calculated as such

Hence C

Just my 2c

Cheers!
J :)
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Re: In the sequence of positive numbers x1, x2, x3, ..., what [#permalink] New post 20 Jan 2014, 09:39
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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).

(1)+(2) From (1) \(x_5=\frac{x_4}{2}\) --> \(\frac{x_4}{2}=\frac{x_4}{x_4+1}\) --> \(x_4=1\) --> \(x_4=1=x_1*(\frac{1}{2})^3\) --> \(x_1=8\). Sufficient.

Answer: C.

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-sequence-of-positive-numbers-x1-x2-x3-what-96206.html
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Re: In the sequence of positive numbers x1, x2, x3, ..., what   [#permalink] 20 Jan 2014, 09:39
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