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

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Senior Manager
Joined: 08 Jun 2004
Posts: 495
Location: Europe
In the sequence of positive numbers x1, x2, x3, ..., what [#permalink]

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14 May 2006, 05:20
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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, 10:40, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
VP
Joined: 29 Dec 2005
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14 May 2006, 07:49
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] ?
Manager
Joined: 23 Jan 2006
Posts: 192

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14 May 2006, 10:57
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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14 May 2006, 11:04
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?
Manager
Joined: 27 Jan 2006
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14 May 2006, 11:25
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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Senior Manager
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14 May 2006, 12:11
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.
Current Student
Joined: 06 Sep 2013
Posts: 1997
Concentration: Finance
Re: In the sequence of positive numbers X1, X2, X3, ..., what is [#permalink]

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20 Jan 2014, 10:35
1
KUDOS
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
Math Expert
Joined: 02 Sep 2009
Posts: 39755
Re: In the sequence of positive numbers x1, x2, x3, ..., what [#permalink]

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20 Jan 2014, 10:39
4
KUDOS
Expert's post
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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.

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, 10:39
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