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

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

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07 Jul 2014, 00:57
ravih wrote:
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?

Short answer would be YES.
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In the sequence of positive numbers x1, x2, x3, ..., what is the value [#permalink]

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03 Aug 2015, 02:23
In the sequence of positive numbers x1, x2, x3, ..., what is the value of x1?

(1) xi=$$\frac{x(i−1)}{2}$$ for all integers i>1.

(2) x5=$$\frac{x4}{(x4+1)}$$

[Reveal] Spoiler:
This question has already been discussed in the below thread, but I couldn't post a reply as it is locked:
in-the-sequence-of-positive-numbers-x1-x2-x3-what-29538.html

Bunuel's solution:
1) xi=$$\frac{x(i−1)}{2}$$ 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 x1.

(2) x5=$$\frac{x4}{x4+1}$$ --> we have the relationship between x5 and x4, also insufficient to find x1 (we cannot extrapolate the relationship between x5 and x4 to all consecutive terms in the sequence).

(1)+(2) From (1) x5=$$\frac{x4}{2}$$ --> $$\frac{x4}{2}$$=$$\frac{x4}{(x4+1)}$$ --> x4=1 --> x4=1=x1∗(1/2)^3 --> x1=8. Sufficient.

My question is, for (1)+(2), why can't it be:
From (1) x4=$$\frac{x3}{2}$$ --> $$\frac{x3}{2}$$=$$\frac{x3}{(x3+1)}$$ --> x3=1 --> x3=1=x1∗(1/2)^2 --> x1=4??
Alternatively, if we try to use both (1) and (2) with x1,x2,x3 it will give different solutions?

Last edited by Engr2012 on 03 Aug 2015, 04:55, edited 1 time in total.
Formatted the question

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

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03 Aug 2015, 04:59
visram04 wrote:
In the sequence of positive numbers x1, x2, x3, ..., what is the value of x1?

(1) xi=$$\frac{x(i−1)}{2}$$ for all integers i>1.

(2) x5=$$\frac{x4}{(x4+1)}$$

[Reveal] Spoiler:
This question has already been discussed in the below thread, but I couldn't post a reply as it is locked:
in-the-sequence-of-positive-numbers-x1-x2-x3-what-29538.html

Bunuel's solution:
1) xi=$$\frac{x(i−1)}{2}$$ 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 x1.

(2) x5=$$\frac{x4}{x4+1}$$ --> we have the relationship between x5 and x4, also insufficient to find x1 (we cannot extrapolate the relationship between x5 and x4 to all consecutive terms in the sequence).

(1)+(2) From (1) x5=$$\frac{x4}{2}$$ --> $$\frac{x4}{2}$$=$$\frac{x4}{(x4+1)}$$ --> x4=1 --> x4=1=x1∗(1/2)^3 --> x1=8. Sufficient.

My question is, for (1)+(2), why can't it be:
From (1) x4=$$\frac{x3}{2}$$ --> $$\frac{x3}{2}$$=$$\frac{x3}{(x3+1)}$$ --> x3=1 --> x3=1=x1∗(1/2)^2 --> x1=4??
Alternatively, if we try to use both (1) and (2) with x1,x2,x3 it will give different solutions?

Topics merged.

Please format your question properly as it becomes difficult to understand the terms and variables.

From where are you getting $$\frac{x_3}{2}$$=$$\frac{x_3}{(x_3+1)}$$ ? We only have a relation between $$x_5$$ and $$x_4$$
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Re: In the sequence of positive numbers x1, x2, x3, ..., what [#permalink]

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03 Aug 2015, 06:31
We can't assume x5=$$\frac{x4}{(x4+1)}$$ means, x4=$$\frac{x3}{(x3+1)}$$ and x3=$$\frac{x2}{(x2+1)}$$ and so on?

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

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03 Aug 2015, 06:34
visram04 wrote:
We can't assume x5=$$\frac{x4}{(x4+1)}$$ means, x4=$$\frac{x3}{(x3+1)}$$ and x3=$$\frac{x2}{(x2+1)}$$ and so on?

No, definitely not, unless

1. It is mentioned in the stem
2. You can calculate that particular relation.

The equation you have mentioned between $$x_4$$ and $$x_3$$ can not be proved for both the points mentioned above.

Case in point, once you calculate that $$x_1 = 8$$

$$x_2 = 4$$
$$x_3 = 2$$
$$x_4 = 1$$
$$x_5 = 0.5$$

So, $$x_4 \neq \frac{x_3}{x_3+1}$$

Furthermore, for your statement to hold true, the question should have mentioned

$$x_i \neq \frac{x_i}{x_i+1}$$

instead of a particular value relation (example, $$x_4$$ and $$x_5$$)

Also, if ever you find that the solutions you get after solving 2 statements separately are contradictory, then you have made some mistake as per GMAT's guidelines, the 2 statements provided can not contradict each other.

Hope this helps.
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Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

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

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17 Jan 2016, 06:27
testprep2010 wrote:
In the sequence of positive numbers $$x_1$$, $$x_2$$, $$x_3$$, ..., what is the value of $$x_1$$?

(1) $$x_i=\frac{x_{(i-1)}}{2[/fraction (2) [m]x_5=[fraction]x_4/x_4+1}$$

This is not my strongest topic, but I just want to share my experience with this type of questions.
One can solve this type of questions if you have a general formula (sometimes given in the question stem) and concrete values for at least two other terms in the sequence.

Question: We are not given any formula here, we are just asked to find a value of X1.
(1) It's just a general formula, that gives us the relaionship of any two terms in the sequence, but we don't have any concrete values. Not sufficient
(2) Here we are given ONLY a relationship between X5 and X4, but you cannot just use this relationship for other terms, X4 and X5 could by any positive values. Not sufficient.
(1) + (2): x4=x4/x4+1 = x4/2, ok, so you can find the x4, in the same manner you can find x3 etc. so , STOP, there is no need to calculate further, one can see here, that it's possible to find x1

Would appreciate some comments from math experts. I have seen many questions of this type, and there are always about a general formula and some concrete values, which we can use to find any term in the sequence.
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Re: In the sequence of positive numbers x1, x2, x3, ..., what [#permalink]

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16 Jul 2016, 01:43
testprep2010 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 $$i>1$$.

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

We need both statement
Statement 1 s giving the formula for terms greater than 1
so it cannot be used to calculate the 1st term. INSUFFICIENT

Statement 2 is giving a value for 5th term.
But it is not giving a formula to tell how that term was calculated
so cannot be used. INSUFFICIENT

Both together will yield a value for 4th term, 3term and 2nd term.
Then the 1st term can be easily calculated by observing the relationship between 3rd 4th and 5th term SUFFICIENT

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

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16 Jul 2016, 01:43
testprep2010 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 $$i>1$$.

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

We need both statement
Statement 1 s giving the formula for terms greater than 1
so it cannot be used to calculate the 1st term. INSUFFICIENT

Statement 2 is giving a value for 5th term.
But it is not giving a formula to tell how that term was calculated
so cannot be used. INSUFFICIENT

Both together will yield a value for 4th term, 3term and 2nd term.
Then the 1st term can be easily calculated by observing the relationship between 3rd 4th and 5th term SUFFICIENT

_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

Kudos [?]: 365 [0], given: 36

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

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16 Jul 2016, 01:44
testprep2010 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 $$i>1$$.

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

We need both statement
Statement 1 s giving the formula for terms greater than 1
so it cannot be used to calculate the 1st term. INSUFFICIENT

Statement 2 is giving a value for 5th term.
But it is not giving a formula to tell how that term was calculated
so cannot be used. INSUFFICIENT

Both together will yield a value for 4th term, 3term and 2nd term.
Then the 1st term can be easily calculated by observing the relationship between 3rd 4th and 5th term SUFFICIENT

_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

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

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09 Aug 2017, 22:34
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Re: In the sequence of positive numbers x1, x2, x3, ..., what   [#permalink] 09 Aug 2017, 22:34

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

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