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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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New post 07 Jul 2014, 00:57
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Re: In the sequence of positive numbers x1, x2, x3, ..., what [#permalink]

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

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New post 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
Answer C

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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New post 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) \(x_5=\frac{x_4}{x_4+1}\)


Answer is C
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

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

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New post 19 May 2018, 21:40
Is my eye sight weak? Or is the image too bad? I couldn't recognise 5 on x5. It looked like xs.
Re: In the sequence of positive numbers x1, x2, x3, ..., what   [#permalink] 19 May 2018, 21:40

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