It is currently 17 Oct 2017, 17:53

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41873

Kudos [?]: 128604 [0], given: 12180

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

Show Tags

New post 07 Jul 2014, 00:57

Kudos [?]: 128604 [0], given: 12180

Intern
Intern
avatar
B
Joined: 14 Jul 2015
Posts: 28

Kudos [?]: 11 [0], given: 10

GMAT 1: 710 Q49 V39
Reviews Badge
In the sequence of positive numbers x1, x2, x3, ..., what is the value [#permalink]

Show Tags

New post 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

Kudos [?]: 11 [0], given: 10

Expert Post
Math Forum Moderator
avatar
B
Joined: 20 Mar 2014
Posts: 2676

Kudos [?]: 1722 [0], given: 792

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
In the sequence of positive numbers x1, x2, x3, ..., what [#permalink]

Show Tags

New post 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 \(x_4\)
_________________

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
Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.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

Kudos [?]: 1722 [0], given: 792

Intern
Intern
avatar
B
Joined: 14 Jul 2015
Posts: 28

Kudos [?]: 11 [0], given: 10

GMAT 1: 710 Q49 V39
Reviews Badge
Re: In the sequence of positive numbers x1, x2, x3, ..., what [#permalink]

Show Tags

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?

Kudos [?]: 11 [0], given: 10

Expert Post
Math Forum Moderator
avatar
B
Joined: 20 Mar 2014
Posts: 2676

Kudos [?]: 1722 [0], given: 792

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
In the sequence of positive numbers x1, x2, x3, ..., what [#permalink]

Show Tags

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.
_________________

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
Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.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

Kudos [?]: 1722 [0], given: 792

Director
Director
User avatar
Joined: 10 Mar 2013
Posts: 593

Kudos [?]: 458 [0], given: 200

Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
GMAT ToolKit User
In the sequence of positive numbers x1, x2, x3, ..., what [#permalink]

Show Tags

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.
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Share some Kudos, if my posts help you. Thank you !

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Kudos [?]: 458 [0], given: 200

Director
Director
User avatar
Joined: 04 Jun 2016
Posts: 647

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

GMAT 1: 750 Q49 V43
Re: In the sequence of positive numbers x1, x2, x3, ..., what [#permalink]

Show Tags

New post 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) \(x_5=\frac{x_4}{x_4+1}\)


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
_________________

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
Director
User avatar
Joined: 04 Jun 2016
Posts: 647

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

GMAT 1: 750 Q49 V43
Re: In the sequence of positive numbers x1, x2, x3, ..., what [#permalink]

Show Tags

New post 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) \(x_5=\frac{x_4}{x_4+1}\)


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
_________________

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
Director
User avatar
Joined: 04 Jun 2016
Posts: 647

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

GMAT 1: 750 Q49 V43
Re: In the sequence of positive numbers x1, x2, x3, ..., what [#permalink]

Show Tags

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
_________________

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

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16760

Kudos [?]: 273 [0], given: 0

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

Show Tags

New post 09 Aug 2017, 22:34
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 273 [0], given: 0

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

Go to page   Previous    1   2   [ 30 posts ] 

Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.