December 17, 2018 December 17, 2018 06:00 PM PST 07:00 PM PST Join our live webinar and learn how to approach Data Sufficiency and Critical Reasoning problems, how to identify the best way to solve each question and what most people do wrong. December 17, 2018 December 17, 2018 10:00 PM PST 11:00 PM PST From Dec 5th onward, American programs will start releasing R1 decisions. Chat Rooms: We have also assigned chat rooms for every school so that applicants can stay in touch and exchange information/update during decision period.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51261

Re: In the sequence of positive numbers x1, x2, x3, ..., what
[#permalink]
Show Tags
06 Jul 2014, 23:57



Intern
Joined: 14 Jul 2015
Posts: 25

Re: In the sequence of positive numbers x1, x2, x3, ..., what
[#permalink]
Show Tags
03 Aug 2015, 05:31
We can't assume x5=\(\frac{x4}{(x4+1)}\) means, x4=\(\frac{x3}{(x3+1)}\) and x3=\(\frac{x2}{(x2+1)}\) and so on?



CEO
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

In the sequence of positive numbers x1, x2, x3, ..., what
[#permalink]
Show Tags
03 Aug 2015, 05:34
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.



Director
Joined: 10 Mar 2013
Posts: 503
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

In the sequence of positive numbers x1, x2, x3, ..., what
[#permalink]
Show Tags
17 Jan 2016, 05:27
testprep2010 wrote: In the sequence of positive numbers \(x_1\), \(x_2\), \(x_3\), ..., what is the value of \(x_1\)?
(1) \(x_i=\frac{x_{(i1)}}{2[/fraction (2) [m]x_5=[fraction]x_4/x_4+1}\) 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): x 4=x 4/x 4+1 = x 4/2, ok, so you can find the x 4, in the same manner you can find x 3 etc. so , STOP, there is no need to calculate further, one can see here, that it's possible to find x 1Answer 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



Director
Joined: 04 Jun 2016
Posts: 571

Re: In the sequence of positive numbers x1, x2, x3, ..., what
[#permalink]
Show Tags
16 Jul 2016, 00:44
testprep2010 wrote: In the sequence of positive numbers \(x_1\), \(x_2\), \(x_3\), ..., what is the value of \(x_1\)?
(1) \(x_i=\frac{x_{(i1)}}{2}\) 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 semiretired.



Intern
Joined: 14 Aug 2015
Posts: 30
Location: India
Concentration: Other, Technology
WE: Engineering (Retail)

Re: In the sequence of positive numbers x1, x2, x3, ..., what
[#permalink]
Show Tags
19 May 2018, 20:40
Is my eye sight weak? Or is the image too bad? I couldn't recognise 5 on x5. It looked like xs.



Manager
Joined: 20 Apr 2018
Posts: 175
Concentration: Technology, Nonprofit
WE: Analyst (NonProfit and Government)

Re: In the sequence of positive numbers x1, x2, x3, ..., what
[#permalink]
Show Tags
11 Oct 2018, 21:10
Bunuel wrote: In the sequence of positive numbers \(x_1\), \(x_2\), \(x_3\), ..., what is the value of \(x_1\)?
(1) \(x_i=\frac{x_{(i1)}}{2}\) 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. Bunuel I got this wrong because I thought x1 = 0 is also a solution. But since the question says it is a sequence of positive numbers, I guess I cannot assume that. On a slightly different note, can the values in a sequence be a constant?



Math Expert
Joined: 02 Sep 2009
Posts: 51261

Re: In the sequence of positive numbers x1, x2, x3, ..., what
[#permalink]
Show Tags
11 Oct 2018, 22:21
sandman13 wrote: Bunuel wrote: In the sequence of positive numbers \(x_1\), \(x_2\), \(x_3\), ..., what is the value of \(x_1\)?
(1) \(x_i=\frac{x_{(i1)}}{2}\) 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. Bunuel I got this wrong because I thought x1 = 0 is also a solution. But since the question says it is a sequence of positive numbers, I guess I cannot assume that. On a slightly different note, can the values in a sequence be a constant? Yes, all terms in a sequence can be the same. For example, {1, 1, 1, 1, ...}.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 23 Oct 2018
Posts: 2

Re: In the sequence of positive numbers x1, x2, x3, ..., what
[#permalink]
Show Tags
18 Nov 2018, 14:12
Why are we allowed to apply the information found in 1) to the question stem? The sequence in part 1) is defined for all integers i>1, yet in this case the question stem wants us to find the value of 1? For this reason i thought the answer should be E). Please help



Intern
Joined: 20 Aug 2018
Posts: 27

In the sequence of positive numbers x1, x2, x3, ..., what
[#permalink]
Show Tags
24 Nov 2018, 16:57
A video with a more thorough explanation can be found here: https://www.youtube.com/watch?v=3l0g2OPhI_oStatement (1) gives us a general equation that can be applied to any value of x. Helpful, but not sufficient. Statement (2) gives us an equation that is specific to x5; it does not necessarily apply to every other value of x. Perhaps helpful, but not sufficient. In combination, however, we can now write two equations with two unknowns (x5 and x4). Any time you have two unknows, you can solve for both of them if you have two equations that are different from each other (as we do here), so without doing any math we know that we can find a value for x4, and then we could go back and use the equation in statement (1) to find x1. Answer C.
_________________
http://www.crushthegmat.org




In the sequence of positive numbers x1, x2, x3, ..., what &nbs
[#permalink]
24 Nov 2018, 16:57



Go to page
Previous
1 2
[ 30 posts ]



