GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 17 Dec 2018, 06:41

R1 Decisions:

Michigan Ross Chat (US calls are expected today)  |  UCLA Anderson Chat  (Calls expected to start at 7am PST; Applicants from Asia will hear first)


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 in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • 10 Keys to nail DS and CR questions

     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.
  • R1 Admission Decisions: Estimated Decision Timelines and Chat Links for Major BSchools

     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.

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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51261
Re: In the sequence of positive numbers x1, x2, x3, ..., what  [#permalink]

Show Tags

New post 06 Jul 2014, 23:57
Intern
Intern
avatar
B
Joined: 14 Jul 2015
Posts: 25
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, 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
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2633
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, 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
Director
User avatar
B
Joined: 10 Mar 2013
Posts: 503
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, 05:27
testprep2010 wrote:
In the sequence of positive numbers \(x_1\), \(x_2\), \(x_3\), ..., what is the value of \(x_1\)?

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


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

Director
Director
User avatar
B
Joined: 04 Jun 2016
Posts: 571
GMAT 1: 750 Q49 V43
Re: In the sequence of positive numbers x1, x2, x3, ..., what  [#permalink]

Show Tags

New post 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) \(x_i=\frac{x_{(i-1)}}{2}\) 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.

Intern
Intern
avatar
B
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

New post 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
Manager
User avatar
G
Joined: 20 Apr 2018
Posts: 175
Concentration: Technology, Nonprofit
WE: Analyst (Non-Profit and Government)
Premium Member
Re: In the sequence of positive numbers x1, x2, x3, ..., what  [#permalink]

Show Tags

New post 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) \(x_i=\frac{x_{(i-1)}}{2}\) 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.

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
User avatar
V
Joined: 02 Sep 2009
Posts: 51261
Re: In the sequence of positive numbers x1, x2, x3, ..., what  [#permalink]

Show Tags

New post 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) \(x_i=\frac{x_{(i-1)}}{2}\) 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.

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
B
Joined: 23 Oct 2018
Posts: 2
Re: In the sequence of positive numbers x1, x2, x3, ..., what  [#permalink]

Show Tags

New post 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
Intern
avatar
Joined: 20 Aug 2018
Posts: 27
In the sequence of positive numbers x1, x2, x3, ..., what  [#permalink]

Show Tags

New post 24 Nov 2018, 16:57
A video with a more thorough explanation can be found here:
https://www.youtube.com/watch?v=3l0g2OPhI_o

Statement (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

GMAT Club Bot
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 ] 

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  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.