Find all School-related info fast with the new School-Specific MBA Forum

It is currently 20 Aug 2014, 11:01

Flash Sale:

The Economist GMAT Tutor - 15% Off All Courses


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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Director
Director
User avatar
Joined: 08 Jun 2004
Posts: 502
Location: Europe
Followers: 1

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

GMAT Tests User
In the sequence of positive numbers x1, x2, x3, ..., what [#permalink] New post 14 May 2006, 04:20
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

68% (02:01) correct 33% (00:47) wrong based on 86 sessions
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}

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-sequence-of-positive-numbers-x1-x2-x3-what-96206.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 20 Jan 2014, 09:40, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Kaplan Promo CodeKnewton GMAT Discount CodesGMAT Pill GMAT Discount Codes
VP
VP
User avatar
Joined: 29 Dec 2005
Posts: 1351
Followers: 6

Kudos [?]: 28 [0], given: 0

GMAT Tests User
Re: DS: Sequence [#permalink] New post 14 May 2006, 06:49
M8 wrote:
In the sequence of positive numbers X1, X2, X3, ..., what is the value of X1?

1) X(i) = X(i-1)/2
2) X(5) = X(4)/X(4)+1


do you mean X(5) = X(4)/X(4)+1 ......... as .......... X(5) = [X(4)/X(4)] + 1
or as X(5) = X(4)/[X(4)+1] ?
Manager
Manager
avatar
Joined: 23 Jan 2006
Posts: 193
Followers: 1

Kudos [?]: 2 [0], given: 0

GMAT Tests User
Re: DS: Sequence [#permalink] New post 14 May 2006, 09:57
M8 wrote:
In the sequence of positive numbers X1, X2, X3, ..., what is the value of X1?

1) X(i) = X(i-1)/2
2) X(5) = X(4)/X(4)+1


1) tells us nothing of the values of the terms
2) tells us nothing of the sequence

together:

from 1: Each term is half of the preceeding term.
from 2: the only way for this stmt to be true and to follow the seqyence is if x(4) = 1. Therefore, x(1) = 8.

C
Director
Director
avatar
Joined: 16 Aug 2005
Posts: 950
Location: France
Followers: 1

Kudos [?]: 8 [0], given: 0

GMAT Tests User
 [#permalink] New post 14 May 2006, 10:04
In the sequence of positive numbers X1, X2, X3, ..., what is the value of X1?

1) X(i) = X(i-1)/2
2) X(5) = X(4)/X(4)+1

From (1), X(1) = x(0)/2
Not Sufficient

From (2), X(1) = X(0)/{X(0) + 1}
Not Sufficient.

Taking both together, lets assume X(0) = a
Thus a/2 = a/(a+1)

Solving for a yields a=1

Hence C

What is OA?
Manager
Manager
User avatar
Joined: 27 Jan 2006
Posts: 157
Location: Europe
Followers: 1

Kudos [?]: 2 [0], given: 0

GMAT Tests User
Re: DS: Sequence [#permalink] New post 14 May 2006, 10:25
M8 wrote:
In the sequence of positive numbers X1, X2, X3, ..., what is the value of X1?

1) X(i) = X(i-1)/2
2) X(5) = X(4)/X(4)+1




hm..interesting..

step1) from2), x(5)=2 cuz, X(4)/x(4) = 1
step2) from1) x(5)=x(4)/2 =2 so x(4)=4

... thus, C
_________________

Stay hungry, Stay foolish

Director
Director
User avatar
Joined: 08 Jun 2004
Posts: 502
Location: Europe
Followers: 1

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

GMAT Tests User
Re: DS: Sequence [#permalink] New post 14 May 2006, 11:11
Professor wrote:
do you mean X(5) = X(4)/X(4)+1 ......... as .......... X(5) = [X(4)/X(4)] + 1
or as X(5) = X(4)/[X(4)+1] ?


Sorry Prof, of course X(4)/[X(4)+1]. I do not know how to depict small digits in the sequence in this forum so I just depicted them in parentheses.
1 KUDOS received
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1628
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 11

Kudos [?]: 152 [1] , given: 254

GMAT ToolKit User
Re: In the sequence of positive numbers X1, X2, X3, ..., what is [#permalink] New post 20 Jan 2014, 09:35
1
This post received
KUDOS
M8 wrote:
In the sequence of positive numbers X1, X2, X3, ..., what is the value of X1?

1) X(i) = X(i-1)/2
2) X(5) = X(4)/X(4)+1


Solve it this way

Statement 1

xi = x (i-1) /2 ....(1)

Clearly insuff

Statement 2

x5 = x4/(x4+1)

Clearly Insuff

Both statements

From (1) x5 = x4/2

From 2 x5 = x4/(x4+1)

Combine both x4 = 1

Work down till X1, or simply know that having the ratio and a value in the sequence then X1 can be calculated as such

Hence C

Just my 2c

Cheers!
J :)
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19030
Followers: 3361

Kudos [?]: 24386 [1] , given: 2677

Re: In the sequence of positive numbers x1, x2, x3, ..., what [#permalink] New post 20 Jan 2014, 09:39
1
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-sequence-of-positive-numbers-x1-x2-x3-what-96206.html
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: In the sequence of positive numbers x1, x2, x3, ..., what   [#permalink] 20 Jan 2014, 09:39
    Similar topics Author Replies Last post
Similar
Topics:
11 Experts publish their posts in the topic In the sequence of positive numbers x1, x2, x3, ..., what testprep2010 20 21 Jun 2010, 14:58
2 In the sequence of positive numbers x_1 , x_2 , x_3 ,... Vyacheslav 4 10 Jan 2010, 13:43
In the sequence of positive numbers x_1, x_2, x_3 what vaivish1723 1 12 Jun 2009, 22:27
1 If the sequence x{_1} , x{_2} , x{_3} , ...., x{_n} , ....is jimmylow 3 17 Jul 2008, 02:03
If the sequence X(1), X(2), X(3),...,X(n),..is such that rahulraao 5 08 Oct 2005, 03:18
Display posts from previous: Sort by

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

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.