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

It is currently 01 Sep 2014, 11:07

Happy Labor Day:

Free Access to New GMATClub Tests for all GMATClub Members!!


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 a certain sequence the difference between the (N-1)th

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 12 Feb 2006
Posts: 117
Followers: 1

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

GMAT Tests User
In a certain sequence the difference between the (N-1)th [#permalink] New post 22 Feb 2007, 20:55
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

60% (02:10) correct 40% (01:04) wrong based on 55 sessions
In a certain sequence the difference between the (N-1)th and Nth element equals the Nth element (N is any positive integer). What is the fourth element of this sequence?

(1) The first element of the sequence is 1.
(2) The third element of the sequence is 1/4.
[Reveal] Spoiler: OA
2 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 12 Mar 2006
Posts: 372
Schools: Kellogg School of Management
Followers: 2

Kudos [?]: 27 [2] , given: 3

GMAT Tests User
 [#permalink] New post 22 Feb 2007, 21:05
2
This post received
KUDOS
a(n) = nth element in the sequence

this means that a(n-1) - a(n) = a(n) => a(n-1) = 2*a(n) => a(n) = a(n-1)/2

so if we go on substituting this formula until n = 1 on the RHS we get

a(n) = a(1)/2^(n-1)

so a(4) = a(1)/2^3

so either stat1 or stat2 can be used to get the ans

my ans is D
Intern
Intern
avatar
Joined: 02 Mar 2007
Posts: 31
Followers: 0

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

 [#permalink] New post 06 Mar 2007, 15:20
If you know the rule that connects two consecutive numbers in a sequence and if you are given also a number in that sequence you can easily figure out any other member of this sequence. Basic algebra ;)
Director
Director
avatar
Joined: 12 Jun 2006
Posts: 539
Followers: 1

Kudos [?]: 13 [0], given: 1

GMAT Tests User
 [#permalink] New post 06 Mar 2007, 16:30
Prude_sb,

Please explain how you went from:
a(n-1) - a(n) = a(n)

to:
a(n-1) = 2*a(n)
Senior Manager
Senior Manager
avatar
Joined: 12 Mar 2006
Posts: 372
Schools: Kellogg School of Management
Followers: 2

Kudos [?]: 27 [0], given: 3

GMAT Tests User
 [#permalink] New post 06 Mar 2007, 19:09
ggarr wrote:
Prude_sb,

Please explain how you went from:
a(n-1) - a(n) = a(n)

to:
a(n-1) = 2*a(n)


a(n-1) - a(n) = a(n)

=> a(n-1) = a(n) + a(n)
=> a(n-1) = 2*a(n)
Director
Director
User avatar
Joined: 19 Mar 2007
Posts: 524
Followers: 2

Kudos [?]: 5 [0], given: 0

GMAT Tests User
 [#permalink] New post 09 Apr 2007, 22:28
prude_sb wrote:
a(n) = nth element in the sequence

this means that a(n-1) - a(n) = a(n) => a(n-1) = 2*a(n) => a(n) = a(n-1)/2

so if we go on substituting this formula until n = 1 on the RHS we get

a(n) = a(1)/2^(n-1)

so a(4) = a(1)/2^3


so either stat1 or stat2 can be used to get the ans

my ans is D



Could anybody please explain how Prude has obtained powers in the equation marked above?
SVP
SVP
User avatar
Joined: 01 May 2006
Posts: 1816
Followers: 8

Kudos [?]: 88 [0], given: 0

GMAT Tests User
 [#permalink] New post 09 Apr 2007, 22:50
nick_sun wrote:
prude_sb wrote:
a(n) = nth element in the sequence

this means that a(n-1) - a(n) = a(n) => a(n-1) = 2*a(n) => a(n) = a(n-1)/2

so if we go on substituting this formula until n = 1 on the RHS we get

a(n) = a(1)/2^(n-1)

so a(4) = a(1)/2^3


so either stat1 or stat2 can be used to get the ans

my ans is D



Could anybody please explain how Prude has obtained powers in the equation marked above?


Once we have a(n) = a(n-1)/2, we can calculate the relation in term n-2, n-3.... 1.

Notice that it's geometry sequence with r=1/2. Formulas helps us to conclude directly.

This is a full detailed way to arrive at the answer :)

a(n)
= a(n-1)/2 >>> with n-1
= 1/2 * (a(n-2)/2) >>> with n-2
= 1/2 * 1/2 * (a(n-3)/2) >>> with n-3
= (1/2)^3 * a(n-3)
= (1/2)^p * a(n-p) >>> with n-p

Then, if p = n-1, we have:
a(n)
= (1/2)^p * a(n-p)
= (1/2)^(n-1) * a(n-(n-1))
= (1/2)^(n-1) * a(1)
Intern
Intern
avatar
Joined: 28 Mar 2009
Posts: 23
Followers: 1

Kudos [?]: 19 [0], given: 0

Re: Sequence DS [#permalink] New post 18 May 2009, 20:06
Please correct me if I'm wrong, the answers appears to be A. Option 2 by itself seems to be insufficient as it can lead to one of two sequences:

i) 1, 0.5, 0.25, 0.125
In this sequence the fourth term is 0.125

ii) 0, 0, 0.25, 0.5
Here the fourth term is 0.5

Can anyone check whether my calculations are correct or not.
Thanks
Intern
Intern
User avatar
Joined: 07 Jan 2005
Posts: 8
Location: New York
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: Sequence DS [#permalink] New post 23 Aug 2009, 10:16
Good try (I had not thought the solution could be the second sequence too)

BUT I see you missed a stated fact
N is a positive number.This fact rejects your second sequence ( 0 is neither + or -ve)

mujimania wrote:
Please correct me if I'm wrong, the answers appears to be A. Option 2 by itself seems to be insufficient as it can lead to one of two sequences:

i) 1, 0.5, 0.25, 0.125
In this sequence the fourth term is 0.125

ii) 0, 0, 0.25, 0.5
Here the fourth term is 0.5

Can anyone check whether my calculations are correct or not.
Thanks
Intern
Intern
avatar
Joined: 09 Dec 2009
Posts: 34
Followers: 0

Kudos [?]: 5 [0], given: 7

Re: [#permalink] New post 19 Jun 2010, 12:09
ppetkov wrote:
If you know the rule that connects two consecutive numbers in a sequence and if you are given also a number in that sequence you can easily figure out any other member of this sequence. Basic algebra ;)


Is this correct? Can someone confirm? This could save us some time in DS questions.
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 25236
Followers: 3428

Kudos [?]: 25215 [1] , given: 2702

Re: Re: [#permalink] New post 19 Jun 2010, 12:48
1
This post received
KUDOS
Expert's post
JoyLibs wrote:
ppetkov wrote:
If you know the rule that connects two consecutive numbers in a sequence and if you are given also a number in that sequence you can easily figure out any other member of this sequence. Basic algebra ;)


Is this correct? Can someone confirm? This could save us some time in DS questions.


Yes it's correct.

For arithmetic (or geometric) progression if you know:

- any particular two terms,
- any particular term and common difference (common ratio),
- any particular term and the formula for n_th term,
- the sum of the sequence and either any term or common difference (common ratio),

then you will be able to calculate any missing value of given sequence.
_________________

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

CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2793
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 177

Kudos [?]: 933 [0], given: 235

GMAT Tests User Reviews Badge
Re: Sequence DS [#permalink] New post 18 Sep 2010, 08:11
bz9 wrote:
Here is another sequence question I could use some help on. I guess the answer correctly, but I'm having a hard time wrapping my head around sequence questions.

In a certain sequence the difference between the (N-1)th and Nth element equals the Nth element (N is any positive integer). What is the fourth element of this sequence?

1. The first element of the sequence is 1.
2. The third element of the sequence is 1/4.


There is no information of total number of terms.

T_{N-1} - T_{N} =T_{N}

T_{N-1} = T_{N} +T_{N}

T_{N-1} = 2*T_{N}

1. The first element is 1

=> T_1 = 2* T_2 => T_1 = 2^2 * T_3 => T_1 = 2^3 * T_4
Since T_1 is given, this is sufficient.

2. T_3 = 1/4 using same reason above this is also sufficient.

Hence D

Moreover
T_{N-1} = 2*T_{N} represents GP series with ratio =1/2. We only need to know the value of any term to find the whole series.
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

Director
Director
avatar
Status: Apply - Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 17 Jul 2010
Posts: 693
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas
Followers: 14

Kudos [?]: 71 [0], given: 15

GMAT Tests User
Re: Sequence DS [#permalink] New post 18 Sep 2010, 08:20
hoping_for_stern wrote:
Good try (I had not thought the solution could be the second sequence too)

BUT I see you missed a stated fact
N is a positive number.This fact rejects your second sequence ( 0 is neither + or -ve)

mujimania wrote:
Please correct me if I'm wrong, the answers appears to be A. Option 2 by itself seems to be insufficient as it can lead to one of two sequences:

i) 1, 0.5, 0.25, 0.125
In this sequence the fourth term is 0.125

ii) 0, 0, 0.25, 0.5
Here the fourth term is 0.5

Can anyone check whether my calculations are correct or not.
Thanks


Why does N being a positive number mean that the sequence consists of positive numbers? Isn't n just the index? Or should the statement have been a_n is positive? Also when it says the difference between an and an-1, people have used
an-1 - an = an

what about
an - an-1 = an => in which case an-1 would be 0 and that situation is perhaps avoided by saying an is positive?
_________________

Consider kudos, they are good for health

CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2793
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 177

Kudos [?]: 933 [0], given: 235

GMAT Tests User Reviews Badge
Re: Sequence DS [#permalink] New post 18 Sep 2010, 08:23
mainhoon wrote:
hoping_for_stern wrote:
Good try (I had not thought the solution could be the second sequence too)

BUT I see you missed a stated fact
N is a positive number.This fact rejects your second sequence ( 0 is neither + or -ve)

mujimania wrote:
Please correct me if I'm wrong, the answers appears to be A. Option 2 by itself seems to be insufficient as it can lead to one of two sequences:

i) 1, 0.5, 0.25, 0.125
In this sequence the fourth term is 0.125

ii) 0, 0, 0.25, 0.5
Here the fourth term is 0.5

Can anyone check whether my calculations are correct or not.
Thanks


Why does N being a positive number mean that the sequence consists of positive numbers? Isn't n just the index? Or should the statement have been a_n is positive? Also when it says the difference between an and an-1, people have used
an-1 - an = an

what about
an - an-1 = an => in which case an-1 would be 0 and that situation is perhaps avoided by saying an is positive?


if a_{n-1} = 0 => the whole sequence is 0.....but when you will use the statements, the value of terms are non-zero hence you a_{n-1} = 0 is not true.
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

Director
Director
avatar
Status: Apply - Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 17 Jul 2010
Posts: 693
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas
Followers: 14

Kudos [?]: 71 [0], given: 15

GMAT Tests User
Re: Sequence DS [#permalink] New post 18 Sep 2010, 08:36
I have a distinct feeling that the original question clearly ruled out an = 0, that is was not saying N is positive (as posted here).. But now that brings up an interesting question - can the stem conflict with the statements? In other words do we have to take the statements to be true?

There was another example where the statements were not needed to answer the question, just the stem was enough.. xy<yz<0..
_________________

Consider kudos, they are good for health

CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2793
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 177

Kudos [?]: 933 [0], given: 235

GMAT Tests User Reviews Badge
Re: Sequence DS [#permalink] New post 18 Sep 2010, 08:40
mainhoon wrote:
I have a distinct feeling that the original question clearly ruled out an = 0, that is was not saying N is positive (as posted here).. But now that brings up an interesting question - can the stem conflict with the statements? In other words do we have to take the statements to be true?

There was another example where the statements were not needed to answer the question, just the stem was enough.. xy<yz<0..


I dont think in gmat you will get such questions.....
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

BSchool Thread Master
avatar
Joined: 19 Feb 2010
Posts: 401
Followers: 19

Kudos [?]: 120 [0], given: 76

GMAT Tests User
Re: Re: [#permalink] New post 18 Oct 2010, 20:22
Bunuel wrote:
JoyLibs wrote:
ppetkov wrote:
If you know the rule that connects two consecutive numbers in a sequence and if you are given also a number in that sequence you can easily figure out any other member of this sequence. Basic algebra ;)


Is this correct? Can someone confirm? This could save us some time in DS questions.


Yes it's correct.

For arithmetic (or geometric) progression if you know:

- any particular two terms,
- any particular term and common difference (common ratio),
- any particular term and the formula for n_th term,
- the sum of the sequence and either any term or common difference (common ratio),

then you will be able to calculate any missing value of given sequence.


Wow, that is very important information. Thank you Bunuel.
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4691
Location: Pune, India
Followers: 1090

Kudos [?]: 4884 [0], given: 163

Re: Sequence DS [#permalink] New post 20 Oct 2010, 05:13
Expert's post
mujimania wrote:
Please correct me if I'm wrong, the answers appears to be A. Option 2 by itself seems to be insufficient as it can lead to one of two sequences:

i) 1, 0.5, 0.25, 0.125
In this sequence the fourth term is 0.125

ii) 0, 0, 0.25, 0.5
Here the fourth term is 0.5

Can anyone check whether my calculations are correct or not.
Thanks


It is given in the question that t(n-1) - t(n) = t(n), so t(n) = t(n-1)/2
Every subsequent term should be half of the previous term. Statement II does not lead to 0, 0, 0.25, 0.5 since the difference between 3rd and 4th terms is 0.25 which should be equal to the fourth term but it is not. The fourth term is 0.5 here. It only leads to the first sequence and hence statement II alone is sufficient.

Statements never ever contradict the data of the question stem or each other for that matter. They only provide additional information or repeat what we already have.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Manager
Manager
avatar
Joined: 25 Aug 2010
Posts: 98
Followers: 1

Kudos [?]: 4 [0], given: 1

GMAT Tests User
Re: Sequence DS [#permalink] New post 20 Oct 2010, 05:50
very good post....

first time i tried to go with the numbers and end up with a mess...

If i go and try to put some numbers in it, i would end up with the mess...

a(n_1) - a(n) = a(n)

==> a(n_1) = 2* a(n))
a(n-2) = 2* a(n_1)
==> 2*2* a(n)

----> I can get some where in the seq the value for (1) option and (2) option...
Re: Sequence DS   [#permalink] 20 Oct 2010, 05:50
    Similar topics Author Replies Last post
Similar
Topics:
2 Data Sufficiency: In a certain year, the difference between ryguy904 2 01 Aug 2008, 16:22
In a certain sequence the difference between the (N-1)st and marcodonzelli 1 02 Mar 2008, 03:25
8 Experts publish their posts in the topic In a certain year, the difference between Mary's and Jim's alimad 10 25 Nov 2007, 19:12
10 Experts publish their posts in the topic In a certain year, the difference between Mary's and Jim's a ricokevin 7 25 Apr 2007, 06:54
In a certain year, the difference between Mary's and Jim's yaron 2 27 Aug 2005, 03:56
Display posts from previous: Sort by

In a certain sequence the difference between the (N-1)th

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

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®.