Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49300

In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk
[#permalink]
Show Tags
05 Mar 2014, 02:20
Question Stats:
69% (01:41) correct 31% (02:55) wrong based on 668 sessions
HideShow timer Statistics
The Official Guide For GMAT® Quantitative Review, 2ND EditionIn the sequence \(x_0, \ x_1, \ x_2, \ ... \ x_n\), each term from \(x_1\) to \(x_k\) is 3 greater than the previous term, and each term from \(x_{k+1}\) to \(x_n\) is 3 less than the previous term, where \(n\) and \(k\) are positive integers and \(k<n\). If \(x_0=x_n=0\) and if \(x_k=15\), what is the value of \(n\)? (A) 5 (B) 6 (C) 9 (D) 10 (E) 15 Problem Solving Question: 131 Category: Algebra Sequences Page: 78 Difficulty: 600 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
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




Math Expert
Joined: 02 Sep 2009
Posts: 49300

Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk
[#permalink]
Show Tags
05 Mar 2014, 02:20
SOLUTIONIn the sequence \(x_0, \ x_1, \ x_2, \ ... \ x_n\), each term from \(x_1\) to \(x_k\) is 3 greater than the previous term, and each term from \(x_{k+1}\) to \(x_n\) is 3 less than the previous term, where \(n\) and \(k\) are positive integers and \(k<n\). If \(x_0=x_n=0\) and if \(x_k=15\), what is the value of \(n\)?(A) 5 (B) 6 (C) 9 (D) 10 (E) 15 Probably the easiest way will be to write down all the terms in the sequence from \(x_0=0\) to \(x_n=0\). Note that each term from from \(x_0=0\) to \(x_k=15\) is 3 greater than the previous and each term from \(x_{k+1}\) to \(x_n\) is 3 less than the previous term: So we'll have: \(x_0=0\), 3, 6, 9, 12, \(x_k=15\), 12, 9, 6, 3, \(x_n=0\). So we have 11 terms from \(x_0\) to \(x_n\) thus \(n=10\). Answer: D.
_________________
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




SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1834
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk
[#permalink]
Show Tags
05 Mar 2014, 20:25
Answer = D = 10 Series will be formed as below starting from x0 = 0 & ending up with x10 = 0 xk = 15 0, 3, 6, 9, 12, 15, 12, 9, 6, 3, 0
_________________
Kindly press "+1 Kudos" to appreciate



Manager
Joined: 28 May 2014
Posts: 56

Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk
[#permalink]
Show Tags
26 Jul 2014, 22:17
Bunuel,
If the total terms ins sequence are 11, how is the no of terms n 10? Can you please explain? Thanks in advance.



Math Expert
Joined: 02 Sep 2009
Posts: 49300

In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk
[#permalink]
Show Tags
27 Jul 2014, 03:25



Manager
Joined: 28 May 2014
Posts: 56

Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk
[#permalink]
Show Tags
27 Jul 2014, 06:53
Yes so the correct ans should be 11 which is not present in any of the options.



Math Expert
Joined: 02 Sep 2009
Posts: 49300

Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk
[#permalink]
Show Tags
27 Jul 2014, 09:28



Director
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 669
Location: United States (CA)
Age: 38
GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42
WE: Education (Education)

In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk
[#permalink]
Show Tags
10 Aug 2016, 19:39
Attached is a visual that should help.
Attachments
Screen Shot 20160810 at 7.23.00 PM.png [ 89.74 KiB  Viewed 11316 times ]
_________________
Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching, both inperson (San Diego, CA, USA) and online worldwide, since 2002.
One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V (1 question wrong).
You can download my official testtaker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y94hlarr Date of Birth: 09 December 1979.
GMAT Action Plan and Free EBook  McElroy Tutoring
Contact: mcelroy@post.harvard.edu



Intern
Joined: 18 Mar 2017
Posts: 38

Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk
[#permalink]
Show Tags
02 Apr 2017, 09:51
Bunuel wrote: kotela wrote: In the sequence \(x_0, \ x_1, \ x_2, \ ... \ x_n\), each term from \(x_1\) to \(x_k\) is 3 greater than the previous term, and each term from \(x_{k+1}\) to \(x_n\) is 3 less than the previous term, where \(n\) and \(k\) are positive integers and \(k<n\). If \(x_0=x_n=0\) and if \(x_k=15\), what is the value of \(n\)?
A.5 B. 6 C. 9 D. 10 E. 15
How can i approach these kind of problems??? Probably the easiest way will be to write down all the terms in the sequence from \(x_0=0\) to \(x_n=0\). Note that each term from from \(x_0=0\) to \(x_k=15\) is 3 greater than the previous and each term from \(x_{k+1}\) to \(x_n\) is 3 less than the previous term: So we'll have: \(x_0=0\), 3, 6, 9, 12, \(x_k=15\), 12, 9, 6, 3, \(x_n=0\). So we have 11 terms from \(x_0\) to \(x_n\) thus \(n=10\). Answer: D. Hope it helps. Bunuel: if each term from \(x_{k+1}\) to \(x_n\) is 3 less than the previous term and if we have k=15, why don't we start at \(x_{15+1}\) = \(x_{16}\)? This would then change the numbers in the sequence to \(x_k=16\) = 13, 10, 7, 4, 1 ??? Thanks for your help!



Math Expert
Joined: 02 Sep 2009
Posts: 49300

Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk
[#permalink]
Show Tags
19 Apr 2017, 08:02
guenthermat wrote: Bunuel wrote: kotela wrote: In the sequence \(x_0, \ x_1, \ x_2, \ ... \ x_n\), each term from \(x_1\) to \(x_k\) is 3 greater than the previous term, and each term from \(x_{k+1}\) to \(x_n\) is 3 less than the previous term, where \(n\) and \(k\) are positive integers and \(k<n\). If \(x_0=x_n=0\) and if \(x_k=15\), what is the value of \(n\)?
A.5 B. 6 C. 9 D. 10 E. 15
How can i approach these kind of problems??? Probably the easiest way will be to write down all the terms in the sequence from \(x_0=0\) to \(x_n=0\). Note that each term from from \(x_0=0\) to \(x_k=15\) is 3 greater than the previous and each term from \(x_{k+1}\) to \(x_n\) is 3 less than the previous term: So we'll have: \(x_0=0\), 3, 6, 9, 12, \(x_k=15\), 12, 9, 6, 3, \(x_n=0\). So we have 11 terms from \(x_0\) to \(x_n\) thus \(n=10\). Answer: D. Hope it helps. Bunuel: if each term from \(x_{k+1}\) to \(x_n\) is 3 less than the previous term and if we have k=15, why don't we start at \(x_{15+1}\) = \(x_{16}\)? This would then change the numbers in the sequence to \(x_k=16\) = 13, 10, 7, 4, 1 ??? Thanks for your help! How did you get that k=15? We are given that \(x_k=15\), not k = 15. Also, the fact that \(x_k=15\) does not mean that \(x_{k+1}=16\). We are told that each term from \(x_{k+1}\) to \(x_n\) is 3 less than the previous term. Thus \(x_{k+1}\) is 3 less than the previous term which is \(x_k=15\), so \(x_{k+1}=12\)
_________________
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: 18 Mar 2017
Posts: 38

In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk
[#permalink]
Show Tags
21 Apr 2017, 11:35
Bunuel wrote: How did you get that k=15? We are given that \(x_k=15\), not k = 15. Also, the fact that \(x_k=15\) does not mean that \(x_{k+1}=16\). We are told that each term from \(x_{k+1}\) to \(x_n\) is 3 less than the previous term. Thus \(x_{k+1}\) is 3 less than the previous term which is \(x_k=15\), so \(x_{k+1}=12\)
But if we are told that (a) \(x_k=15\) and that (b) each term from \(x_{k+1}\) to \(x_n\) is 3 less, then the term after \(x_k=15\) – so \(x_{k+1}\) – will be the starting term for this reduction of 3, won't it? But if you say that the sequence is 12, \(x_k=15\), 12, then you already start reducing by 3 as of \(x_k=15\) which is not \(x_{k+1}\). Do you understand my issue?



Math Expert
Joined: 02 Sep 2009
Posts: 49300

Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk
[#permalink]
Show Tags
21 Apr 2017, 11:49
guenthermat wrote: Bunuel wrote: How did you get that k=15? We are given that \(x_k=15\), not k = 15. Also, the fact that \(x_k=15\) does not mean that \(x_{k+1}=16\). We are told that each term from \(x_{k+1}\) to \(x_n\) is 3 less than the previous term. Thus \(x_{k+1}\) is 3 less than the previous term which is \(x_k=15\), so \(x_{k+1}=12\)
But if we are told that (a) \(x_k=15\) and that (b) each term from \(x_{k+1}\) to \(x_n\) is 3 less, then the term after \(x_k=15\) – so \(x_{k+1}\) – will be the starting term for this reduction of 3, won't it? But if you say that the sequence is 12, \(x_k=15\), 12, then you already start reducing by 3 as of \(x_k=15\) which is not \(x_{k+1}\). Do you understand my issue? Each term from \(x_{k+1}\) is 3 less than the previous term. So, \(x_{k+1}\) is the first term which is 3 less than the previous term.
_________________
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



Manager
Joined: 21 Jun 2017
Posts: 85

Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk
[#permalink]
Show Tags
07 Oct 2017, 08:40
mydreammba wrote: In the sequence \(x_0, \ x_1, \ x_2, \ ... \ x_n\), each term from \(x_1\) to \(x_k\) is 3 greater than the previous term, and each term from \(x_{k+1}\) to \(x_n\) is 3 less than the previous term, where \(n\) and \(k\) are positive integers and \(k<n\). If \(x_0=x_n=0\) and if \(x_k=15\), what is the value of \(n\)?
A. 5 B. 6 C. 9 D. 10 E. 15
How can i approach these kind of problems??? Working with the givens, X0 is your starting point. When you see this kind of sequence problem, it is best to just write the numbers out as if it were on a number line  helps with organization. N is just a variable which represents the integers place in line. N is not related to the value of the sequencing digits. If it helps, personify math, and imagine these digits are waiting in line, and N is their ticket number. X0, X1, X2, X3, X4, Xk (or X5), X6, X7, X8, X9, X10(Xn)  0, 3, 6 , 9, 12, 15 12 9 6 3 0 So the value of Xn is 0; but the question asks for the value of N alone, meaning its place in line. Therefore, excluding X0, because 0 is not a value, we can conclude that the value for N is 10.
Answer is (D)



Director
Joined: 09 Mar 2016
Posts: 876

Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk
[#permalink]
Show Tags
27 Mar 2018, 12:49
Bunuel wrote: SOLUTION
In the sequence \(x_0, \ x_1, \ x_2, \ ... \ x_n\), each term from \(x_1\) to \(x_k\) is 3 greater than the previous term, and each term from \(x_{k+1}\) to \(x_n\) is 3 less than the previous term, where \(n\) and \(k\) are positive integers and \(k<n\). If \(x_0=x_n=0\) and if \(x_k=15\), what is the value of \(n\)?
(A) 5 (B) 6 (C) 9 (D) 10 (E) 15
Probably the easiest way will be to write down all the terms in the sequence from \(x_0=0\) to \(x_n=0\). Note that each term from from \(x_0=0\) to \(x_k=15\) is 3 greater than the previous and each term from \(x_{k+1}\) to \(x_n\) is 3 less than the previous term:
So we'll have: \(x_0=0\), 3, 6, 9, 12, \(x_k=15\), 12, 9, 6, 3, \(x_n=0\). So we have 11 terms from \(x_0\) to \(x_n\) thus \(n=10\).
Answer: D. if \(x_n=0\) and we are asked to find the value of the value of \(n\) ? and there are total 11 terms, and \(x_n=0\) is last term .... why are we saying that \(x_n = x_10\) are we asked to find the last value of n why are we counting 10 terms only , ok we count from zero ? so ? if i count from zero there are 11 terms ... whats point to think is it 10 ? and the tenth term is 3 by the way right ? totally confused by the question so many questions becaus of only one question.... i got into the habit of mutliplying questions
_________________
In English I speak with a dictionary, and with people I am shy.



BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 3136
Location: India
GPA: 3.12

Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk
[#permalink]
Show Tags
27 Mar 2018, 13:55
dave13 wrote: Bunuel wrote: SOLUTION
In the sequence \(x_0, \ x_1, \ x_2, \ ... \ x_n\), each term from \(x_1\) to \(x_k\) is 3 greater than the previous term, and each term from \(x_{k+1}\) to \(x_n\) is 3 less than the previous term, where \(n\) and \(k\) are positive integers and \(k<n\). If \(x_0=x_n=0\) and if \(x_k=15\), what is the value of \(n\)?
(A) 5 (B) 6 (C) 9 (D) 10 (E) 15
Probably the easiest way will be to write down all the terms in the sequence from \(x_0=0\) to \(x_n=0\). Note that each term from from \(x_0=0\) to \(x_k=15\) is 3 greater than the previous and each term from \(x_{k+1}\) to \(x_n\) is 3 less than the previous term:
So we'll have: \(x_0=0\), 3, 6, 9, 12, \(x_k=15\), 12, 9, 6, 3, \(x_n=0\). So we have 11 terms from \(x_0\) to \(x_n\) thus \(n=10\).
Answer: D. if \(x_n=0\) and we are asked to find the value of the value of \(n\) ? and there are total 11 terms, and \(x_n=0\) is last term .... why are we saying that \(x_n = x_10\) are we asked to find the last value of n why are we counting 10 terms only , ok we count from zero ? so ? if i count from zero there are 11 terms ... whats point to think is it 10 ? and the tenth term is 3 by the way right ? totally confused by the question so many questions becaus of only one question.... i got into the habit of mutliplying questions Hi dave13Writing down the terms helps(Here, \(x_k\) is nothing but \(x_5\)) \(x_0\)\(x_1\)\(x_2\)\(x_3\)\(x_4\)\(x_5\)\(x_6\)\(x_7\)\(x_8\)\(x_9\)\(x_{10}\) 03691215129630 Hope this helps you!
_________________
You've got what it takes, but it will take everything you've got




Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk &nbs
[#permalink]
27 Mar 2018, 13:55






