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In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk

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In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink] New post 05 Mar 2014, 01:20
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

Problem Solving
Question: 131
Category: Algebra Sequences
Page: 78
Difficulty: 600


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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink] New post 05 Mar 2014, 01:20
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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.
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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.


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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink] New post 05 Mar 2014, 19:25
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
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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink] New post 08 Mar 2014, 11:40
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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.
_________________

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.


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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink] New post 26 Jul 2014, 21:17
Bunuel,

If the total terms ins sequence are 11, how is the no of terms n 10? Can you please explain? Thanks in advance.
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In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink] New post 27 Jul 2014, 02:25
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sri30kanth wrote:
Bunuel,

If the total terms ins sequence are 11, how is the no of terms n 10? Can you please explain? Thanks in advance.


Yes, the number of terms is 11 but we start from x_0, not from x_1, hence n=10.
_________________

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.


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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink] New post 27 Jul 2014, 05:53
Yes so the correct ans should be 11 which is not present in any of the options.
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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink] New post 27 Jul 2014, 08:28
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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk [#permalink] New post 28 Jul 2014, 08:27
Got it now. Thanks a lot Bunuel.
Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk   [#permalink] 28 Jul 2014, 08:27
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