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If a1, a2, a3, ..., an, ... is a sequence such that an = 2n [#permalink ]
28 Mar 2012, 00:57

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If a1, a2, a3, ..., an, ... is a sequence such that an = 2n for all n>= 1, is ai greater than aj?

(1) i is add and j is even.

(2) i^2 > j^2

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Re: If a1, a2, a3, ..., an, ... is a sequence such that an = 2n [#permalink ]
28 Mar 2012, 01:12
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eybrj2 wrote:

If a1, a2, a3, ..., an, ... is a sequence such that an = 2n for all n>= 1, is ai greater than aj? (1) i is add and j is even. (2) i^2 > j^2

Since given that \(a_n = 2n\), for all \(n\geq{1}\) then:

\(a_1=2*1=2\);

\(a_2=2*2=4\);

\(a_3=2*3=6\);

\(a_4=2*4=8\);

...

Basically we have a sequence of positive even numbers. Question asks whether \(a_i>a_j\)? So, it basically asks whether \(i>j\)?

(1) i is add and j is even. Not sufficient.

(2) i^2 > j^2 --> since \(i\) and \(j\) are both positive integers (they represent index numbers) then \(i>j\). Sufficient.

Answer: B.

Hope it's clear.

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Re: If a1, a2, a3, ..., an, ... is a sequence such that an = 2n [#permalink ]
31 Mar 2012, 10:08

Bunuel wrote:

eybrj2 wrote:

If a1, a2, a3, ..., an, ... is a sequence such that an = 2n for all n>= 1, is ai greater than aj? (1) i is add and j is even. (2) i^2 > j^2

Since given that \(a_n = 2n\), for all \(n\geq{1}\) then:

\(a_1=2*1=2\);

\(a_2=2*2=4\);

\(a_3=2*3=6\);

\(a_4=2*4=8\);

...

Basically we have a sequence of positive even numbers. Question asks whether \(a_i>a_j\)? So, it basically asks whether \(i>j\)?

(1) i is add and j is even. Not sufficient.

(2) i^2 > j^2 --> since \(i\) and \(j\) are both positive integers (they represent index numbers) then \(i>j\). Sufficient.

Answer: B.

Hope it's clear.

though answer will remain B

But

if i & j are index numbers and in sequence J>I

M i correct?

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Math Expert

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Re: If a1, a2, a3, ..., an, ... is a sequence such that an = 2n [#permalink ]
31 Mar 2012, 10:38
GMATD11 wrote:

Bunuel wrote:

eybrj2 wrote:

If a1, a2, a3, ..., an, ... is a sequence such that an = 2n for all n>= 1, is ai greater than aj? (1) i is add and j is even. (2) i^2 > j^2

Since given that \(a_n = 2n\), for all \(n\geq{1}\) then:

\(a_1=2*1=2\);

\(a_2=2*2=4\);

\(a_3=2*3=6\);

\(a_4=2*4=8\);

...

Basically we have a sequence of positive even numbers. Question asks whether \(a_i>a_j\)? So, it basically asks whether \(i>j\)?

(1) i is add and j is even. Not sufficient.

(2) i^2 > j^2 --> since \(i\) and \(j\) are both positive integers (they represent index numbers) then \(i>j\). Sufficient.

Answer: B.

Hope it's clear.

though answer will remain B

But

if i & j are index numbers and in sequence J>I

M i correct?

Not sure I understood your question, but i>j because it's given that i^2 > j^2.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!! PLEASE READ AND FOLLOW: 12 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 ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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 ? 25 extra-hard Quant Tests GMAT Club Premium Membership - big benefits and savings

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Re: If a1, a2, a3, ..., an, ... is a sequence such that an = 2n [#permalink ]
31 Mar 2012, 21:21

Vote for B Given So we have set of consicative number & n>=1 {2,4,6,8,10.....} is ai>aj (A) i + j = even o + o = e e + e = e so, if (i>j) then ai>aj if(i<j) then ai<aj if (i=j) then aai=aj data not suffficient (B) i^2 > j^2 we know for sure that i > j as n>=1 - i & j cannot be -ve data sufficient

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Re: If a1, a2, a3, ..., an, ... is a sequence such that an = 2n [#permalink ]
06 Oct 2013, 10:04

Bunuel wrote:

eybrj2 wrote:

If a1, a2, a3, ..., an, ... is a sequence such that an = 2n for all n>= 1, is ai greater than aj? (1) i is add and j is even. (2) i^2 > j^2

Since given that \(a_n = 2n\), for all \(n\geq{1}\) then:

\(a_1=2*1=2\);

\(a_2=2*2=4\);

\(a_3=2*3=6\);

\(a_4=2*4=8\);

...

Basically we have a sequence of positive even numbers. Question asks whether \(a_i>a_j\)? So, it basically asks whether \(i>j\)?

(1) i is add and j is even. Not sufficient.

(2) i^2 > j^2 --> since \(i\) and \(j\) are both positive integers (they represent index numbers) then \(i>j\). Sufficient.

Answer: B.

Hope it's clear.

Can't index numbers be decimals ever?

Math Expert

Joined: 02 Sep 2009

Posts: 29856

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Kudos [? ]:
53965
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Re: If a1, a2, a3, ..., an, ... is a sequence such that an = 2n [#permalink ]
06 Oct 2013, 10:14
jlgdr wrote:

Bunuel wrote:

eybrj2 wrote:

If a1, a2, a3, ..., an, ... is a sequence such that an = 2n for all n>= 1, is ai greater than aj? (1) i is add and j is even. (2) i^2 > j^2

Since given that \(a_n = 2n\), for all \(n\geq{1}\) then:

\(a_1=2*1=2\);

\(a_2=2*2=4\);

\(a_3=2*3=6\);

\(a_4=2*4=8\);

...

Basically we have a sequence of positive even numbers. Question asks whether \(a_i>a_j\)? So, it basically asks whether \(i>j\)?

(1) i is add and j is even. Not sufficient.

(2) i^2 > j^2 --> since \(i\) and \(j\) are both positive integers (they represent index numbers) then \(i>j\). Sufficient.

Answer: B.

Hope it's clear.

Can't index numbers be decimals ever?

n in \(a_n\) shows which term is \(a_n\) in sequence so it cannot be a decimal.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!! PLEASE READ AND FOLLOW: 12 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 ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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 ? 25 extra-hard Quant Tests GMAT Club Premium Membership - big benefits and savings

Re: If a1, a2, a3, ..., an, ... is a sequence such that an = 2n
[#permalink ]
06 Oct 2013, 10:14

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