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If a1, a2, a3, ..., an, ... is a sequence such that an = 2n

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If a1, a2, a3, ..., an, ... is a sequence such that an = 2n  [#permalink]

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New post 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 odd 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]

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New post 28 Mar 2012, 01:12
1
2
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]

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New post 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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Re: If a1, a2, a3, ..., an, ... is a sequence such that an = 2n  [#permalink]

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New post 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.
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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

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

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New post 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]

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New post 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?
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Joined: 02 Sep 2009
Posts: 51218
Re: If a1, a2, a3, ..., an, ... is a sequence such that an = 2n  [#permalink]

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New post 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.
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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: If a1, a2, a3, ..., an, ... is a sequence such that an = 2n  [#permalink]

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New post 16 Jul 2016, 00:15
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


(1) i is odd and j is even.
Not Sufficient. We don't know whether the odd or the even is bigger in magnitude

(2) i^2 > j^2
Sufficient :- Since numbers are non negative it means there is no surprises of mistakenly squaring a smaller negative.
A bigger squared value means a bigger base value
so i>j

Sufficient

Answer is B
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Re: If a1, a2, a3, ..., an, ... is a sequence such that an = 2n  [#permalink]

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New post 07 Aug 2018, 22:25
1
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.



Hi @Buneul,

The sequence is 2,4,6,8,10..... so its a arithmetic sequence of consecutive even numbers. So the question is asking in the sequence does a(i) come after a(j).

I did not understand the statement 1. Looks like a typographical error . Should its verbiage be i+j=even.

In view of my understanding of statement 1 could you help me clear my inference about the question.

a(1)=2, a(2)=4, a(3)=6, a(4)=8
From Condition
Stmt 1: i+j =even
i=1 . j=3 then i+j= even so a(i)<a(j) but if i=3 and j=1 then a(i)>a(j) So Insufficient.

Stmt 2: i^2>j^2 so i > j , so in the sequence a(j) < a(i)

Can we infer this a(j) comes before a(i) in the sequence
You have mentioned that i and j are index numbers . What are index numbers?

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

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New post 08 Aug 2018, 02:15
Probus 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.



Hi @Buneul,

The sequence is 2,4,6,8,10..... so its a arithmetic sequence of consecutive even numbers. So the question is asking in the sequence does a(i) come after a(j).

I did not understand the statement 1. Looks like a typographical error . Should its verbiage be i+j=even.

In view of my understanding of statement 1 could you help me clear my inference about the question.

a(1)=2, a(2)=4, a(3)=6, a(4)=8
From Condition
Stmt 1: i+j =even
i=1 . j=3 then i+j= even so a(i)<a(j) but if i=3 and j=1 then a(i)>a(j) So Insufficient.

Stmt 2: i^2>j^2 so i > j , so in the sequence a(j) < a(i)

Can we infer this a(j) comes before a(i) in the sequence
You have mentioned that i and j are index numbers . What are index numbers?

Probus


(1) reads: i is odd and j is even.

Edited. Thank you.
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Resources:
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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: If a1, a2, a3, ..., an, ... is a sequence such that an = 2n &nbs [#permalink] 08 Aug 2018, 02:15
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If a1, a2, a3, ..., an, ... is a sequence such that an = 2n

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