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Manager  Joined: 31 Oct 2011
Posts: 213
If a1, a2, a3, ..., an, ... is a sequence such that an = 2n  [#permalink]

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 58427
Re: If a1, a2, a3, ..., an, ... is a sequence such that an = 2n  [#permalink]

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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.

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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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.

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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Joined: 02 Sep 2009
Posts: 58427
Re: If a1, a2, a3, ..., an, ... is a sequence such that an = 2n  [#permalink]

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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.

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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Manager  Joined: 28 Jul 2011
Posts: 159
Re: If a1, a2, a3, ..., an, ... is a sequence such that an = 2n  [#permalink]

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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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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.

Hope it's clear.

Can't index numbers be decimals ever?
Math Expert V
Joined: 02 Sep 2009
Posts: 58427
Re: If a1, a2, a3, ..., an, ... is a sequence such that an = 2n  [#permalink]

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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.

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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GMAT 1: 750 Q49 V43 Re: If a1, a2, a3, ..., an, ... is a sequence such that an = 2n  [#permalink]

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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

(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

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

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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.

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
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Probus

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Math Expert V
Joined: 02 Sep 2009
Posts: 58427
Re: If a1, a2, a3, ..., an, ... is a sequence such that an = 2n  [#permalink]

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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.

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.
_________________ Re: If a1, a2, a3, ..., an, ... is a sequence such that an = 2n   [#permalink] 08 Aug 2018, 03:15
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