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

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Math Expert
Joined: 02 Sep 2009
Posts: 42356

Kudos [?]: 133204 [0], given: 12439

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

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18 Dec 2014, 06:51
00:00

Difficulty:

35% (medium)

Question Stats:

78% (00:58) correct 22% (01:30) wrong based on 121 sessions

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Tough and Tricky questions: Sequences.

If a1, a2, a3, . . . , an, . . . is a sequence such that $$a_n=2n$$ for all n ≥ 1, is $$a_i$$ greater than $$a_j$$ ?

(1) i is odd and j is even
(2) i^2 > j^2

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 06 Oct 2017, 07:48, edited 2 times in total.

Kudos [?]: 133204 [0], given: 12439

Manager
Joined: 14 Dec 2014
Posts: 55

Kudos [?]: 40 [1], given: 14

Location: India
Concentration: Technology, Finance
GPA: 3.87
WE: Programming (Computer Software)
Re: If a1, a2, a3, . . . , an, . . . is a sequence such that an=2n for all [#permalink]

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18 Dec 2014, 07:47
1
KUDOS
1. Since we dont know the value of i and j it is difficult to judge the value a_i or a_j. Insufficient

2. i^2>j^2
i>j since sequence is valid only for +ve numbers we can ignore negative values
so. a(i) always greater than a(j) for i>j since a(i)=2i and a(j)=2j.. Sufficient.

Ans B
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Kudos [?]: 40 [1], given: 14

Manager
Joined: 20 Feb 2013
Posts: 76

Kudos [?]: 34 [1], given: 45

Location: India
GMAT 1: 690 Q49 V34
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Re: If a1, a2, a3, . . . , an, . . . is a sequence such that an=2n for all [#permalink]

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19 Dec 2014, 10:37
1
KUDOS
If a1, a2, a3, . . . , an, . . . is a sequence such that a_n=2n for all n ≥ 1, is a_i greater than a_j ?

(1) i is odd and j is even
(2) i^2 > j^2

Solution:
Here each term is twice of previous term. Need to identify whether i > j?

Statement 1: i is odd and j is even
Doesn't provide any relation between i and j - Insufficient

Statement 2: i^2 > j^2
Since a_i and a_j are terms of sequence, i and j must be positive integers.
Thus i must be greater than j and hence Statement 2 alone is Sufficient.

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Kudos [?]: 34 [1], given: 45

Math Expert
Joined: 02 Sep 2009
Posts: 42356

Kudos [?]: 133204 [1], given: 12439

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

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22 Dec 2014, 07:50
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Expert's post
Bunuel wrote:

Tough and Tricky questions: Sequences.

If a1, a2, a3, . . . , an, . . . is a sequence such that $$a_n=2n$$ for all n ≥ 1, is $$a_i$$ greater than $$a_j$$ ?

(1) i is odd and j is even
(2) i^2 > j^2

Kudos for a correct solution.

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.

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Kudos [?]: 133204 [1], given: 12439

Intern
Joined: 05 Oct 2014
Posts: 23

Kudos [?]: 12 [1], given: 88

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

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06 Oct 2017, 07:46
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The correct answer is Option B.

Bunuel : please provide OA after review.

Kudos [?]: 12 [1], given: 88

Math Expert
Joined: 02 Sep 2009
Posts: 42356

Kudos [?]: 133204 [0], given: 12439

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

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06 Oct 2017, 07:49
chipsy wrote:
The correct answer is Option B.

Bunuel : please provide OA after review.

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Kudos [?]: 133204 [0], given: 12439

Re: If a1, a2, a3, . . . , an, . . . is a sequence such that an=2n for all   [#permalink] 06 Oct 2017, 07:49
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