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

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1 00:00

Difficulty:   25% (medium)

Question Stats: 74% (01:31) correct 26% (01:39) wrong based on 171 sessions

### HideShow timer Statistics 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.

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Originally posted by Bunuel on 18 Dec 2014, 06:51.
Last edited by Bunuel on 06 Oct 2017, 07:48, edited 2 times in total.
Manager  Joined: 14 Dec 2014
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Re: If a1, a2, a3, . . . , an, . . . is a sequence such that an=2n for all  [#permalink]

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

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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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Math Expert V
Joined: 02 Sep 2009
Posts: 56237
Re: If a1, a2, a3, . . . , an, . . . is a sequence such that an=2n for all  [#permalink]

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

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The correct answer is Option B.

Bunuel : please provide OA after review.
Math Expert V
Joined: 02 Sep 2009
Posts: 56237
Re: If a1, a2, a3, . . . , an, . . . is a sequence such that an=2n for all  [#permalink]

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chipsy wrote:
The correct answer is Option B.

Bunuel : please provide OA after review.

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

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Hi Bunuel please the question does not tell you if i or j is ≥ 1 and that is why i chose E.
Math Expert V
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Posts: 56237
Re: If a1, a2, a3, . . . , an, . . . is a sequence such that an=2n for all  [#permalink]

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chisichei wrote:
Hi Bunuel please the question does not tell you if i or j is ≥ 1 and that is why i chose E.

i and j are index numbers indicating which position a number has in the sequence. The sequence starts with a1, so both i and j must be more than or equal to 1.
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Re: If a1, a2, a3, . . . , an, . . . is a sequence such that an=2n for all  [#permalink]

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_________________ Re: If a1, a2, a3, . . . , an, . . . is a sequence such that an=2n for all   [#permalink] 22 May 2019, 04:19
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