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

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

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New post Updated on: 06 Oct 2017, 06:48
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A
B
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E

Difficulty:

  25% (medium)

Question Stats:

74% (01:32) correct 26% (01:41) wrong based on 199 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


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Originally posted by Bunuel on 18 Dec 2014, 05:51.
Last edited by Bunuel on 06 Oct 2017, 06:48, edited 2 times in total.
Added the OA.
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Re: If a1, a2, a3, . . . , an, . . . is a sequence such that an=2n for all  [#permalink]

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New post 18 Dec 2014, 06:47
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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New post 19 Dec 2014, 09:37
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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.

Answer 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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New post 22 Dec 2014, 06:50
1
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.

Answer: 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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New post 06 Oct 2017, 06:46
1
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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New post 06 Oct 2017, 06:49
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Re: If a1, a2, a3, . . . , an, . . . is a sequence such that an=2n for all  [#permalink]

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New post 18 Mar 2018, 01:06
Hi Bunuel please the question does not tell you if i or j is ≥ 1 and that is why i chose E.
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Re: If a1, a2, a3, . . . , an, . . . is a sequence such that an=2n for all  [#permalink]

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New post 18 Mar 2018, 04:51
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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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 for all &nbs [#permalink] 18 Mar 2018, 04:51
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