Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 15 Jul 2019, 23:28

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

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

### Show Tags

Updated on: 06 Oct 2017, 07:48
1
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.

_________________

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
Posts: 51
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]

### Show Tags

18 Dec 2014, 07:47
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
_________________
If you like my posts appreciate them with Kudos
Cheers!!
Manager
Joined: 20 Feb 2013
Posts: 74
Location: India
GMAT 1: 690 Q49 V34
WE: Information Technology (Computer Software)
Re: If a1, a2, a3, . . . , an, . . . is a sequence such that an=2n for all  [#permalink]

### Show Tags

19 Dec 2014, 10:37
2
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.

_________________
If my post is helpful/correct, consider giving Kudos..
Math Expert
Joined: 02 Sep 2009
Posts: 56237
Re: If a1, a2, a3, . . . , an, . . . is a sequence such that an=2n for all  [#permalink]

### Show Tags

22 Dec 2014, 07:50
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.

_________________
Intern
Joined: 05 Oct 2014
Posts: 24
Concentration: Finance, Entrepreneurship
Re: If a1, a2, a3, . . . , an, . . . is a sequence such that an=2n for all  [#permalink]

### Show Tags

06 Oct 2017, 07:46
1
The correct answer is Option B.

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

### Show Tags

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

Bunuel : please provide OA after review.

_____________________
_________________
Intern
Joined: 01 Jun 2016
Posts: 5
Re: If a1, a2, a3, . . . , an, . . . is a sequence such that an=2n for all  [#permalink]

### Show Tags

18 Mar 2018, 02:06
Hi Bunuel please the question does not tell you if i or j is ≥ 1 and that is why i chose E.
Math Expert
Joined: 02 Sep 2009
Posts: 56237
Re: If a1, a2, a3, . . . , an, . . . is a sequence such that an=2n for all  [#permalink]

### Show Tags

18 Mar 2018, 05:51
1
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.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 11649
Re: If a1, a2, a3, . . . , an, . . . is a sequence such that an=2n for all  [#permalink]

### Show Tags

22 May 2019, 04:19
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If a1, a2, a3, . . . , an, . . . is a sequence such that an=2n for all   [#permalink] 22 May 2019, 04:19
Display posts from previous: Sort by