GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 10 Dec 2018, 01:01

# Dec 10th is GMAT Club's BDAY :-)

Free GMAT Club Tests & Quizzes for 24 hrs to celebrate together!

### 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

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Free lesson on number properties

December 10, 2018

December 10, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.
• ### Free GMAT Prep Hour

December 11, 2018

December 11, 2018

09:00 PM EST

10:00 PM EST

Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.

# 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: 51056
If a1, a2, a3, . . . , an, . . . is a sequence such that an=2n for all  [#permalink]

### Show Tags

Updated on: 06 Oct 2017, 06:48
00:00

Difficulty:

25% (medium)

Question Stats:

74% (01:32) correct 26% (01:41) wrong based on 199 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, 05:51.
Last edited by Bunuel on 06 Oct 2017, 06:48, edited 2 times in total.
Manager
Joined: 14 Dec 2014
Posts: 53
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, 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
_________________

If you like my posts appreciate them with Kudos
Cheers!!

Manager
Joined: 20 Feb 2013
Posts: 75
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, 09:37
1
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: 51056
Re: If a1, a2, a3, . . . , an, . . . is a sequence such that an=2n for all  [#permalink]

### Show Tags

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.

_________________
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, 06:46
1
The correct answer is Option B.

Bunuel : please provide OA after review.
Math Expert
Joined: 02 Sep 2009
Posts: 51056
Re: If a1, a2, a3, . . . , an, . . . is a sequence such that an=2n for all  [#permalink]

### Show Tags

06 Oct 2017, 06:49
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, 01:06
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: 51056
Re: If a1, a2, a3, . . . , an, . . . is a sequence such that an=2n for all  [#permalink]

### Show Tags

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.
_________________
Re: If a1, a2, a3, . . . , an, . . . is a sequence such that an=2n for all &nbs [#permalink] 18 Mar 2018, 04:51
Display posts from previous: Sort by