It is currently 19 Nov 2017, 05:00

### 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 June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 31 Oct 2011
Posts: 338

Kudos [?]: 1252 [0], given: 18

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

### Show Tags

28 Mar 2012, 01:57
7
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

71% (00:58) correct 29% (01:17) wrong based on 272 sessions

### HideShow timer Statistics

If a1, a2, a3, ..., an, ... is a sequence such that an = 2n for all n>= 1, is ai greater than aj?

(1) i is add and j is even.

(2) i^2 > j^2
[Reveal] Spoiler: OA

Kudos [?]: 1252 [0], given: 18

Math Expert
Joined: 02 Sep 2009
Posts: 42247

Kudos [?]: 132655 [1], given: 12331

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

### Show Tags

28 Mar 2012, 02:12
1
KUDOS
Expert's post
eybrj2 wrote:
If a1, a2, a3, ..., an, ... is a sequence such that an = 2n for all n>= 1, is ai greater than aj?

(1) i is add and j is even.

(2) i^2 > j^2

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.

Hope it's clear.
_________________

Kudos [?]: 132655 [1], given: 12331

Manager
Joined: 10 Nov 2010
Posts: 246

Kudos [?]: 412 [0], given: 22

Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19
GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)
Re: If a1, a2, a3, ..., an, ... is a sequence such that an = 2n [#permalink]

### Show Tags

31 Mar 2012, 11:08
Bunuel wrote:
eybrj2 wrote:
If a1, a2, a3, ..., an, ... is a sequence such that an = 2n for all n>= 1, is ai greater than aj?

(1) i is add and j is even.

(2) i^2 > j^2

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.

Hope it's clear.

But
if i & j are index numbers and in sequence J>I
M i correct?
_________________

The proof of understanding is the ability to explain it.

Kudos [?]: 412 [0], given: 22

Math Expert
Joined: 02 Sep 2009
Posts: 42247

Kudos [?]: 132655 [0], given: 12331

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

### Show Tags

31 Mar 2012, 11:38
GMATD11 wrote:
Bunuel wrote:
eybrj2 wrote:
If a1, a2, a3, ..., an, ... is a sequence such that an = 2n for all n>= 1, is ai greater than aj?

(1) i is add and j is even.

(2) i^2 > j^2

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.

Hope it's clear.

But
if i & j are index numbers and in sequence J>I
M i correct?

Not sure I understood your question, but i>j because it's given that i^2 > j^2.
_________________

Kudos [?]: 132655 [0], given: 12331

Manager
Joined: 28 Jul 2011
Posts: 233

Kudos [?]: 161 [0], given: 16

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

### Show Tags

31 Mar 2012, 22:21
Vote for B

Given
So we have set of consicative number

& n>=1

{2,4,6,8,10.....}

is ai>aj

(A) i + j = even
o + o = e
e + e = e

so,
if (i>j) then ai>aj
if(i<j) then ai<aj
if (i=j) then aai=aj

data not suffficient

(B)

i^2 > j^2

we know for sure that i > j as n>=1 - i & j cannot be -ve

data sufficient

Kudos [?]: 161 [0], given: 16

Current Student
Joined: 06 Sep 2013
Posts: 1972

Kudos [?]: 740 [0], given: 355

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

### Show Tags

06 Oct 2013, 11:04
Bunuel wrote:
eybrj2 wrote:
If a1, a2, a3, ..., an, ... is a sequence such that an = 2n for all n>= 1, is ai greater than aj?

(1) i is add and j is even.

(2) i^2 > j^2

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.

Hope it's clear.

Can't index numbers be decimals ever?

Kudos [?]: 740 [0], given: 355

Math Expert
Joined: 02 Sep 2009
Posts: 42247

Kudos [?]: 132655 [0], given: 12331

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

### Show Tags

06 Oct 2013, 11:14
jlgdr wrote:
Bunuel wrote:
eybrj2 wrote:
If a1, a2, a3, ..., an, ... is a sequence such that an = 2n for all n>= 1, is ai greater than aj?

(1) i is add and j is even.

(2) i^2 > j^2

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.

Hope it's clear.

Can't index numbers be decimals ever?

n in $$a_n$$ shows which term is $$a_n$$ in sequence so it cannot be a decimal.
_________________

Kudos [?]: 132655 [0], given: 12331

Non-Human User
Joined: 09 Sep 2013
Posts: 15686

Kudos [?]: 282 [0], given: 0

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

### Show Tags

29 Jan 2016, 06:35
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.
_________________

Kudos [?]: 282 [0], given: 0

Director
Joined: 04 Jun 2016
Posts: 647

Kudos [?]: 376 [0], given: 36

GMAT 1: 750 Q49 V43
Re: If a1, a2, a3, ..., an, ... is a sequence such that an = 2n [#permalink]

### Show Tags

16 Jul 2016, 01:15
eybrj2 wrote:
If a1, a2, a3, ..., an, ... is a sequence such that an = 2n for all n>= 1, is ai greater than aj?

(1) i is add and j is even.

(2) i^2 > j^2

(1) i is odd and j is even.
Not Sufficient. We don't know whether the odd or the even is bigger in magnitude

(2) i^2 > j^2
Sufficient :- Since numbers are non negative it means there is no surprises of mistakenly squaring a smaller negative.
A bigger squared value means a bigger base value
so i>j

Sufficient

_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

Kudos [?]: 376 [0], given: 36

Non-Human User
Joined: 09 Sep 2013
Posts: 15686

Kudos [?]: 282 [0], given: 0

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

### Show Tags

30 Jul 2017, 09:09
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.
_________________

Kudos [?]: 282 [0], given: 0

Re: If a1, a2, a3, ..., an, ... is a sequence such that an = 2n   [#permalink] 30 Jul 2017, 09:09
Display posts from previous: Sort by