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# A special sequence of numbers is written as 2, 9, 28, 65, 12

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Intern
Joined: 04 Mar 2012
Posts: 37
A special sequence of numbers is written as 2, 9, 28, 65, 12  [#permalink]

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22 May 2012, 08:16
1
6
00:00

Difficulty:

55% (hard)

Question Stats:

71% (02:48) correct 29% (02:11) wrong based on 168 sessions

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A special sequence of numbers is written as 2, 9, 28, 65, 126 …….Find the ratio of the 7th term to the 15th term.

A. 1/4
B. 1/2
C. 129/422
D. 43/422
E. 43/129

couldn't get the logic behind the terms in the sequence
Manager
Joined: 21 May 2012
Posts: 92
Location: United States (CA)
Re: special sequence of numbers is written as 2, 9, 28, 65  [#permalink]

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22 May 2012, 08:24
3
1
Sequence is

$$1^3+1...2^3+1...3^3+1.....7^3+1.....15^3+1$$

Ratio thus is

$$\frac{7^3+1}{15^3+1}$$

Not sure what the quick way to simplify this is...
Intern
Joined: 28 Feb 2012
Posts: 21
GMAT 1: 700 Q48 V39
WE: Information Technology (Computer Software)
Re: A special sequence of numbers is written as 2, 9, 28, 65, 12  [#permalink]

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24 May 2012, 09:17
4
gmihir wrote:
A special sequence of numbers is written as 2, 9, 28, 65, 126 …….Find the ratio of the 7th term to the 15th term.

A. 1/4
B. 1/2
C. 129/422
D. 43/422
E. 43/129

couldn't get the logic behind the terms in the sequence

The series as pointed out already is $$(1^3+1) , (2^3+1) , (3^3+1) , (4^3+1)..$$
So, ratio of the 7th term to the 15th term = $$7^3+1/15^3+1$$

Simplify it as $$(7+1)(7^2 - 7*1 + 1)/(15+1)(15^2 - 15*1 + 1)$$
because $$a^3 + b^3 = (a+b)(a^2-ab+b^2)$$

So, our ratio is $$8*43/16*211 = 43/422$$

SVP
Joined: 06 Sep 2013
Posts: 1706
Concentration: Finance
Re: special sequence of numbers is written as 2, 9, 28, 65  [#permalink]

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13 Jan 2014, 09:39
1
Cares wrote:
Sequence is

$$1^3+1...2^3+1...3^3+1.....7^3+1.....15^3+1$$

Ratio thus is

$$\frac{7^3+1}{15^3+1}$$

Not sure what the quick way to simplify this is...

Well I'll tel you what I did

You end up with 344/3375

I just used what I call 'Brute Force Heavy discount shorcut' and ended up with 3/33 = 1/11 approx

So among the answer choices the only one that made sence was D

Not sure if there is another approach that might be more elegant

Cheers!
J

PS. After reflecting on this...

Actually what one can do is the following:

Once you get to (7/15)^3 then this is approx 1/8

Only answer choice that even comes close to 1/8 is answer choice D

Hence D it is!
Non-Human User
Joined: 09 Sep 2013
Posts: 9405
Re: A special sequence of numbers is written as 2, 9, 28, 65, 12  [#permalink]

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30 Dec 2018, 22:59
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Re: A special sequence of numbers is written as 2, 9, 28, 65, 12 &nbs [#permalink] 30 Dec 2018, 22:59
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