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2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = ? * 2^9 *

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2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = ? * 2^9 * [#permalink]

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\(2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8\) = ?

* 2^9
* 2^10
* 2^16
* 2^35
* 2^37
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Kudos [?]: 709 [1], given: 1

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Joined: 29 Mar 2008
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Re: PS : GMAT Prep [#permalink]

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New post 07 Oct 2008, 08:19
amitdgr wrote:
\(2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8\) = ?

* 2^9
* 2^10
* 2^16
* 2^35
* 2^37


=>2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8

=> 2+ [2^1 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8]
The term in the square bracket is in geometric progression i.e, of teh form a, ar, ar^2, ar^3 etc....
Where, a= 1st term, r= 2nd term/1st term (ratio of the two consecutive terms)

Sum of the terms in GP = a(r^n-1)/(r-1)
Here, r=2, n=8, a=2
[2^1 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8] = 2(2^8-1)/(2-1) => 2(2^8-1)

Going back to the problem:
2+ [2^1 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8]
=> 2+ 2(2^8-1)
=> 2+2^9-2
=>2^9

Hence (A)
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Re: PS : GMAT Prep [#permalink]

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New post 07 Oct 2008, 09:44
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amitdgr wrote:
\(2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8\) = ?

* 2^9
* 2^10
* 2^16
* 2^35
* 2^37


2+2 = 2^2 , 2^2 + 2^2 = 2*2^2 = 2^3 , 2^3+2^3 = 2*2^3 = 2^4

THUS THE EXPRESSION BOILS DOWN TO

2^8 +2^8 = 2*2^8 = 2^9

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Re: PS : GMAT Prep [#permalink]

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New post 07 Oct 2008, 10:05
Thanks guys :) 2^9 is the right answer .... I made serious careless mistake while counting :) I failed to see the pattern while on the test ... I recognized it when I was reviewing :)

Thanks again
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"You have to find it. No one else can find it for you." - Bjorn Borg

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Re: PS : GMAT Prep   [#permalink] 07 Oct 2008, 10:05
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2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = ? * 2^9 *

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