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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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VP
Joined: 30 Jun 2008
Posts: 1033

Kudos [?]: 709 [1], given: 1

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

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07 Oct 2008, 06:05
1
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Question Stats:

100% (00:37) correct 0% (00:00) wrong based on 21 sessions

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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
_________________

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

Kudos [?]: 709 [1], given: 1

Senior Manager
Joined: 29 Mar 2008
Posts: 348

Kudos [?]: 96 [0], given: 0

Re: PS : GMAT Prep [#permalink]

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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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"Leave no stone unturned."
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Kudos [?]: 96 [0], given: 0

SVP
Joined: 05 Jul 2006
Posts: 1751

Kudos [?]: 432 [1], given: 49

Re: PS : GMAT Prep [#permalink]

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07 Oct 2008, 09:44
1
KUDOS
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

Kudos [?]: 432 [1], given: 49

VP
Joined: 30 Jun 2008
Posts: 1033

Kudos [?]: 709 [0], given: 1

Re: PS : GMAT Prep [#permalink]

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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
_________________

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

Kudos [?]: 709 [0], given: 1

Re: PS : GMAT Prep   [#permalink] 07 Oct 2008, 10:05
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