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Roots

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Source: — Problem Solving |
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by cramya » Mon Nov 10, 2008 9:17 pm
Whats unique about powers of 2 is

2^1+2^1 = 2 ^ 2 (i.e 2+2 =4)
2^2+2^2 = 2^3 etc... (i.e 4+4 = 8)
2^3+2^3 = 2^4 ....so on

If you keep doing this in the problem above u will end up with
2^8 + 2^8 = 2 ^ 9

Hope this helps! Let me know if u still hv questions
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Re: Roots

by logitech » Mon Nov 10, 2008 9:43 pm
[email protected] wrote:2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8=

Ans) 2^9
2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8= ANSWER

if you multiply both side with 2

( 2^2+2^2+2^3+2^4+2^5+2^6+2^7+2^8 )+2^9=2*ANSWER

ANSWER+2^9=2*ANSWER

Answer = 2^9

This approach is called the BUSINESSMAN, but if you stop by at financing department Cramya can show you the other way, which will keep you in the office after 6PM while others play GOLF outside

:lol:
LGTCH
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"DON'T LET ANYONE STEAL YOUR DREAM!"
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by cramya » Mon Nov 10, 2008 10:04 pm
You crack me up big time ; now u have got NAMES for your god and me can only understand :-) solutions!

You are something I tell u...
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by logitech » Mon Nov 10, 2008 10:10 pm
cramya wrote:You crack me up big time ; now u have got NAMES for your solutions!

You are soemthing I tell u...
I am trying to keep this place and myself entertained. I take notes of all your solution and shortcuts. You are a great help Cramya.

stop@800 and codesnoker are great GMATers as well. I am hoping that we can all beat the shit out of GMAT and enroll into programs we have all been dreaming of...

Thank you keeping this forum rolling and sharing your wisdom and knowledge.

Should you have any question, please do not hesitate to contact me :lol: This part is killing me :lol:
LGTCH
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by cramya » Tue Nov 11, 2008 10:52 am
Received a PM to explain more



Whats unique about powers of 2 is

2^1+2^1 = 2 ^ 2 (i.e 2+2 =4)
2^2+2^2 = 2^3 etc... (i.e 4+4 = 8)
2^3+2^3 = 2^4 (i.e 8+8=16 i.e 2^3=8 2^4=16))....so on


Problem is 2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8

= 2^1+2^1+2^2+2^3+2^4+2^5+2^6+2^7+2^8(2^1+2^1= 2 ^2 i.e. 2+2=4)

= 2^2+2^2+2^3+2^4+2^5+2^6+2^7+2^8(2^2+2^2 = 2^3 i.e. 4+4=8)

= 2^3+2^3+2^4+2^5+2^6+2^7+2^8(2^3+2^3=2^4 i.e 8+8=16)

= 2^4+ 2^4+2^5+2^6+2^7+2^8 (2^4+2^4=2^5 i.e. 16+16=32)

= 2^5+2^5+2^6+2^7+2^8 (2^5+2^5=2^6)

= 2^6+2^6+2^7+2^8 (2^6+2^6 = 2^7)

=2^7+2^7+2^8 (2^7+2^7=2^8)

=2^8+2^8(2^8+2^8=2^9)

=2^9

Sophia,let me know if u still have questions.
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by orel » Fri Dec 05, 2008 6:25 am
this solution and explanation was amazing! thank you Cramya!
if not a secret: how do you know all this?
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