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# If 3^k+3^k = (3^9)^(3^9)-3^k, Then k=? (A) 11/3 (B) 11/2 (C)

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If 3^k+3^k = (3^9)^(3^9)-3^k, Then k=? (A) 11/3 (B) 11/2 (C) [#permalink]  17 Jan 2006, 11:06
If 3^k+3^k = (3^9)^(3^9)-3^k, Then k=?

(A) 11/3
(B) 11/2
(C) 242
(D) 310
(E) 3^11 â€“ 1
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"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

- Bernard Edmonds

Last edited by giddi77 on 17 Jan 2006, 15:12, edited 1 time in total.
VP
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C.

3^k + 3^k = 2.3^k = ((3^9)^3*9) - 3^k.
3.3^k = ((3^(9*27))

Thus, K+1 = 9*27 = 243.

Thus, k = 242.
Senior Manager
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3^k + 3^k = (3^9)^3^9 - 3^k

3*(3^k) = 3 ^ (9 * 3^9 ) = 3^(3^2 * 3^9) = 3^(3^11)

3^k+1 = 3^(3^11)

So k+1 = 3^11

So k = 3^11 -1

CEO
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Its E

(3^11) -1

Giddi77,

Initially I got confused because answer choice E is 311 -1 instead of 3^11 -1.
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Senior Manager
Joined: 13 Jun 2005
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looks like giddi forgot the 3^11
VP
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ps_dahiya wrote:
Its E

(3^11) -1

Giddi77,

Initially I got confused because answer choice E is 311 -1 instead of 3^11 -1.

Sir you are right! I have edited the question. It was an artifact of the copy and paste in the browser. Sorry about that.
_________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

- Bernard Edmonds

SVP
Joined: 16 Oct 2003
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Yes got E after some struggle. Very nice question.
Director
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yups E it is...
cud guess the value by just looking at the choices but took almost 4 min to get the real value
Manager
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Good question. Couldn't figure it out but learned a lot.

Thanks.
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