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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] New post 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 – 1
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Last edited by giddi77 on 17 Jan 2006, 15:12, edited 1 time in total.
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 [#permalink] New post 17 Jan 2006, 12:13
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.
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 [#permalink] New post 17 Jan 2006, 12:25
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

Answer is E
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 [#permalink] New post 17 Jan 2006, 13:58
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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 [#permalink] New post 17 Jan 2006, 14:19
looks like giddi forgot the 3^11
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 [#permalink] New post 17 Jan 2006, 15:13
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.
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 [#permalink] New post 17 Jan 2006, 19:02
Yes got E after some struggle. Very nice question.
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 [#permalink] New post 17 Jan 2006, 21:41
yups E it is...
cud guess the value by just looking at the choices but took almost 4 min to get the real value
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 [#permalink] New post 24 Jan 2006, 06:29
Good question. Couldn't figure it out but learned a lot.

Thanks.
  [#permalink] 24 Jan 2006, 06:29
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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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