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If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?

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If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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New post Updated on: 01 Sep 2014, 02:54
2
11
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

63% (02:15) correct 37% (02:29) wrong based on 257 sessions

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If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?

(A) 11/3
(B) 11/2
(C) 242
(D) 3^10
(E) 3^11 - 1

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Originally posted by giddi77 on 17 Jan 2006, 12:06.
Last edited by Bunuel on 01 Sep 2014, 02:54, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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New post 01 Sep 2014, 20:09
7
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\(3^k + 3^k = (3^9)^{(3^9)} - 3^k\)

\(3 * 3^k = 3^{(3^2 * 3^9)}\)

\(3^{k+1} = 3^{(3^{11})}\)

Equating the powers as bases are same

\(k + 1 = 3^{11}\)

\(k = 3^{11} - 1\)

Answer = E
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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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New post 17 Jan 2006, 13:13
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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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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New post 17 Jan 2006, 13:25
2
2
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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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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New post 17 Jan 2006, 14:58
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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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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New post 17 Jan 2006, 15:19
looks like giddi forgot the 3^11
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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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New post 17 Jan 2006, 16:13
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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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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New post 17 Jan 2006, 20:02
Yes got E after some struggle. Very nice question.
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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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New post 17 Jan 2006, 22:41
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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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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New post 24 Jan 2006, 07:29
Good question. Couldn't figure it out but learned a lot.

Thanks.
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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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New post 31 Aug 2014, 00:53
chiragr wrote:
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



Can you explain the LHS part of this equation? How did you get k+1 ?
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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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New post 01 Sep 2014, 02:55
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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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New post 02 Feb 2017, 12:12
giddi77 wrote:
If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?

(A) 11/3
(B) 11/2
(C) 242
(D) 3^10
(E) 3^11 - 1


3^k + 3^k = (3^9)^(3^9) - 3^k

3^k + 3^k + 3^k = (3^9)^(3^9)

Note that on the left side, when we add 3^k to itself three times, we have 3(3^k).

3(3^k) = (3^9)^(3^9)

3^(k + 1) = 3^((3^2)(3^9))

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

Since the bases are equal, we can equate the exponents:

k + 1 = 3^11

k = 3^11 - 1

Answer: E
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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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New post 06 Nov 2018, 04:18
Hi ,
I was able to solve it but took about 7 mints :(.. my initial approach was :
3^k+3^k+3^k = (3^9)^(3^9)
3(3)^k =3(3^8)^(3^9)
3^k=(3^8)^(3^9)
k=8*(3^9)
I wasnt able to proceed beyond this and hence went back and re worked on it using the approach given by Brunnel. But out of curiousity, can anyone help me with where I went wrong in my approach?
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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?   [#permalink] 06 Nov 2018, 04:18
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