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

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Joined: 21 Sep 2003
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If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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Updated on: 01 Sep 2014, 02:54
2
11
00:00

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

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

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

Equating the powers as bases are same

$$k + 1 = 3^{11}$$

$$k = 3^{11} - 1$$

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##### General Discussion
Director
Joined: 20 Sep 2005
Posts: 977
Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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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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Posts: 362
Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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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

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

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

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

Thanks.
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Posts: 6
Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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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

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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01 Sep 2014, 02:55
AkshayDavid wrote:
chiragr 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*(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

Can you explain the LHS part of this equation? How did you get k+1 ?

3*3^k = 3^(k+1).

Hope it's clear.
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Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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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

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Posts: 18
Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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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?
Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?   [#permalink] 06 Nov 2018, 04:18
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