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Director  Joined: 21 Sep 2003
Posts: 975
Location: USA
If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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2
11 00:00

Difficulty:   55% (hard)

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

### HideShow timer Statistics 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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"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

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.
SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1787
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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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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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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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  Joined: 05 Jan 2006
Posts: 362
Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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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

CEO  Joined: 20 Nov 2005
Posts: 2649
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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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
Manager  Joined: 13 Jun 2005
Posts: 244
Location: Haverhill, MA
Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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looks like giddi forgot the 3^11
Director  Joined: 21 Sep 2003
Posts: 975
Location: USA
Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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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
Posts: 1646
Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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Yes got E after some struggle. Very nice question.
Director  Joined: 04 Oct 2005
Posts: 516
Location: Chicago
Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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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  Joined: 19 Jul 2005
Posts: 60
Location: Atlanta
Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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Good question. Couldn't figure it out but learned a lot.

Thanks.
Intern  Joined: 23 Jul 2013
Posts: 6
Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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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 ?
Math Expert V
Joined: 02 Sep 2009
Posts: 56307
Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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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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Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2822
Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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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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Intern  B
Joined: 18 Jul 2018
Posts: 18
Re: If 3^k + 3^k = (3^9)^(3^9) - 3^k, then k = ?  [#permalink]

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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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