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If 2^x+2*3^y+3 = 576, where x and y are integers, what is x + y?

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Joined: 02 Sep 2009
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If 2^x+2*3^y+3 = 576, where x and y are integers, what is x + y?  [#permalink]

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New post 22 Jan 2019, 01:29
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

68% (01:18) correct 32% (01:49) wrong based on 25 sessions

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Joined: 31 Oct 2013
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Concentration: Accounting, Finance
GPA: 3.68
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Re: If 2^x+2*3^y+3 = 576, where x and y are integers, what is x + y?  [#permalink]

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New post 22 Jan 2019, 01:36
Bunuel wrote:
If \(2^{x+2}*3^{y+3} = 576\), where x and y are integers, what is x + y?


A 2
B 3
C 5
D 6
E 8



At first we need to factorize 576.

\(576 = 3*192 = 3*2*96 =3*2*3*32 = 3*2*3*2^2*2^3. = 2^63^2.\)

Given

\(2^{x+2}*3^{y+3} = 576\)

\(2^{x+2}*3^{y+3} = 2^63^2\)

x + 2 = 6

x = 4.

again,

y + 3 = 2

y = -1.

Total: x+ y = 4 - 1 = 3.

B is the correct answer.

GMAT Club Bot
Re: If 2^x+2*3^y+3 = 576, where x and y are integers, what is x + y?   [#permalink] 22 Jan 2019, 01:36
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If 2^x+2*3^y+3 = 576, where x and y are integers, what is x + y?

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