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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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Math Expert
Joined: 02 Sep 2009
Posts: 53066
If 2^x+2*3^y+3 = 576, where x and y are integers, what is x + y?  [#permalink]

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22 Jan 2019, 00:29
00:00

Difficulty:

25% (medium)

Question Stats:

79% (01:17) correct 21% (01:55) wrong based on 17 sessions

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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

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Joined: 31 Oct 2013
Posts: 1163
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If 2^x+2*3^y+3 = 576, where x and y are integers, what is x + y?  [#permalink]

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22 Jan 2019, 00:36
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.

Re: If 2^x+2*3^y+3 = 576, where x and y are integers, what is x + y?   [#permalink] 22 Jan 2019, 00:36
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