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Intern  Joined: 06 Oct 2014
Posts: 10
If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 79% (02:16) correct 21% (02:48) wrong based on 187 sessions

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If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?

A. -10
B. -5
C. -4
D. 3
E. 7

Attachments Screen Shot 2014-11-29 at 7.09.16 PM.png [ 15.14 KiB | Viewed 4381 times ]

Originally posted by FTS185 on 29 Nov 2014, 19:10.
Last edited by Bunuel on 30 Nov 2014, 05:58, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Math Expert V
Joined: 02 Sep 2009
Posts: 58396
Re: If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?  [#permalink]

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FTS185 wrote:
If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?

A. -10
B. -5
C. -4
D. 3
E. 7

$$2^y = 4^{(5x + 3)}$$ --> $$2^y = 2^{2(5x + 3)}$$ --> $$y = 2(5x + 3)$$;

$$3^{(x - 7)} = 9^y$$ --> $$3^{(x - 7)} = 3^{2y}$$ --> $$x-7=2y$$.

From above $$x = -1$$ and $$y=-4$$ --> $$x +y = -5$$.

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Re: If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?  [#permalink]

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1
2^y = 4^(5x + 3)
2^y=2^2(5x+3)
y=10x+6 ........... 1

3^(x - 7) = 9^y
3^(x-7)=3^2y
x-7=2y ............. 2

put value of y=10x+6 in eq 2
x-7=2(10x+6)
x-7=20x+12
19x=-19
x=-1

therefore, y= -10+6
y=-4

x+y= -1-4= -5

Ans - B
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Re: If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?  [#permalink]

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2
$$2^y = 4^{(5x + 3)}$$

$$2^y = 2^{2(5x+3)}$$

y = 10x+6 ........... (1)

$$3^{(x - 7)} = 9^y$$

$$3^{(x-7)}=3^{2y}$$

x-7 = 2y ............. (2)

x-7 = 2*(10x+6)

x = -1 & y = -4

x+y = -1 -4 = -5

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Re: If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?  [#permalink]

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Hello from the GMAT Club BumpBot!

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_________________ Re: If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?   [#permalink] 22 Oct 2018, 00:33
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