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# If 3^7 – 3^5 = (2^x)(3^y), where x and y are integers, what is x + y?

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Math Expert
Joined: 02 Sep 2009
Posts: 58432
If 3^7 – 3^5 = (2^x)(3^y), where x and y are integers, what is x + y?  [#permalink]

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22 Jan 2019, 01:02
00:00

Difficulty:

15% (low)

Question Stats:

82% (00:53) correct 18% (01:31) wrong based on 36 sessions

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If $$3^7 – 3^5 = (2^x)(3^y)$$, where x and y are integers, what is x + y?

A 2
B 3
C 8
D 15
E 243

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Joined: 31 Oct 2013
Posts: 1465
Concentration: Accounting, Finance
GPA: 3.68
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Re: If 3^7 – 3^5 = (2^x)(3^y), where x and y are integers, what is x + y?  [#permalink]

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22 Jan 2019, 01:05
Bunuel wrote:
If $$3^7 – 3^5 = (2^x)(3^y)$$, where x and y are integers, what is x + y?

A 2
B 3
C 8
D 15
E 243

Given,

$$3^7 – 3^5 = (2^x)(3^y)$$

$$3^5(3^2 -1) = 2^x3^y$$

$$3^5 2^3 = 2^x3^y$$

x= 3 and y= 5.

x + y = 3 + 5 = 8.

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Joined: 09 Nov 2015
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Re: If 3^7 – 3^5 = (2^x)(3^y), where x and y are integers, what is x + y?  [#permalink]

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22 Jan 2019, 01:16
3^5(3^2-1)=(2^x)(3^y)
3^5 2^3 =(2^x)(3^y)
x=3
y=5

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Concentration: Sustainability, Marketing
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Re: If 3^7 – 3^5 = (2^x)(3^y), where x and y are integers, what is x + y?  [#permalink]

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22 Jan 2019, 04:43
Bunuel wrote:
If $$3^7 – 3^5 = (2^x)(3^y)$$, where x and y are integers, what is x + y?

A 2
B 3
C 8
D 15
E 243

solve expression we get :
2^x*3^y = 3^5*2^3
x+y = 8
IMO C
Re: If 3^7 – 3^5 = (2^x)(3^y), where x and y are integers, what is x + y?   [#permalink] 22 Jan 2019, 04:43
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