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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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Joined: 02 Sep 2009
Posts: 53020
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, 00:02
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Difficulty:

25% (medium)

Question Stats:

82% (01:00) correct 18% (01:45) wrong based on 25 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: 1138
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
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, 00:05
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
Posts: 61
Concentration: Strategy, Technology
WE: Information Technology (Computer Software)
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, 00:16
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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Joined: 18 Aug 2017
Posts: 1880
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
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, 03:43
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
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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] 22 Jan 2019, 03:43
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