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GRE Prep Club Team Member
Joined: 20 Feb 2017
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If x and y are integers and 15^x + 15^{(x+1)}/4^y = 15^y what is the
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04 May 2021, 03:34
04 May 2021, 03:34
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If x and y are integers and \(\frac{15^x + 15^{(x+1)}}{4^y} = 15^y\) what is the value of x?
A. 2
B. 3
C. 4
D. 5
E. Cannot be determined
A. 2
B. 3
C. 4
D. 5
E. Cannot be determined
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Status:Founder & Quant Trainer
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Re: If x and y are integers and 15^x + 15^{(x+1)}/4^y = 15^y what is the
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04 May 2021, 06:04
04 May 2021, 06:04
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GeminiHeat wrote:
If x and y are integers and \(\frac{15^x + 15^{(x+1)}}{4^y} = 15^y\) what is the value of x?
A. 2
B. 3
C. 4
D. 5
E. Cannot be determined
A. 2
B. 3
C. 4
D. 5
E. Cannot be determined
\(\frac{15^x + 15^{(x+1)}}{4^y} = 15^y\)
\(\frac{15^x + (15^x)(15)}{4^y} = 15^y\)
\(\frac{15^x(1 + 15)}{4^y} = 15^y\)
\(\frac{16}{4^y} = \frac{15^y}{15^x}\)
\(4^{2-y} = 15^{y-x}\)
This is only possible, when both the sides have a power of \(0\)
Therefore, \(2 - y = 0 = y - x\)
i.e. \(x = y = 2\)
Hence, option A
gmatclubot
Re: If x and y are integers and 15^x + 15^{(x+1)}/4^y = 15^y what is the [#permalink]
04 May 2021, 06:04
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