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If x is a positive integer, is the value of y - z at least twice the

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New post 20 Aug 2019, 02:22
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Re: If x is a positive integer, is the value of y - z at least twice the  [#permalink]

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New post 20 Aug 2019, 02:23
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Re: If x is a positive integer, is the value of y - z at least twice the  [#permalink]

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New post 20 Aug 2019, 06:55
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Bunuel wrote:
If x is a positive integer, is the value of y - z at least twice the value of \(3^x - 5^x\) ?

(1) \(y = 3^{x + 1}\) and \(z = 5^{x + 1}\)

(2) \(x = 5\)


Given: x is a positive integer

Asked: Is the value of y - z at least twice the value of \(3^x - 5^x\) ?
\(y-z \geq 3^x - 5^x\)

(1) \(y = 3^{x + 1}\) and \(z = 5^{x + 1}\)
\(y = 3^{x + 1} = 3*3^x\)
\(z = 5^{x + 1}=5*5^x\)
\(y-z = 3*3^x - 5*5^x = 2(3^x - 5^x) + (3^x - 3*5^x)\)
\(5^x > 3^x\) when x is a positive integer
\((3^x - 3*5^x) < 0\)
\(y-z = 3*3^x - 5*5^x = 2(3^x - 5^x) + (3^x - 3*5^x) < 2(3^x - 5^x)\)
SUFFICIENT

(2) \(x = 5\)
Value of y & z are unknown
NOT SUFFICIENT

IMO A
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Re: If x is a positive integer, is the value of y - z at least twice the   [#permalink] 20 Aug 2019, 06:55
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