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

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Math Expert
Joined: 02 Sep 2009
Posts: 58005
If x is a positive integer, is the value of y - z at least twice the  [#permalink]

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20 Aug 2019, 02:22
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Difficulty:

45% (medium)

Question Stats:

74% (01:56) correct 26% (02:32) wrong based on 19 sessions

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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) $$x = 5$$

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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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20 Aug 2019, 02:23
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) $$x = 5$$

Similar question from OG: https://gmatclub.com/forum/if-n-is-a-po ... 44344.html
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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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20 Aug 2019, 06:55
1
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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