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Is x - 4 > y ? (1) 3^x - 3^(x-5) > 242*3^y (2) x is a positive integer

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Bunuel
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Is x - 4 > y ? (1) 3^x - 3^(x-5) > 242*3^y (2) x is a positive integer [#permalink] Is x - 4 > y ? (1) 3^x - 3^(x-5) > 242*3^y (2) x is a positive integer   04 Oct 2023, 01:30
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Question Stats:

61% (02:32) correct 39% (02:13) wrong based on 79 sessions
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Is \(x - 4 > y\)?


(1) \(3^x - 3^{(x-5)} > 242 * 3^y\)

(2) x is a positive integer



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A
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GMATinsight
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Re: Is x - 4 > y ? (1) 3^x - 3^(x-5) > 242*3^y (2) x is a positive integer [#permalink] Is x - 4 > y ? (1) 3^x - 3^(x-5) > 242*3^y (2) x is a positive integer   04 Oct 2023, 02:52
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Bunuel wrote:
Is \(x - 4 > y\)?


(1) \(3^x - 3^{(x-5)} > 242 * 3^y\)

(2) x is a positive integer



Question: Is \(x - 4 > y\)?

Statement 1: \(3^x - 3^{(x-5)} > 242 * 3^y\)

i.e. \(3^{x-4}[ 3^4 - 3] > 242 * 3^y\)
i.e. \(3^{x-4-y}[81 - 1] > 242\)
i.e. \(3^{x-4-y} > 242/80\)
i.e. \(3^{x-4-y} > 3.025\)
i.e. {x-4-y} > 1
i.e. x-4 > y
SUFFICIENT

Statement 2: x is a positive integer
NOT SUFFICIENT

Answer: Option A
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Re: Is x - 4 > y ? (1) 3^x - 3^(x-5) > 242*3^y (2) x is a positive integer [#permalink] Is x - 4 > y ? (1) 3^x - 3^(x-5) > 242*3^y (2) x is a positive integer   04 Oct 2023, 05:00
GMATinsight I think you have an error in your post above. In your first step, 3^X-4 is not correctly distributed to the second term. It should be [3^4-3^(-1)].
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Re: Is x - 4 > y ? (1) 3^x - 3^(x-5) > 242*3^y (2) x is a positive integer [#permalink] Is x - 4 > y ? (1) 3^x - 3^(x-5) > 242*3^y (2) x is a positive integer   05 Oct 2023, 14:03
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Bunuel wrote:
Is \(x - 4 > y\)?


(1) \(3^x - 3^{(x-5)} > 242 * 3^y\)

(2) x is a positive integer



This is a Data Sufficiency Butler Question



We need to know whether \(x-y>4 \)

(1) \(3^x - 3^{(x-5)} > 242 * 3^y\)

\(\frac{3^x*3^5 - 3^x}{3^5}> 242 * 3^y \)

\(\frac {3^x(3^5 - 1)}{3^5}> 242 * 3^y \)

\(\frac {3^x*{242}}{3^5}> 242 * 3^y \)

\(3^x> 3^5 * 3^y \)

\(x-y>5\)

SUFF.


(2) x is a positive integer

INSUFF.

Ans A

Hope it helps.
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Re: Is x - 4 > y ? (1) 3^x - 3^(x-5) > 242*3^y (2) x is a positive integer [#permalink]
05 Oct 2023, 14:03
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Bunuel
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