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x is an integer greater than 1.

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x is an integer greater than 1. [#permalink] New post 24 Dec 2015, 07:11
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Question Stats:

65% (00:55) correct 34% (00:54) wrong based on 143 sessions
x is an integer greater than 1.

Quantity A
Quantity B
\(3^{(x+1)}\)
\(4^x\)


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


Practice Questions
Question: 3
Page: 156
Difficulty: hard
[Reveal] Spoiler: OA

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Re: x is an integer greater than 1. [#permalink] New post 24 Dec 2015, 07:20
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We have x is an integer greater than 1.

Now we have here:


\(3^(^x^+^1^)\) compared to \(4^x\)

which can be rewritten as:

\(3 * 3^x\) compared to \(4^x\)

or

\(3\) compared to \(\frac{4^x}{3^x}\)

or \(3\) compared to \(1.3333^x\)

Now we can see that for some values of x such as 2 and 3 Quantity A is bigger for every other value of x Quantity B is greater.

Thus D is the correct option.
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Re: x is an integer greater than 1. [#permalink] New post 29 Mar 2016, 08:45
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I don't get how you got from 3^(x+1) to 3 * 3^x exactly, and what values you used to show statements not to be sufficient
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Re: x is an integer greater than 1. [#permalink] New post 10 Apr 2016, 19:52
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Attached is a visual that should help.
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Screen Shot 2016-04-10 at 8.51.29 PM.png
Screen Shot 2016-04-10 at 8.51.29 PM.png [ 103.12 KiB | Viewed 6909 times ]


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Re: x is an integer greater than 1. [#permalink] New post 10 Apr 2016, 19:59
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Here is a visual version of sandy's answer (yes, you can do that when numbers have common exponents). You could also argue that it's unnecessary to even try x=4 because \(\frac{4}{3}^x\) will eventually get very large as x increases, whereas 3 is a constant and thus stays the same.
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Screen Shot 2016-04-10 at 8.58.16 PM.png
Screen Shot 2016-04-10 at 8.58.16 PM.png [ 89.58 KiB | Viewed 6910 times ]


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Re: x is an integer greater than 1. [#permalink] New post 15 Oct 2019, 15:26
Interesting question
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Re: x is an integer greater than 1. [#permalink] New post 24 Oct 2019, 22:14
At x=1, A is greater
At x=4, B is greater

So we cannot say for sure which number would be greater.

Hence, D is the Answer.
Re: x is an integer greater than 1.   [#permalink] 24 Oct 2019, 22:14
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