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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:

66% (00:55) correct 33% (00:46) wrong based on 68 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.
Attachments

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 5413 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.
Attachments

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 5413 times ]


_________________

Harvard grad and verified 99% GRE scorer, offering high-quality private GRE tutoring and coaching, both in-person (San Diego, CA, USA) and online worldwide, since 2002.

GRE Action Plan and Free E-Book - McElroy Tutoring

Personal Best GRE Score: 168/170 Quant (95%), 169/170 Verbal (99%), 5.5 AWA (98%)

GRE Vocab Capacity - Amazon.com

Vince and Brian's Free GRE PowerPrep Explanations

My GRE AMA on Reddit

Check Me Out on GMAT Club

My GRE Subreddit: r/GREpreparation

Re: x is an integer greater than 1.   [#permalink] 10 Apr 2016, 19:59
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