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x is an integer greater than 1. [#permalink]
 24 Dec 2015, 07:11
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Question Stats:
65% (00:50) correct
34% (00:45) wrong based on 293 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
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Re: x is an integer greater than 1. [#permalink]
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]
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]
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 [ 103.12 KiB | Viewed 10083 times ]
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Re: x is an integer greater than 1. [#permalink]
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 [ 89.58 KiB | Viewed 10080 times ]
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Re: x is an integer greater than 1. [#permalink]
15 Oct 2019, 15:26
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Interesting question
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Re: x is an integer greater than 1. [#permalink]
24 Oct 2019, 22:14
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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.
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Re: x is an integer greater than 1. [#permalink]
12 May 2020, 06:22
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Sanpreet wrote: 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. Be careful. The question tells us that x is an integer greater than 1. That said, the correct answer is still D
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Re: x is an integer greater than 1. [#permalink]
30 May 2020, 11:44
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This became more clear to me AFTER I answered the question and I graphed each of the values. At the lower values of x (like at 0, 1, 2, 3), 3^(x+1) is greater than 4^x. But at the extremes, 4^x quickly becomes greater for all values of x Attachment: 
Capture.JPG [ 43.52 KiB | Viewed 1958 times ]
So, plugging in numbers via trial and error is all well and good, but you really gotta think about the big picture. If you can't intuitively think about what the graphs might look like, try values that are a little bigger than sequential; this is where the test makers can get you!!
Attachments
Capture2.JPG [ 20.05 KiB | Viewed 1956 times ]
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Re: x is an integer greater than 1.
[#permalink]
30 May 2020, 11:44
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