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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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

Attached is a visual that should help.

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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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Interesting question

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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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


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!!

The graphs are helpful. Don't make the same mistake I did (but probably wouldn't on the test). I usually try 3 values but this time I thought I had enough info after trying two: x=2; A=27, B=16 so either it must be A or D. x=3; A=81, B= 64. I see that the gap between the two has gotten bigger with a bigger x value so I just chose A. If I had tried an extreme like I am supposed to, ie 1000, I would have seen that B can be greater... or even if I had just tried 4.