GRE question on plugging in values

GRE Quant Problem Solving
1

While going through some of the videos, I noticed that a lot of Math problems require plugging in of values to arrive at the answer. For example, in this question below:

x is an integer greater than 1.
A = 3^(x+1)
B = 4^x

That is, 3 raised to the power (x+1) and 4 raised to the power x.

I plugged in the integers 2 and 3 as x, and determined A to be greater than B in both cases. I marked A as the answer.
However, I saw in the video that Greg goes on to plug in x = 4 as well, and determined that B is greater than A. Hence, D is the answer since we cannot determine the relationship conclusively.

My question is: Until when do we go on plugging in values, hoping to get at least one case that is different from the previous cases? What if in this question I had to go on till x=8? That does not seem like the most efficient method.

This is a common mistake I’ve been making. I stop after a few values and fail to consider that one value of x which disproves my analysis. Would be great if I could get some help on this!

2

For this question, we have A which has a smaller base but higher exponent, and B which is the opposite: larger base, smaller exponent. When you test out small x values like 2, 3, A>B. But, instinctively, you should be on the look out for a point where the “pattern” of A>B might flip because of the larger base."

So know that ETS won’t write a question in which you need to plug in an obscene # of numbers, but try to be comprehensive using the clues you get from the type of question it is. Also, you could use the calculator to enter in a much larger exponent x, such as trying x = 7 or something. Just keep track of the number of times you multiply 3x3… and 4x4…

3

This is a good way to approach these questions. I’ll keep this in mind as I continue to practice. Thanks a ton! :slight_smile: