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!