If x is an integer, is 4^x < 3^(x+1)?
1)x is positive..
I used x=1/2,1,2 to plug in.. and I found 1 is sufficient.. but I didn't use 4 to plug in which yields no to the prompt..
How to determine what nos to plug in and when to stop plugging in?
This will come through practice.
The good thing is - there are n number of ways to solve a question. the bad thing is - you need to find the fastest. There is no need to plug a 100 numbers in this case. You just need to find whether the situation holds true for every positive x or not. Your first step should always be to reduce the number of ' numbers you need to plug in' .
First, I'd suggest you put an '=' instead of the </> sign. so essentially 4^x = 3^x * 3.
This is one way of quickly finding what number to plug. Find the value of x that satisfies the equation. This is your critical point. Use a few values to the left of this and a few to the right.
so is 4^x<3^x*3
or (4/3)^x<3 (because 3^x is always positive you can bring it to the LHS)
for 1 it is true for 10000000 it is not. hence, the statement is insufficient.
MacFauz's method is good as well.