Problem Solving

https://www.beatthegmat.com/mba/2009/09/ ... ute-values

Who else sees a problem with the below problem.

What is x? (Data Sufficiency)

(1) | x | < 2

(2) | x | = 3x - 2


As discussed above, AV equations give 2 solutions and AV inequalities give 2 endpoints of ranges. In this sense, we know that neither Statement (1) nor Statement (2) is sufficient, right? Not so fast.

Statement (1) gives us a range, and tells us that -2 < x < 2.
Per strategy above, we can split Statement (2) into the following two equations:
x = 3x -2, and

-x = 3x - 2

x =1

x = 1/2


It seems that even with (1) and (2) TOGETHER, we still would not know whether x = 1 or x = 1/2. However, these questions emphasize the need of plugging back into the original equation to check your answer.

If we were to plug in x = 1/2 into | x | = 3x - 2, we would get 1/2 = -1/2, which is NOT true. Since this solution cannot exist, only x = 1 is our solution. Answer Choice (B).

I am lost as to why the hell do we even need to calculate the second equation if we are going to reject the solution found from it. What is the right way of solving the problem ? Do we ignore the second equation when there is a variable on both sides of the equation ?

Well, The solution given above is the correct way to proceed.

As you are saying why we need to find the solution when we reject it. Its not like we are finding the solution and rejecting it. Its the whole process to find the valid solution.

So 2nd statement gives only one valid solution and the only way to find it , is to solve the equation and then validate the solution thus found, back into equation.