If mod x + 4 = 2 then x = ?

1) x^2 not equal to 4
2) x^2 = 36

I have tried solving the question and pretty much through it. I am not sure why option 2 is sufficient along with option 1.

Below is my solution

Case 1 -
|x + 4| = x + 4 = 2 makes x = -2. On back-check answer is consistent with the initial assumption that x + 4 is positive.

When x = -2, x + 4 = 2, which is indeed positive. This means that x = -2 is a good answer.

Case 2 -
x + 4 is negative makes |x + 4| = -x - 4 = 2. This means that -x = 6 or x = -6. Again we back-check: -6 + 4 = -2, which is negative.

So there are two answers to this problem: x = -2 or x = -6.

Now, getting to our stmts:

1. means that x is neither 2 or -2. This eliminates x = -2 and leaves x = -6. So 1 is sufficient.

2. x^2 = 36 makes x as 6 or -6. QUERY - At this point, we are sure that x = -6 corresponds to the main equation answer but how does it eliminate x=-2? It actually gives no infor if x =-2 should be discarded. Should I assume the overlapping value of -6 should be taken in this case? Please advice.

With the info in the problem statement and option 2, we have two equations

|x+4| = 2 with a solution set of x = {-6, -2}; and
x^2 = 36 with a solution set of x = {-6, +6}

the fundamental rule of solving equations is that the final solution should satisfy both the equations and only -6 does that.

As to your question of why we should disregard - 2, by that logic why didn't you question the reason for disregarding +6 in the second case.

Remember that just because the first equation is mentioned in the problem statement doesn't give it any precedence over the second, both of them have equal standing and hence the acceptable solution is only that value which satisfy both the equations.

Nice response, thanks!

_________________
Jamie Nelson
ManhattanGMAT Instructor

nice explanation!

yay

_________________
Tim Sanders
Manhattan GMAT Instructor