Data Sufficiency

If |x+2|=4, what is the value of x?
(1) x^2 ≠ 4;
(2) x^2 = 36;

I understand why statement (2) is sufficient, but I don't see how the statement (1) could be sufficient.
The answer is D

hi
according to the problem, the value of x could be x=2 if x>=-2, or x could be x=-6 if x<-2
(1) says that x does not equal 2, or -2, so the only value of x left is x=-6
as |-6+2|=|-4|=4
1 st is also suff

I can't seem to remember how to solve the equation |x+2|=4. I know, it's something simple, but it doesn't ring the bell. Isn't it a system of equations:

If x+2>0, then x+2=4
or
If x+2<0, then ???

Could you please remind me how to solve this equation?

Thank you in advance

Hey deight,

Great question - absolute value questions seem to look a lot trickier than they really need to be.

Think about it this way: If the absolute value of x is 4, then that means that x is either 4 or -4, right?

Well, if the absolute value of (x + 2) is 4, then:

x + 2 = 4

or

x + 2 = -4

Probably the most natural way to approach these is just to remember that each absolute value "interior" has two solutions - the positive and negative value. So just treat that "interior" of the absolute value bracket as two different problems and you'll find both solutions.

Here, x + 2 = -4 is the negative option, meaning that x = -6.

Thank you, Brian!

It's a great way to think about the problems with absolute values.

Now I have just another question. If we solve the original equation, we get two answers (2 and -6), but it's not sufficient enough (for GMAT), because we want to have a single solution, right?

Exactly right, deight - to be sufficient a statement must yield EXACTLY ONE answer to the question. So if it asks:

What is the value...

You need to be able to arrive at only one answer.


And if it asks a Yes/No...

You need the answer to be ALWAYS Yes or ALWAYS No - you can't have any room for doubt.