How many values can the integer \(p=|x+3|-|x-3|\) assume?

A)6
B)7
C)13
D)12
E)Infinite values

My own question, as always any feedback is appreciated
Click here for the OE.

Good job arpanpatnaik, vinaymimani!

Official explanation

The function \(|x+3|-|x-3|\) for values \(\geq{}3\) equals \(6\), and for values \(\leq{}-3\) equals \(-6\)
For the middle values it follows the equation \(2x\) (as the users above correctly say)

However there is a quicker way to get to the answer than counting the possible values.

Its upper limit is \(6\), its lower limit is \(-6\) and the function \(2x\) is monotonic and increasing (and continuous), so will assume all values between 6 and -6 included.
(This is not theory necessary for the GMAT, but if notice the fact that \(2x\) must pass for all values between 6 and -6, you can save time)

So the values that the integer p can assume are \(-6,-5,...,0,...,5,6\) TOT=\(13\)

The correct answer is C

For for clarity, below there is the graph of \(|x+3|-|x-3|\) that will make my explanation more clear.

How many values can the integer \(p=|x+3|-|x-3|\) assume?

A)6
B)7
C)13
D)12
E)Infinite values

My own question, as always any feedback is appreciated
Click here for the OE.