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.
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.