Zarrolou wrote:
Just one thing before I proceed, my option E "cannot be determined" sounds good as possible answer.
Some users wrote to me saying that is the first thing that came into their mind when they saw the question. What do you think?
Thanks again Mike
I agree with Mike. 'Cannot be determined' is not a valid GMAT option. You probably wanted to say 'Infinite values'.
By the way, it's a very nice question. I think it has many subtle takeaways
p = |x+3| - |x-3|
First thing to realize here is that p needs to be an integer, not x.
Another thing, when you subtract two mods, the result takes the same value over a wide range.
____________________ -3 ___________x ___________3_________________________
<----------------------------<-----------------------------------------------------------------These are the two points -3 and 3 on the number line. We need to find
'the distance from -3' - 'the distance from 3' = p
i.e red line - green line.
Notice that the red line will cancel the part of green line to the left of -3 and hence red line - green line will always be -6 for all value to the left of -3.
Similarly, red line - green line will be 6 for all values to the right of 3.
The tricky values are the ones lying in between -3 and 3. When x = -3, we get p = -6. For some point between -3 and 3, we will get p = -5, -4, -3, -2.... 6. So there will be 13 values.
e.g. p = 5
If you move 0.5 to the right of -3, distance from -3 will be 0.5 and distance from 3 will be 5.5.
0.5 - 5.5 = -5
and so on...
_________________
Karishma
Veritas Prep GMAT Instructor
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