Equation:

Now y=|x|=|x^2-4|
As both sides are positive, we can square the two sides.
\(x^2=x^4-8x^2+16……..x^4-9x^2+16=0\)
An equation of degree 4 will have 4 values of x. We can find the values through determinant of factorisation but can be left as it will not be in scope of GMAT to find 4 factors. In some cases, however, we can have same values of x leading to lesser than 4. For example x^4=16 has only two different values 2 and -2.
Answer is 4


Graphic solution

y=|x| will give you a linear equation. But as y is non negative for all values of x, we will have the line in shape of V above x axis and symmetrical to y axis.
Next y=|x^2-4| will be a parabola. If it were y=x^2-4, the parabola would have cut these lines twice. However due to MOD, the parabola will once again move up above x-axis and we will have TWO more intersections.
Thus, total 4.


D
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