D

Step 1: Understand the concept of the center of mass (COM). The center of mass of a system of particles is given by the formula:
$$ x_{cm} = \frac{\sum m_i x_i}{\sum m_i} $$
where $m_i$ is the mass of each particle and $x_i$ is the position of each particle.

Step 2: Given that the center of mass is located at the origin (0), it implies that the weighted average of the x-coordinates of the particles must equal zero.

Step 3: Therefore, if some particles have positive x-coordinates, there must be enough negative x-coordinates from other particles to balance the total to zero. Conversely, if all particles were positive (Option A), or all negative (Option B), then the center of mass cannot be at the origin.

Step 4: If all particles had non-negative x-coordinates (Option C), the center of mass could never be at the origin unless all particles are located exactly at the origin, which is a very specific case that doesn't apply generally.

Conclusion: Hence, the correct option is that the particles may have some with positive and others with negative x-coordinates (Option D). Therefore, the answer is D.