Suppose the "Poor" and "Rich" Have Identical Demand Functions for Good

Suppose the "poor" and "rich" have identical demand functions for good X but only differ in income (I) .

At a given price of X,the price elasticity of their individual demand curves is such that

A) the rich person's demand is more elastic than the poor person's.
B) the poor person's demand is more elastic than the rich person's.
C) the poor person's demand is as elastic as the rich person's.
D) the rich person's demand is as elastic as the poor person's.