To determine if a bond is covalent or ionic without knowing the electronegativities is to see if it is a metal-nonmetal bond or a nonmetal-nonmetal bond. Metal-nonmetal bonds are ALWAYS ionic, and nonmetal-nonmetal bonds are ALWAYS covalent. A is the metal-nonmetal bond and thus ionic. B & C are both nonmetal-nonmetal bonds and thus covalent.
Polarity:
To determine if a covalent bond is polar or not, we need to see how far apart the elements are away from one another. The further away the elements are from one another the more polar the bond. Nonmetal elements bonded to themselves are ALWAYS nonpolar see compound C. For B, the elements are far apart and are still covalent, so these bonds are polar.
