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I will just add to what Martin said. We need to find which of the given numbers CANNOT be odd (i.e. it is always even) given that a,b,c are odd integers. So u have to find which of the given choices is always even.
Just remember the basic rules of numbers (as martin wrote)
Product of even number with any integer is always even and some of two odds is always even.
Then just a glance of choices will tell that answer is (E).
-Vicks

Good point. I guess then that the rules for / are the same for * PROVIDED that the division is an integer.

The problem in question asks which one CANNOT be an integer. In choice D 4c/(b+a) COULD be an integer, but aplying the rules you find that it CANNOT be an ODD.