In multiplication of the two digit numbers wx and cx, where w, x, and

Given : wx*cx = _ _ _ . Asked is w+c-x.

(1). If three digits of the product are all the same, then the product has only 9 possibilities which are :
(111, 222, 333, 444, .....................,888,999).
Now, we already know that 111= 37*3, hence all the possibilities can be re-written as follows:
(3*37 , 6*37 , 9*37 ,.....................,24*37,27*37)
Only the last possibility matches the given sets of conditions. Hence 27*37=999, because in this case ten's place is the same digit for both 27 as well as 37. So, w+c-x = 2+3-7 = -4 (Easily deduced). Hence SUFFICIENT !

(2). This mentions that x and w + c are both odd numbers. There are many possibilities.
We know only ODD+EVEN=ODD. So,either of (w,c) are (odd,even) or (even,odd). And x =ODD.
Case1. Let's say for one possibility, x=1; w=2; c=3 . This also satisfies the inital given condition that multiplication of the two digit numbers gives 3 digited product. Hence, So, w+c-x = 2+3-1 = 4.
Case2. Now for another possibility, say x=3; w=1; c=2. This also satisfies the inital given condition that multiplication of the two digit numbers gives 3 digited product. Hence, So, w+c-x = 1+2-3 = 0.
(There could be many other cases too but we can conclude from 2 cases only.)
So both the case gives a different answer, hence we cannot arrive at a unique solution from (2). Hence INSUFFICIENT !

So, the final answer to the question should be option A.