We know that remainders are less than divisor and equal to or be more than 0.
Hence, 0<= w < y and 0<= z< x
Adding both,
0 <= w+z (required by stem) < x+y
Since its a could be question , lets try to prove them right. Lets back solve and substitute.
A) Can 0<= x-y < x+y ? YES -2y<0 or y>0 , which is a possible solution. So, there must be some numbers. Maybe true.
B) Can 0<= x+y < x+y ? No why ? Can 0<= 0 < 0 be possible ? No . So, can never be true.
C) Can 0<= y< x+y ? Yes 0<= 0 < x . Hence, inequality holds. There maybe some values that can satisfy the equations. Hence, can be true.
If one cannot analyze, plug simple numbers. Works !
Regards
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