GMAT prep Problem, from the official Gmat prep

If XY + Z = x(Y+Z) which f the following must be true

A. X=0 and Z=0

B. X=1 and Y=1

C. Y=1 and Z=0

D. X=1 or Y=0

E. X=1 or Z=0

I Checked the answers and both b and C must be true, which obviously cant be...

B- 1 +Z = 1 + Z

C. X +0 = X+ 0

Where am I wrong???

Thanks