Distribute the right side:
xy+z = xy+xz

Cancel the xy from both sides:
z = xz

In order for this to be true, either x=1 (z=z) or z=0 (0=0).

Therefore, the answer is E.

thanks Beny! You got it right...and it makes sense now!

But ans (e) states : x = 1 "AND" z = 0 -- however the explaination given concludes x=1 "OR" z = 0 . Thus to satisfy equation z = xz both the conditions need not to satisfy however ans (e) implies that. I think the only condition that MUST be true is (a) i.e. x = 0 "AND" z = 0.

Any comments please.

amitamit2020 wrote:But ans (e) states : x = 1 "AND" z = 0 -- however the explaination given concludes x=1 "OR" z = 0 . Thus to satisfy equation z = xz both the conditions need not to satisfy however ans (e) implies that. I think the only condition that MUST be true is (a) i.e. x = 0 "AND" z = 0.

Any comments please.

A cant be the answer as

ATQ z=xz

If x=0 this means z too is 0 or 1 or 2.....or can be any number

So value of Z cant be determined.

So answer is z=0 and x=1

I got the same equation z = xz

but I dont understand why X and Z both cannot be 0 ?

I agree if x=1 and z=0 the equation is satisfied, but cant understand why choice A does not work.

Would appreciate if some one could explain.

thanks a lot

Yop I think we r all at the equation : z = xz. Now as pointed out by amitamit2020 (a very good observation u can say!), the option E is having "AND" with it. But tell me one thing amitamit2020 - is it not satisfying the equation now if z = 0 and x = 1? But with option A, we are putting a controversy about "Is 0 multiplied by 0 1?" So I think Jaspreet is right! What do u say guys?
Correct me if I am wrong

we all agree that the equation simplifies to z =x*z

if x=1 z=z and z can be any value, not necessairly 0

if x=0 z must be 0, or else the equation is false.

try out in the original equation
if x=1
XY+Z= X(Y+Z) results in
y+z=y+z
0 = 0, regardless of the value of Z so E can't be right, even if z were 999 the equation would hold true.

if x=0
XY+Z= X(Y+Z) results in
z=0
therefore the answer should be A x=0 and z=0

charmingirl8 already stated that the OA is E, but it makes no sense to me. what is the origin of this question?

agps wrote:we all agree that the equation simplifies to z =x*z

if x=1 z=z and z can be any value, not necessairly 0

if x=0 z must be 0, or else the equation is false.

try out in the original equation
if x=1
XY+Z= X(Y+Z) results in
y+z=y+z
0 = 0, regardless of the value of Z so E can't be right, even if z were 999 the equation would hold true.

if x=0
XY+Z= X(Y+Z) results in
z=0
therefore the answer should be A x=0 and z=0

charmingirl8 already stated that the OA is E, but it makes no sense to me. what is the origin of this question?

that is because charmingirl8 has got the answer options wrong .. the ans is E and the the answer choice E says x=1 or z=0 ...

.. also people make a note that the question asks what "must be " true and not what "could be" true .. makes a huge difference...