xy +z = xy+xz
now xz = z
in that case either x can ne 1 or z can be 0
the option E gives the answer

anu009 wrote:xy +z = xy+xz
now xz = z
in that case either x can ne 1 or z can be 0
the option E gives the answer

To finish up the algebra:

xz = z

xz - z = 0

z(x - 1) = 0

z = 0 or x = 1

fantastic, thanks guys.

while i see it can be solved algebraically, how come x=0 and z=0 doesn't work?

no matter what I plug in for y won't both sides be 0?

pkw209 wrote:while i see it can be solved algebraically, how come x=0 and z=0 doesn't work?

no matter what I plug in for y won't both sides be 0?

x=0 and z=0 do "work". That means x COULD be 0 while z COULD be 0. But this is a MUST be true question. So, we need to find a necessary solution. Choice A is a possible but not a necessary solution.

Thanks. Would it be correct to assume that for all must be true questions, you need to solve algebraically to get the answer?

pkw209 wrote:Thanks. Would it be correct to assume that for all must be true questions, you need to solve algebraically to get the answer?

No, not necessarily. You could have picked numbers but you would need to check every answer choice, elimintaing impossible choices. Then, you would have narrowed it down A and E. At that point you would have to ask yourself which HAS to be true.

Because this is a must be true question, we could have been partial to the choices that say "or" rather than semicolon (semicolon is just "and").

(This is because an "and" is more likely to be something that could be false compared to an "or".)

Thanks, Testluv. Extremely helpful response as usual