must be true?

[sanju09]

If x y + z =x (y + z), which of 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



OA E

[moutar]

xy + z = x(y + z)

xy + z = xy + xz

z = xz

z - xz = 0

z(1 - x) = 0

Therefore z = 0 or x = 1.

Answer E.

[odod]

Can anyone disprove B?

I am trying to sub in the answer choices and I see B being correct as well.

Thanks for your help

[moutar]

"which of the following must be true?"

All of B doesn't have to be true because y can take any value if x = 1.

[odod]

I dont understand your post.......


If X = 1 and Y = 1

Then I get the followiing by substituting in..

(1)(1) + Z = 1(1+Z)
1 + Z = 1+Z

They both equal each othe so wouldn't that make B correct?

[odod]

I dont understand your post.......


If X = 1 and Y = 1

Then I get the followiing by substituting in..

(1)(1) + Z = 1(1+Z)
1 + Z = 1+Z

They both equal each othe so wouldn't that make B correct?

[moutar]

The question is what has to happen. If x is 1, y doesn't have to be 1, it can be anything. It's asking for the exact situation where the equation is true.

The way you are thinking all of the options would work.

[GID09]

Why not A?

If X is 0, Z must be 0...

For rest of the equations you get one or two variables i.e x=x or y+z = y+z(so variables could be of any value, not necessarily the value given in choices).

Correct me if I am wrong.

[sanju09]

Why not A?

If X is 0, Z must be 0...

For rest of the equations you get one or two variables i.e x=x or y+z = y+z(so variables could be of any value, not necessarily the value given in choices).

Correct me if I am wrong.

We should always read the question with full care, "a and b" and "a or b" are not same things. In "must be true" kind of questions, the implications from the question stem form the answer, pick n plug policy is sometimes risky here. The work by moutar is genuine in this case.

[lav]

the point is , question MUST be read first and then the answer
not the other way round

[moutar]

Why not A?

If X is 0, Z must be 0...

For rest of the equations you get one or two variables i.e x=x or y+z = y+z(so variables could be of any value, not necessarily the value given in choices).

Correct me if I am wrong.

You are wrong because if z = 0, then x can equal anything.

[GID09]

Thanks all!