What type of question ?

[Xbond]

If XY+Z = X(Y+Z), which of the following must be

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

Can you help me to understand how to resolve this kind of PS ?

[vr4indian]

I will go for E

Explanation.

XY+Z = X(Y+Z)

xy +z = xy + xz ------------eq1

To cover max. values for X, Y, Z we will go with OR option instead of And option

Take 4 as first option

for X =1 its perfectly okay but if we take Y =0 means z = xz , which can be false.

Take 5 as second option
If we consider X =1 then equation will be y + z = y +z , this will be valid for all the values of Y and Z

Now considerZ =0 , so eq1 will become xy = xy , which is again valid for any valiues of X and Z

..
PS.
I think B can be valid answer.. but just because of AND clause i rulled out it.

Vishal Shah
Pune

[Xbond]

OK, Could you clarify how you select between AND & OR ?

[lunarpower]

If XY+Z = X(Y+Z), which of the following must be

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

Can you help me to understand how to resolve this kind of PS ?

well, the first thing you want to do is simplify the original "given" statement.
distribute to get xy + z = xy + xz
then subtract xy from both sides (remember, subtracting a quantity from both sides is always "safe") to give z = xz.

DO NOT DIVIDE BY Z at this point. if you don't know this, then this should be a MAJOR MAJOR takeaway: NEVER divide by a variable, unless you are absolutely sure that the variable is nonzero.
if you have a variable that could possibly be zero (which is most variables), then FACTOR IT OUT instead of dividing by it.

z = xz
0 = xz - z
0 = z(x - 1)
0 = z or 0 = x - 1
0 = z or 1 = x

ans = (e)

--

note that you could just plug in numbers to test these answers. for instance, if you wanted to test (e), the correct answer, you'd plug in z = 0 and x other than 1, and then x = 1 and z other than 0. (the fact that you're only obeying one of the conditions at a time cements the "or" part; if it were "and", then it would only work if you satisfied both conditions at once.)

[khudania]

E

Looking at the statement, its clear that Z has to be 0 for the statement to be true. So eliminate answer choices that do not have 0.

Plug in the other numbers in the remaining options & E works out.

[Xbond]

Thks a lot