Xbond wrote: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)
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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.)
Ron has been teaching various standardized tests for 20 years.
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