GMAT Math

If xy+z=x(y+z), which of the following must be true?

A. x=0 and z=o
B. x=1 and y=1
C. y=1 and z=0
D. x=1 and y=0
E. x=1 and z=0

OA E

xy+z=x(y+z)

xy + z = xy + xz

z = xz

z * (1-x) = 0

z = 0 and x = 1. E

Hey guys,

A huge distinction here - the question as written contains a pretty major typo. Answer choice E should read:

x = 1 or z = 0

"And" is not necessarily the case here, as if x = 1, then it doesn't matter what z is. Consider:

x = 1, y = 2, z = 3

1(2) + 3 = 1(2 + 3)
2 + 3 = 2 + 3

And if z = 0, then it doesn't matter what x is:

x = 13, y = 9, z = 0

13(9) + 0 = 13(9 + 0)
13(9) = 13(9)


The "catch" to this problem as it was written in the OG is that an "and" in a MUST BE TRUE question is tricky - it's just a huge standard of proof. But "or" is easier to prove. The conclusion "either I'm right or I'm wrong" covers everything, but the conclusion "I'm right" requires exactly one outcome - I'm right. "Or" in a must-be-true means a much different thing than "and", and that's what's most important to take away from this one.