xy+z=x(y+z)
xy+z=xy+xz
xy's cancel and you're left with:
z=xz
z-xz=0
z(1-x)=0
z=0 1-x=0
x=1
E
if xy+z
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truplayer256
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sureshbala
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I guess the option must x = 1 or z = 0.
For the given statement to be true it is sufficient it either x =1 or z =0. So this must be true. x = 1, z =0 both these together need not be true.
For the given statement to be true it is sufficient it either x =1 or z =0. So this must be true. x = 1, z =0 both these together need not be true.
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Brent@GMATPrepNow
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The key word here is must.bstalling wrote:if xy+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 and y=0
e) x=1 and z=0
OA e
So, for example, consider answer choice A. While it's possible that x = 0 and z = 0, it need not be the case.
For example, x=1, y=1 and z=1 is another solution to the equation. So, this eliminates A.
The solution . . .
Given: xy+z = x(y+z)
Expand: xy+z = xy + xz
Subtract xy from both sides: z = xz
Rearrange: xz - z = 0
Factor: z(x-1) = 0
This tells us that z = 0 or x = 1
Answer: E
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Brent
Brent Hanneson - Creator of GMATPrepNow.com
