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If xy+z = x(y+z), which of the following must be true? 1,

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If xy+z = x(y+z), which of the following must be true? 1, [#permalink] New post 09 Dec 2007, 20:08
If xy+z = x(y+z), which of the following must be true?

1, x=0 and z=0

2, x=1 and y=1

3, y=1 and z=0

4, x=1 or y=0

5, x=1 or z=0

The correct answer is Choice 5. I selected the right answer through process of elimination but would like to know the best way to get the answer correctly. The way I tried to simplify the equation is defined below, please let me know what I am doing wrong.

xy+z = x(y+z), so
xy+z = xy +xz
z = xy-xy+xz (both xy cancel out)
z = xz (divide both by side by z)
z/z = x
1=x

The solution above does not provide answer to value of z or y. What is the best way to solve this equation? Thanks in advance for your explanation.

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 [#permalink] New post 09 Dec 2007, 21:26
z = xz
and x = 1 (meaning that x is not equal to 0)

The only possible scenario of such equation is when 0 will be = 0, so z = 0 and x = 1
Manager
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 [#permalink] New post 09 Dec 2007, 22:11
Thanks, it helped.

Regards
  [#permalink] 09 Dec 2007, 22:11
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If xy+z = x(y+z), which of the following must be true? 1,

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