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

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

18 Jun 2011, 04:40

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If xy+z=x(y+z), which of the following must be true?
A. x=0 and y=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

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Re: if xy+z=x(y+z) which of the following must be true? [#permalink]

18 Jun 2011, 05:57

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WishMasterUA wrote:

if xy+z=x(y+z) which of the following must be true?
1)X=0 AND Z=0
2)X=1 AND Y=0
3)Y=1 AND Z=0
4)X=1 OR Y=0
5)X=1 OR Z=0

xy+z=xy+xz
z=xz
xz-z=0
z(x-1)=0

Means;
either z=0
OR
x-1=0 i.e. x=1

Ans: "E"
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Re: if xy+z=x(y+z) which of the following must be true? [#permalink]

05 Feb 2012, 21:28

WishMasterUA wrote:

if xy+z=x(y+z) which of the following must be true?
1)X=0 AND Z=0
2)X=1 AND Y=0
3)Y=1 AND Z=0
4)X=1 OR Y=0
5)X=1 OR Z=0

I agree with the answer i.e. X=1 OR Z=0
But can the answer be also X=1 AND Z=0 (provided there was an option) as both of them taken together also satisfy the equation???

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Re: if xy+z=x(y+z) which of the following must be true? [#permalink]

06 Feb 2012, 01:32

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rohitgoel15 wrote:

WishMasterUA wrote:

if xy+z=x(y+z) which of the following must be true?
1)X=0 AND Z=0
2)X=1 AND Y=0
3)Y=1 AND Z=0
4)X=1 OR Y=0
5)X=1 OR Z=0

I agree with the answer i.e. X=1 OR Z=0
But can the answer be also X=1 AND Z=0 (provided there was an option) as both of them taken together also satisfy the equation???

If xy+z=x(y+z), which of the following must be true?
A. x=0 and y=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

Notice that we are asked "which of the following MUST be true"?

xy+z=x(y+z) --> xy+z=xy+xz --> xy cancels out --> xz-z=0 --> z(x-1)=0 --> EITHER z=0 (in this case x can take ANY value) OR x=1 (in this case z can take ANY value).

Addressing your questions: it's not necessary z=0 and x=1 both to be simultaneously true. "AND" in the answer choices means that BOTH values must be true, but "OR" in the answer choices means that EITHER value must be true.

Answer: E.

To elaborate more:
As the expression with y cancels out, we can say that given expression xy+z=x(y+z) does not depend on value of y. Which means that y can take ANY value. So all answer choices which specify the exact value of y are wrong.

Hope it helps.
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Re: if xy+z=x(y+z) which of the following must be true? [#permalink] 06 Feb 2012, 01:32

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

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

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