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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? [#permalink] New post 18 Jun 2011, 03:40
00:00
A
B
C
D
E

Difficulty:

  25% (low)

Question Stats:

72% (01:16) correct 27% (00:24) wrong based on 66 sessions
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
[Reveal] Spoiler: OA
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Re: if xy+z=x(y+z) which of the following must be true? [#permalink] New post 18 Jun 2011, 04:57
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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] New post 05 Feb 2012, 20:28
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] New post 06 Feb 2012, 00:32
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Expert's post
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] New post 13 Aug 2013, 15:31
Bunuel wrote:
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.


Hi Bunuel,

I was wondering if substituting the answer options would be a good approach here? I attempted by substituting the values in each answer option and got both B/D to be valid for the equation in the question. Interestingly, if we simplify the equation we see that in both answer choices we have the value of Y, which is immaterial. It would be great if you can let me know what you think of approaching similar questions through their answer choices.

Thanks!
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Re: if xy+z=x(y+z) which of the following must be true?   [#permalink] 13 Aug 2013, 15:31
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