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]

08 Feb 2007, 21:24

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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 or y = 0
(E) x = 1 or z = 0

[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Dec 2012, 02:41, edited 1 time in total.

Renamed the topic and edited the question.

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Re: Factoring problem: x,y,z [#permalink]

08 Feb 2007, 21:33

above720 wrote:

How would you solve?

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 or y=0
e) x=1 or z=0

xy + z = xy + xz

z = xz

case 1: z not= 0, x = z/z = 1

case 2: z = 0, 0 = x0 = 0

Combining 2 cases: x = 1 or z =0

E. is the answer.

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Re: Factoring problem: x,y,z [#permalink]

13 Mar 2011, 13:25

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dc123 wrote:

why is ans A not a choice?

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 or y = 0
(E) x = 1 or z = 0

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).

Answer: E.

To elaborate more:
As the expression with y cancels out, we can say that equation 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.

Next: "AND" in answer choices means that BOTH values must be true, but "OR" in answer choices means that EITHER value must be true.

Hope it helps.
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Re: Factoring problem: x,y,z [#permalink]

13 Mar 2011, 18:50

i guess you are substituting each options,

Option A holds good, but thats not true in all the cases. Then it wont be a "must be true"

example when x =1 , expression becomes xy+z = x(y+z) => y+z = y+z

So the condition i have chosen x=1 holds good (that is not A).

In short just because it satisfies the expression in one example doesnt mean that its the must.

by solving the expression , you should get z=0 or x=1 , which is a must. Answer is E.

Hope it helps.

dc123 wrote:

why is ans A not a choice?

Re: Factoring problem: x,y,z [#permalink] 13 Mar 2011, 18:50

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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?

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

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