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Which of the following MUST be true?

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by mkbigmoz » Wed Apr 08, 2009 11:59 am
My question is in the spoiler. Thanks

If (y − 1)(z − 3) + 5(z − 3) = 0, then which of the following must be true?



y = −4 and z = −3

y = −4 or z = −3

y = −4 or z = 3

y = 1 and z = 3

y = 1 or z = 3

[spoiler]

Correct: y = −4 or z = 3


My answer was Y=1 and Z=3. Why is this wrong? Doesn't it confirm the stem?[/spoiler]
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by moutar » Wed Apr 08, 2009 12:19 pm
(y − 1)(z − 3) + 5(z − 3) = 0

Factorise out (z-3):

(z - 3){(y - 1) + 5} = 0
(z - 3)(y + 4) = 0

Therefore: z = 3 or y = -4 Answer C
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by mkbigmoz » Wed Apr 08, 2009 12:35 pm
Yes, but if Y is 1 & Z is 3, wouldn't the stem also hold true?
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by moutar » Wed Apr 08, 2009 12:43 pm
"which of the following must be true?"

Your answer satisfies the equation, but y doesn't have to equal 1.
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Re: Which of the following MUST be true?

by dtweah » Wed Apr 08, 2009 6:17 pm
mkbigmoz wrote:My question is in the spoiler. Thanks

If (y − 1)(z − 3) + 5(z − 3) = 0, then which of the following must be true?



y = −4 and z = −3

y = −4 or z = −3

y = −4 or z = 3

y = 1 and z = 3

y = 1 or z = 3

[spoiler]

Correct: y = −4 or z = 3


My answer was Y=1 and Z=3. Why is this wrong? Doesn't it confirm the stem?[/spoiler]
The reason is the Y=1 is Not A solution of the equation or is not Zero of the function. Only such zeros are solutions of functional equations. Always put equations in the form in which you can apply this zero property.
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