Which of the following MUST be true?

[mkbigmoz]

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]

[moutar]

(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

[mkbigmoz]

Yes, but if Y is 1 & Z is 3, wouldn't the stem also hold true?

[moutar]

"which of the following must be true?"

Your answer satisfies the equation, but y doesn't have to equal 1.

[dtweah]

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.