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If (y − 1)(z − 3) + 5(z − 3) = 0

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If (y − 1)(z − 3) + 5(z − 3) = 0

by [email protected] » Sat Dec 27, 2014 10:10 am
Hello everybody! Can anyone help me with this problem solving please?

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

a) y = −4 and z = −3
b) y = −4 or z = −3
c) y = −4 or z = 3
d) y = 1 and z = 3
e) y = 1 or z = 3

Tks!!
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by Brent@GMATPrepNow » Sat Dec 27, 2014 10:22 am
[email protected] wrote:Hello everybody! Can anyone help me with this problem solving please?

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

a) y = −4 and z = −3
b) y = −4 or z = −3
c) y = −4 or z = 3
d) y = 1 and z = 3
e) y = 1 or z = 3
We can combine some terms here to simplify matters.
We have: (y − 1)(z − 3) + 5(z − 3) = 0
In other words, we have something times (z − 3) PLUS something else times (z − 3)
So, we can combine the something and something else.

We get: [(y − 1) + 5](z − 3) = 0
Simplify to get: (y + 4) (z − 3) = 0
For this product to equal zero, it must be the case that y = -4 OR z = 3

Answer: C

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by [email protected] » Sat Dec 27, 2014 12:34 pm
Hi [email protected],

Brent's approach focused on the algebra that you could do to get to the correct answer. There is another way to approach this question though....we can TEST THE ANSWERS

The answer choices provide us with 5 possibilities for what MIGHT be the solutions to the above equation (make the above equation = 0). We just have to figure out which one actually does it.

First off, notice that Z = 3 is in most of the options. Let's see what happens when we TEST Z = 3

(Y - 1)(3 - 3) + 5(3 - 3) =
(Y - 1)(0) + 5(0)
0 + 0 = 0

So, if Z = 3, then the above equation DOES equal 0 (and the value of Y DOESN'T MATTER). This tells us 2 things:

1) Z = 3 is one of the solutions
2) The Y doesn't matter in this scenario (so we don't need an "and", we need an "or" in the correct answer)
Eliminate A, B and D

Between answers C and E, the difference is in the values of Y (-4 or + 1). I'm going to TEST the easier option. What happens when Y = 1....?

(1 - 1)(Z - 3) + 5(Z - 3)
(0)(Z - 3) + 5(Z - 3)
0 + 5(Z - 3)

This would only equal 0 when Z = 3, but it would NOT equal 0 under any other circumstances. This CANNOT be the answer.
Eliminate E

Final Answer: C

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by [email protected] » Sun Jan 04, 2015 1:27 pm
Brent@GMATPrepNow and Rich.C@EMPOWERgmat., tks a lot for your help. It makes a lot of sense!

Brent, the way you solves for the problem is clear and convincing.

Rich, using your reasoning: What happens when Y = 1....?

(1 - 1)(Z - 3) + 5(Z - 3)
(0)(Z - 3) + 5(Z - 3)
0 + 5(Z - 3)

This would only equal 0 when Z = 3, but it would NOT equal 0 under any other circumstances. This CANNOT be the answer.
Eliminate E

But answer D is exactly what you just said before, Y=1 AND Z=3, this must be true.

Am I missing something?

Again, tks a lot for your help!
[email protected]
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by [email protected] » Sun Jan 04, 2015 5:48 pm
Hi [email protected],

The wording of this question is very important - it's asking what MUST be true (in other words, what must ALWAYS be true no matter what?). Usage of the word "and" in this type of scenario means that 2 things MUST be true in EVERY possible answer. We've already proven that if Z=3, then the value of Y DOES NOT MATTER, so the word "and" is NOT something that MUST be true in EVERY possible answer.

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by GMATinsight » Mon Jan 05, 2015 6:18 am
[email protected] wrote:Hello everybody! Can anyone help me with this problem solving please?

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

a) y = −4 and z = −3
b) y = −4 or z = −3
c) y = −4 or z = 3
d) y = 1 and z = 3
e) y = 1 or z = 3

Tks!!
Given equation is (y − 1)(z − 3) + 5(z − 3) = 0

Sum of two parts can be zero only

1) When either both parts are equal to zero which is possible @z=3
OR
2) When one part is cancelling the other term added to it
i.e. (y − 1)(z − 3) = (-5)(z − 3)
i.e. y-1 = -5 i.e. y = -4

Hence,

Answer: Option C
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