Problem Solving

[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

Cheers,
Brent

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

GMAT assassins aren't born, they're made,
Rich

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.

GMAT assassins aren't born, they're made,
Rich