Problem Solving

This looks like a basic math concept of Laws of Operations but I'm missing something still.

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


Shouldn't I just be able to plug in the numbers for the variables and pick any number for the unknown variable and see if the equal on both sides of the equation?

vladmire wrote:This looks like a basic math concept of Laws of Operations but I'm missing something still.

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


Shouldn't I just be able to plug in the numbers for the variables and pick any number for the unknown variable and see if the equal on both sides of the equation?

I would break it down like this,

xy+z = x(y+z)
then
xy+z = xy+xz, subtract xy
z = xz
so the question asks what MUST be true.
let's go one by one
a. x=0 and z=0 Not true, if z=0, then x does NOT have to be 0 to be true. (notice the "and" in the choices?)
b. x=1 and y=1 Not true, we don't even have to know what y is, we need to focus on Z
c. y=1 and z=0 Not true, again, we really want to focus on x or z
d. x= 1 or y= 0 Not true, same as above
e. x=1 or z = 0 I would pick this, if x was 1, then z=1z, true or if z=0, then 0=x0, true again.

Let's even try E in original equation.
if x=1, then 1y+z=1(y+z) , correct
if z=0, then xy+0=x(y+0), xy=xy

so answer is E.

You have to see the key words, and vs. or

Just a tip :

For "which of the following" questions, try to solve from the bottom...

as in solve E first, then D....

You would probably find the answer between E and D...

but may not work always...

from the question we have
xy +z = x(y+z)
-> xy +z = xy + xz
the xy cancells out so
z = xz
-> z -xz = 0
-> z(1 -x) = 0
So either z = 0 OR 1 -x = 0
ie z = 0 or x = 1

E