GMAT Prep Question

[patrik.herzog]

I can't get the following question:

If xy + z = x(y+z), which of the following must be true

x=0 and z=0
x=1 and y=1
y=1 and z=0
x=1 or y=0
x=1 or z=0

Thanks for any help on this!

[Cybermusings]

As far as I am concerned it's Option E...

I.e. either x = 1 or z = 0

Lets take the first scenario when x = 1

xy + z = x (y + z)

xy + z = xy + xz

Therefore z would have to be equal to xz for the Equation to hold true

This is possible when x = 1 (Here xz = z since x is already 1)

Lets take the second scenario when z = 0

xy + z = x(y + z)

xy + z = xy + xz

xy + 0 = xy + 0

Hence it's option E

[patrik.herzog]

For my point of view, there are 4 possible answers..

a) could be correct
x=0 and z=0
-> 0 = 0

b) could be correct
x=1 and y=1
-> 1 + z = 1 + z

c) could be correct
y=1 and z=0
-> x = x

b) wrong
x=1 or y=0
-> y+z = y + Z
-> z = xz

e) could be correct
x=1 or z=0
-> y+z = y+z
-> xy = xy

[aim-wsc]

dont simply put values of x y z in equation, Pratik.

solve it instead.
cybermusings approach is right 8)

[patrik.herzog]

I'm sorry, I don't get cybermusings approach.
Is there another way to explain it?

[800GMAT]

xy + z = x(y+z)

Solving the above equation,
xy + z = xy + xz
z=xz
xz-z=0
z(x-1)=0
therefore, z=0 or x=1

[aim-wsc]

Yes!
800GMAT!

Even cybermusings has "solved equation" like 800GMAT, I hope by now you understood how they approach the problem

[800GMAT]

Thanks aim-wsc.

Cheers

[patrik.herzog]

I still don't get it..

OK, with z=0 or x=1 we have a solution.

But what about x=0 and z=0? Why isn't that true?


Thanks a lot!

[aim-wsc]

its a tricky one.

I still don't get it..

OK, with z=0 or x=1 we have a solution.
But what about x=0 and z=0? Why isn't that true?

b/z u can play with numbers and substitute any damn value for ''y'' to make equation valid.
If you observe it closely u'll realise that y has no role here & therefore u should solve the equation first.

[aim-wsc]

if x=0 & z=0 then I dont have explanation

where's Mark D?

[800GMAT]

The question asks you what must be true

Is it always true that x=0 and z=0?
In other words, is x always 0 and z always 0
No
x can be 1

Since we are able to find another value for x besides 0
(1) does not hold

[aim-wsc]

bingo 8)
i've been loony lately

[yvonne12]

I've been trying to figure out these kinds of questions myself. This was very helpful. thanks