Hi,
Firstly, I have done a search and I couldn't find this question. (I searched for both "xy+z" and "x(y+z)" )
Secondly, I apologise if it is a silly question BUT ...
I ended up getting each of the options other than d as a “must be true”, so obviously I have missed out something basic in my Quant studies. Can someone please tell me what’s wrong with my calculations?
The question is:
If xy + z = x(y+z), which must be true?---
1) x=0 and z=0
substituting the values of x and z in the stem’s equation,
0*y + 0 = 0( y + 0)
and so 0=0 ….. True
2) x=1 and y = 1
substituting the values of x and y in the equation, we get
1*1 +z =1(1+z) and from there,
1+z =1+z …. True
3)y=1 and z =0
substituting the values of y and z in the equation, we get
x*1 +0 =x(1+0)
and so x = x….. True
4)x=0 or y=0
substituting the value of x, we get
0*y +z= 0(y+z)
and so, z=0, which may or may not be true…… so discarded.
5)x=1 or z=0 (official answer)
Thanks.
Shilo
GMATPrep xy + z = x(y+z)
This topic has expert replies
- Stuart@KaplanGMAT
- GMAT Instructor
- Posts: 3225
- Joined: Tue Jan 08, 2008 2:40 pm
- Location: Toronto
- Thanked: 1710 times
- Followed by:614 members
- GMAT Score:800
The problem is with your interpretation of the question.shilotilo wrote:Hi,
Firstly, I have done a search and I couldn't find this question. (I searched for both "xy+z" and "x(y+z)" )
Secondly, I apologise if it is a silly question BUT ...
I ended up getting each of the options other than d as a “must be true”, so obviously I have missed out something basic in my Quant studies. Can someone please tell me what’s wrong with my calculations?
The question is:
If xy + z = x(y+z), which must be true?---
When a question asks "which of the following MUST" be true, we're looking for the option that's true in every possible case.
You interpreted the question as "which of the following COULD be true." Let's look at (a) as an example:
You've shown that x and z COULD each equal 0. However, if we let x, y and z all = 1, we get:1) x=0 and z=0
substituting the values of x and z in the stem’s equation,
0*y + 0 = 0( y + 0)
and so 0=0 ….. True
1*1 + 1 = 1(1+1)
2 = 2
which also works.
As an aside, this question is a lot easier if you simplify the first equation:
xy + z = x(y+z)
xy + z = xy + xz
z = xz
z - xz = 0
z(1 - x) = 0
and we now know that either:
z = 0 or 1 - x = 0
z = 0 or x = 1
which is (e).
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course