If xy+z=x(y+z), which of the following must be true?
A. x=0 and y=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
If xy + z
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I solved it by simplifying or rephrasing question.
xy + z = xy + xz
z = xz
z/z = x
x = 1
Eliminate AC
Next I cannot able to eliminate.
xy + z = xy + xz
z = xz
z/z = x
x = 1
Eliminate AC
Next I cannot able to eliminate.
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The key word here is must.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
B. y = 1 and z = 0
D. x = 1 or y = 0
E. x = 1 or Z = 0
So, for example, consider answer choice A. While it's possible that x = 0 and z = 0, it need not be the case.
For example, x=1, y=1 and z=1 is a solution to the equation. So, this eliminates A.
The solution . . .
Given: xy+z = x(y+z)
Expand: xy+z = xy + xz
Subtract xy from both sides: z = xz
Rearrange: xz - z = 0
Factor: z(x-1) = 0
This tells us that z = 0 or x = 1
Answer: E
Cheers,
Brent
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Once we know that z = xz, we cannot divide both sides by z, because it COULD be the case that z equals zero, and we should never divide by zero.komati_anusha wrote:I solved it by simplifying or rephrasing question.
xy + z = xy + xz
z = xz
z/z = x
x = 1
Eliminate AC
Next I cannot able to eliminate.
Here's why:
We know that (2)(0) = (1)(0)
However, if we try to divide by both sides by 0, we may believe that we get: 2 = 1, which of course is not true.
Cheers,
Brent
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Hi komati_anusha,
There's a discussion of this questions here:
https://www.beatthegmat.com/must-be-true-qs-t278003.html
GMAT assassins aren't born, they're made,
Rich
There's a discussion of this questions here:
https://www.beatthegmat.com/must-be-true-qs-t278003.html
GMAT assassins aren't born, they're made,
Rich