$$Is\ \left|x\right|=y-z?$$
This means absolute value of x = y - z
$$So,\ y-z\ge0$$
Statement 1=> x+y=z
x = - (y+z) or -x = y - z
The conclusion here is that if x>0; y-2<0;
$$but\ if\ x\le0,\ then\ y-z\ge0$$
Then the information provided could not give a definite answer. So, statement 1 is NOT SUFFICIENT.
Statement 2=> x < 0
This does not provide any information relating (y-z). So, statement 2 is NOT SUFFICIENT.
Combining both statement together
From statement 1=> x = -(y-z) OR -x = y-z
From statement 2=> x<0
Therefore, -x=y-z => |x|=y-z
Hence, the both statements combined are SUFFICIENT.
ANSWER = C
Is \(|x| = y - z ?\)
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Source: Beat The GMAT — Data Sufficiency |
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deloitte247
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