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I am a little confused when it got to |x| = -x = y-z. How can an absolute value of x be equals to its negative value ? Absolute values, I thought, have no negatives.
You are right and wrong.
Absolute values have no sign. So |x| is always postive and represents the magnitude of x.
But in this problem, we are talking about x. x, the actual number, does have sign apart from magnitude.
From statement I alone, you cannot say "Sufficient". I is sufficient if the number x is proved to be negative, which is given in statement II. Hence C. The problem with your approach is that you missed the OR part.
|x| = -x or x.
If -x = y-z. then x+y = z
If x = y-z, then y-x = z
So from 1) x+y = z, so -x = y-z and x must be equals to y - z. So (1) is sufficient if x is negative. Nothing is known about the if x is positive. Insufficient.
From 2) all we know is x is less than 0. Insufficient.
Together (2) says that x is negative and 1 proves the negative part of stem. Sufficient
Hello, I think you are missing something here. wht you shd know is that the value of x is dependent on z and Y for instance let say z = 2 and y = 5
From statement one, X = 5-2 = 3, abs(x) = 3
Now flip it around and assume that y = 2 and Z = 5
then x = 2 - 5 = -3, abs(x) = 3.
So why do you say A is not sufficient
Now consider it this way, abs(x) could mean that x is positive or negative.
if x is positive
then we have
from one we have
X = y -z and abs(x) = abs(y-z) and abs(x) = y -z)
If X <0,
then from one it would mean
-x = z-y
X = -(z-y), take the absolute value of x and you get z-y.
meaning A is sufficient.
I don't think you need B to conclude that abs(x) will always be equal to
y -z or z - y.