Data Sufficiency

If y≥0, what is the value of x?

(1) |x−3|≥y

(2) |x−3|≤−y

Mo2men wrote:If y≥0, what is the value of x?

(1) |x−3|≥y

(2) |x−3|≤−y

Statement 1: |x−3| ≥ y
If y=0, then |x-3| ≥ 0.
|x-3| ≥ 0 for any value of x.
Since x can be any value, INSUFFICIENT.

Statement 2: |x-3| ≤ -y
Since an absolute value cannot be less than or equal to a negative value, the right side of this inequality must be NONNEGATIVE:
-y≥0
y≤0.
According to the prompt, 0≤y.
Linking together the inequalities in blue, we get:
0≤y≤0.
The only value that satisfies the resulting inequality is y=0.

Substituting y=0 into |x-3| ≤ -y, we get:
|x-3| ≤ -0
|x-3| ≤ 0.

Since an absolute value cannot be negative, it is not possible that |x-3| < 0.
|x-3| = 0 if x=3.
Thus, the only possible value for x is 3.
SUFFICIENT.

The correct answer is B.

given y>=0

1) |x-3| >= y
x can take any value, because mod will make |x-3| positive
example x = -3
|-6| = 6
INSUFFICIENT

2) |x-3|>= -y
mod will always be positive or 0
mod can never be negative
hence x will be 3 to make y=0 because cannot be negative
x = 3 and y =0
SUFFICIENT

SO B