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.
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