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When I simply each I get:

1) -y + 3 >= 0 >= y + 3
2) y + 3 <= 0 <= -y + 3

What am I doing wrong? Since I have them saying the same thing and only B is sufficient there must be a fault in my logic.

Thanks.

IMO its B

Explanation-

y>=0 is given

[1] |x-3| >=y

=>case x-3 is +ve
x-3 > =y => x > 3+y.. no solution

=>case x-3 is negative => x<3
-x+3 >= y => x =< 3-y.. no solution

[2] |x-3| <= -y

Now, y is a positive number but |x-3| can not be negative.
There the equality will hold only at one point y=0.
=> x= 3.. thus this alone is sufficient.

Hence, B.

Hope it helps!!

If y >= 0, what is the value of x?

Implies (x-3)>y or (x-3)<-y. We don't have a single value of x in this case. So, statement I is insufficient to answer the question.
We know that mod of any number is greater than or equal to(>)0. We also know that y>0, So -y<0. Statement II reads |x - 3| <= -y. We already know that |x - 3|>0 and -y<0. So the only value that satisfies the condition is y = 0, and for all other values -y<0, which isn't possible according to statement II.
So |x-3| = 0, and x = 3
Answer B

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