Since y>=0, you can re-write 1 and 2 as:

1. |x-3| >= 0
2. |x-3| <= 0

Note that by definition absolute value is non-negative. |z| is the distance between z and 0.

1. just states the definition of absolute value. Choose x = 0, then |x-3| = 3. Now choose x = 1, then |x-3| 2. Insufficient.

2. Since absolute value is non-negative, |x-3| CANNOT be less than 0. so |x-3|=0 and therefore x=3.

The answer is B.

I did not understand the explanation for Statement (1)

Per my understanding, for different values of y>0 , we get different values of x. Right?

raleigh wrote:Since y>=0, you can re-write 1 and 2 as:

1. |x-3| >= 0
2. |x-3| <= 0

Note that by definition absolute value is non-negative. |z| is the distance between z and 0.

1. just states the definition of absolute value. Choose x = 0, then |x-3| = 3. Now choose x = 1, then |x-3| 2. Insufficient.

2. Since absolute value is non-negative, |x-3| CANNOT be less than 0. so |x-3|=0 and therefore x=3.

The answer is B.

The question is can you find the value of x?

(1) is that |x-3| >=y. Y is arbitrary. Choose a number for y, say y =0. Then |x-3| >=0. An infinite amount of choices of x satisfy this so we will not be able to find the numeric value for x. Try x = 3. Try x = 4.

They both satisfy the inequality. So x could be 3 or it could be 4. So you cannot answer the question. That is why (1) is insufficient.

The answer is B

we know that MOD X is greater than or equal to 0 but cannot be less
hence B