Data Sufficiency

[email protected] wrote:If y > 0, what is the value of x ?
(1) |x - 3| > y
(2) |x - 3| < -y

Target question: What is the value of x ?

Given: y > 0

Statement 1: |x - 3| > y
There are many values of x and y that meet this condition. Here are two:
Case a: y = 1 and x = 5 (since |5 - 3| > 1). In this case, x = 5
Case b: y = 1 and x = 6 (since |6 - 3| > 1). In this case, x = 6
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: |x - 3| < -y
IMPORTANT: Since it's a given that y > 0 (y is greater than or equal to zero), we can conclude that -y is less than or equal to zero. In other words, -y is equal to either zero or some negative value

Let's examine the possibility that -y equals some negative value: This would mean that |x - 3| < some negative value. This is impossible since the absolute value of anything is always be greater than or equal to zero. So, it would be impossible for -y to equal some negative value.
This means that -y MUST equal 0.
This tells us that |x - 3| < 0
Since |x - 3| cannot be less than zero, it must be true that |x - 3| = 0, in which case x = 3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent