I chose x=1 as the value used in testing Statement (1).
The question becomes :
Is 1-y+1 > 1+y-1?, or
Is 2-y > y?
If y=1, the two sides are equal
If y>1, the answer is 'no'
If y<1, the answer is 'yes'
Statement (1) is insufficient
To test Statement (2), I selected y= -1.
The question becomes:
Is x-(-1)+1 > x+(-1)-1?, or
Is x+2 > x-2 ?
The answer is 'yes', by a difference of '4'.
Note that, if y<0, regardless of the actual value, we subtract a negative number from 'x' on the left-hand side of the inequality.
Thus, x-y will be greater than x. We then add 1 to x-y, so we know that x-y+1 will be greater than x.
On the right-hand side of the equation, we're adding a negative number to x, which will result in a sum that is less than x.
We then subtract 1 from that sum, so we know that the entire expression on the right-hand side of the equation will be less than x.
Since the left-hand side is greater than x, and the right-hand side is less than x, the answer to the question is always 'yes' when y<0.
Therefore, Statement (2) is sufficient
Answer: B
I'm really old, but I'll never be too old to become more educated.
