It can be helpful when approaching a DS yes/no question to ask yourself: when would we get a NO answer?
In this case, when would the absolute value of x *NOT* be greater than y, if x itself is greater than y?
The only time that would be the case is if y is a negative number further away from 0 than x (whether x is positive or negative). If they were both positive, x would have to be further from 0 than y is, i f x > y. So we could rephrase the question as:
Is y positive?
If you frame the question that way before looking at the statements, it's clear that statement 1 is insufficient, but statement 2 is sufficient.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education