Hi, there. I'm happy to give my 2¢ on this.
Prompt: What is the value of y?
Statement #1: 3|x^2 - 4| = y - 2
Don't be faked out by the complicated algebraic expression in terms of x.
We know that |anything| is greater than or equal to zero. This means, y - 2 is greater than or equal to zero. This means y is greater than or equal to 2. y >= 2
By itself, this does not allow us to determine a value for y. Statement #1 by itself is
insufficient.
Statement #2: |3 - y| = 11
If I were doing this problem on my own, I probably would have done Statement #2 first, because it's simpler. Never assume you have to do the DS statements in order.
Here, as you probably realized, we can solve: 3 - y = 11 or 3 - y = -11. That leads to y = -8 or y = +14. By itself, this does not allow us to determine a value for y. Statement #2 by itself is
insufficient.
Statement #1 & #2 Combined:
From #1, we know y >=2
From #2, we know y = -8 or y = +14.
Combining the two conditions, the only possibility is y = 14. Combined, the statements are
sufficient.
Does that make sense? Please let me know if you have any questions on what I've said.
Mike
