This one is from one of the Manhattan CATs:

What is the value of y?

(1) 3|(x^2) – 4| = y – 2

(2) |3 – y| = 11


Here is how I tackle the problem....

Statement 1) Insuff...But tells us y>= 2 (Got this!)

Statement 2) Insuff...here is where I get lost.

I split the absolute value into two cases:

If Y > 3, THEN y = 14
If Y < 3, THEN y = -8

Now I check both statements. I know y>=2. In these type of abs value problems I now check to see what case I am in. But looking at the IF statements I could be in either case. This is where I am lost. Since both IF statements are valid, do I just move on to checking against the THEN statement? Can a Manhattan genius help out on this one?

Since most if's are valid, you need to see if you still can deduce the value of y. The evaluation of the second "if" gives you a contradiction to y>=2, so there's one option left. But...

You made it more complicated than it really is. Look at it that way:

Statement 1 yells you that y>=2.

Statement 2 tells you that y is either -8 or 14.

Neither of them is sufficient but combining them, there's only one option left.

Y=14 is true for y>3

hence the answer shd be E

yeah, you're making life too hard for yourself.

here's the deal: |3 - y| = 11 is an EQUATION. equations have SOLUTIONS, which are values that solve them.
that's it.
in particular, any given value either solves the equation or it doesn't. you can't impose "if"s on the issue of whether a given value solves an equation; if it does, it does, and if it doesn't, it doesn't.
it may be true that "if"s are helpful in FINDING the solutions to an equation, but, once you've found those solutions, you can chuck the "if" and just take the solutions.
so:
the equation |3 - y| = 11 has two solutions, -8 and 14.
if you check each of these, you'll find that it works: |3 - (-8)| = 11, check, and |3 - 14| = 11, check.
done.
so statement (2) just means y = -8 or y = 14.
unconditionally.
there's no need to impose inequality-type restrictions; it's just "y is either this or that".