Hey euro,
Love the question, and I hope I'm not stepping on Rahul's explanation by chiming in but I think this one is full of great strategic takeaways.
A) If it helps, deal with the easier-to-use statement first
Here, the first statement is a mess...an absolute value in a multivariable equation that includes a squared term...I'd probably leave this one alone first, but the second statement is a little more straightforward and can get you started.
B) When performing algebra with absolute values, treat each absolute value as 2 different equations
For statement 2, the expression can be read two ways:
3 - y = 11
or
3 - y = -11
If you just plan to solve it as two different equations you'll make the work much easier (as much as people try desperately to avoid doing multiple equations...there's really no other way). Solving for y we find that:
y = 14 or y = -8
C) When statements are clearly insufficient, ask "Why Are You Here?", and when E seems obvious try to find a way to get C, or at least get close
Returning to statement 1, it's completely useless on its own - with an x variable within the absolute value we can't possibly solve for y. And statement 2 does not solve for x, so we're still stuck with two variables. This is pretty easily not sufficient even with both together, right?
Strategically, know this - they don't give away E answers easily! The only way you should ever select E on a DS problem is when you can point to that "a-ha!" reason that it cannot be solved...you should be able to get one step away but recognize that there's one pesky unknown that just won't go away. Accordingly, before you quickly answer E, you have to get within striking distance of C, and the best way to do that is to try to find some synergy between the two statements.
In this case, why would they give you two variables in statement 1 with no hope of eliminating one in statement 2? The only logical reason is that statement 1 could still be helpful even without solving for x.
So let's investigate - statement 2 was pretty helpful in giving us exactly two options for y:
y is either -8 or it's 14
Can statement 1 eliminate one of those options?
We know that, at a minimum, an absolute value is equal to 0...it can never be negative. If we rephrase statement 1 to solve for y, we get:
y = 3 (|x^2 - 4|) + 2
So y is >= 2 - it cannot possibly be -8. Statement 1 is pretty useless on its own, but in concert with statement 2 it eliminates one of two choices, and therefore the answer is C.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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