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

factor26 wrote:What is the value of y?

(1) 3|x^2 - 4| = y - 2

(2) |3 - y| = 11

OA is C

I understand why statement 2 is insuff - but i'm having trouble working through statement 1. If someone can provide some insight on statement 1 and how this problem is solved? Thanks all!

(1) 3|x² - 4| = y - 2
If x = 2, y = 2, then 3|2² - 4| = 0 and y - 2 = 0; here y = 2
If x = 1, y = 11, then 3|x² - 4| = 3 * |1² - 4| = 9 and y - 2 = 11 - 2 =9; here y = 11
It can be seen that y cannot have any definite value from the info given in statement 1; NOT sufficient.

(2) |3 - y| = 11 implies 3 - y = 11 or 3 - y = -11
Solving we get, y = -8 or y = 14
Again we do not get a definite answer; NOT sufficient.

Combining (1) and (2), we get 3|x² - 4| = y - 2, which implies that |x² - 4| will always be positive and hence the left hand side expression 3|x² - 4| will always be positive. This implies that y - 2 should also be positive.
So, if y - -8 then y - 2 cannot be positive but when y = 14, then y - 2 is positive. So we get a definite value for y; SUFFICIENT.

The correct answer is C.