crackgmat007 wrote:What is the value of y?
(1) 3|x^2 - 4| = y - 2
(2) |3 - y| = 11
Hi guys,
the answer is C.
To have sufficiency, we need to find a single value for y.
Statement 1: "X?!?"...Not sufficient.
Statement 2: Absolute value? "3-y" can be either 11 to the right or 11 to the left of zero. So y equals two different values also. Not sufficient.
Combo:
We can't analyze the first statement without making assumptions. So, let's look at the second one.
"3-y" can be 11 units away from zero in one of two ways:
3-y = 11 or else 3-y = -11
So either y = -8 or else y = 14
The right hand side of the equation in statement two is y-2
If y = 14, then y-2 = 12
and
If y = -8, then y-2 = -10
But if y-2 = -10 we would have:
3*[x^2-4] = -10
Because absolute value is positive or zero, we would have:
3*pos = -10 or 3*0 = -10
Those two equations are clearly impossible.
Therefore, y cannot equal -8.
Leaving only one value (14) for y.
Note: Because we have no info about x, we can treat [x^2-4] as just [some number]. [any number] is either postive or zero.
The statements, although insufficient in isolation, are sufficient in combination. (C)
