Abs Explain

[euro]

What is the value of y?

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

(2) |3 - y| = 11

[spoiler](C)[/spoiler]

[kvcpk]

What is the value of y?

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

(2) |3 - y| = 11

[spoiler](C)[/spoiler]

(1) 3|x^2 - 4| = y - 2
Y value varies for different values of x.
for exaple: when x=0, y = 14
and when x=2, y=2
hence INSUFF

(2) |3 - y| = 11
3-y = 11
implies y=-8
3-y=-11
implies y=14
2 different values. Hence INSUFF

Combining:
y can only be either -8 or 14 as per stmt2. Let us substitute in stmt1.

When y=-8,
3*|x^2-4| = -8-2 = -10
modulus is always positive.
Hence 3*mod is also positive.
Hence it cannot equal -10
So, y cannot be -8

When y=14,
3*|x^2-4| = 14-2 = 12
|x^2-4|=4
positive = positive
We are not concerened about values of X. So we need not simplify it further.

Hence Suff

pick C.

Hope this helps!!

[Rahul@gurome]

What is the value of y?

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

(2) |3 - y| = 11

[spoiler](C)[/spoiler]

Statement 1: 3|x^2 - 4| = (y - 2) => As absolute value cannot be negative, (y - 2) is greater than or equal to zero. We don't know anything about x, thus we cannot determine the value of y.

Not sufficient.

Statement 2: |3 - y| = 11 => (3 - y) = 11 or (3 - y) = -11 => y = -8 or y = 14

Not sufficient.

(1) & (2) Together: y = 14.

The correct answer is C.