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from 2nd we got 2 roots: -8 or 14, check this roots with 1st statement we see that 3|x^2-4| can't be negative, so -8 is out. 14 is left and it's the only choice left.

Here is my take, can the experts confirm please if my approach is correct ?

1. 3|x^2-4|= y-2 gives us 2 values if we open the modulus, for the 2 values y = 3x^2 -10 and y = 14 – 3x^2. NOT SUFFICIENT.

2. |3-y|=11, gives y = -8, 14 if we open the modulus. NOT SUFFICIENT.

Combining 1 and 2. if we put the values y = -8, 14 in 3|x^2-4|= y-2, If y = -8, 3|x^2-4|= -10, not possible as If y = 14, 3|x^2-4|= 12, Only possible value.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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(1) \(3|x^2-4|=y-2\). Now, since we are asked to find the value of y, from this statement we can conclude only that \(y\geq{2}\), as LHS is absolute value which is never negative, hence RHS als cannot be negative. Not sufficient.

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