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What is the value of y?

(1) 3|x^2 – 4| = y – 2

(2) |3 – y| = 11

I understand that (1) alone is insufficient, but the explanation says that from (1) we can determine that y is greater than or equal to 2. Can someone please explain how this is deduced? Thanks!

I understand that (1) alone is insufficient, but the explanation says that from (1) we can determine that y is greater than or equal to 2. Can someone please explain how this is deduced? Thanks!

*note that in (1) "x2" is meant to be x squared

What is the value of y? (1) 3|x^2 -4| = y - 2 (2) |3 - y| = 11

(1) As 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 can not be negative. Not sufficient.

To elaborate more left hand side is some absolute value, absolute value is always non-negative: \(|some \ expression|\geq{0}\), so RHS is also non-negative --> \(y-2\geq{0}\) --> \(y\geq{2}\)

My question is, that in the Manhattan Gmat guide, they always ask you to find solutions of the absolute value equation, and then PLUG both values in to the original equation. In case if one of those values dont match up, then that solution can be eliminated. If in either of the equations , we would find a value which could not work, then could we safely count that as sufficiency for that statement, or would we have to still assume that both are possible so not sufficient?

My question is, that in the Manhattan Gmat guide, they always ask you to find solutions of the absolute value equation, and then PLUG both values in to the original equation. In case if one of those values dont match up, then that solution can be eliminated. If in either of the equations , we would find a value which could not work, then could we safely count that as sufficiency for that statement, or would we have to still assume that both are possible so not sufficient?

As for your question: in DS questions, when we are asked to determine value of an unknown, statement is sufficient if it gives single numerical value of this unknown. So if you have two solutions for a variable out of which one is not valid for some reason then you are left with only one solution and thus the statement is sufficient (of course if you are asked to find the value of this variable).
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