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If x, y and z are all non-zero numbers, what is the value of \(z = \frac{x-y}{2x+y}\)
(1) \(|x|=y\)
(2) \(x=-3\)
(1) \(|x|=y\)
(2) \(x=-3\)
26 Apr 2016, 15:54
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krodin
If x, y and z are all non-zero numbers, what is the value of \(z = \frac{(x-y)}{(2x+y)}\)
(1) \(|x|=y\)
(2) \(x=-3\)
Dear krodin,(1) \(|x|=y\)
(2) \(x=-3\)
I'm happy to respond.
This is a tricky one. If z were not mentioned in the first "if" statement, then the question would have a very different answer. In statement #1, we find out that \(|x|=y\). Naively, this would leave two choices for (x, y), either x = y or x = -y. We might think that x = y is one possibility, but notice that this would make the numerator of the ratio zero, which means the ratio would equal zero, and the conditional statement at the very beginning of the question makes very clear that z cannot equal zero. Therefore, we cannot have x = y. The only possibility from this statement is that x = -y or -x = y. Then
z = (x-y)/(2x+y)
z = [x - (-x)]/[2x + (-x)]
z = (x + x)/(2x - x)
z = (2x)/(x) = 2
This statement leads directly to a numerical answer for z. This statement, alone and by itself, is sufficient.
Statement #2, by itself, tells us about x but not about y. This statement, alone and by itself, is insufficient.
Answer = (A)
Does this make sense?
Mike
