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Re: If xyz 0, is x (y + z) 0? [#permalink]
26 Apr 2015, 13:10

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Re: If xyz 0, is x (y + z) 0? [#permalink]
27 Apr 2015, 00:35

Expert's post

If xyz ≠ 0, is x (y + z) >= 0?

xyz ≠ 0 means that neither of unknowns is 0.

(1) |y + z| = |y| + |z| --> either both \(y\) and \(z\) are positive or both are negative, because if they have opposite signs then \(|y+z|\) will be less than \(|y|+|z|\) (|-3+1|<|-3|+1). Not sufficient, as no info about \(x\).

(2) |x + y| = |x| + |y| --> the same here: either both \(x\) and \(y\) are positive or both are negative. Not sufficient, as no info about \(z\).

(1)+(2) Either all three are positive or all three are negative --> but in both cases the product will be positive: \(x(y+z)=positive*(positive+positive)=positive>0\) and \(x(y+z)=negative*(negative+negative)=negative*negative=positive>0\). Sufficient.

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