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Which two of the following three inequalities must be true xz < 0

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Bunuel
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Which two of the following three inequalities must be true xz < 0 [#permalink] New post   24 Jun 2022, 01:30
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Which two of the following three inequalities must be true \(xz < 0, \ yz < 0,\) and \(yx < 0\)?

(1) \(xy^2z < 0\)

(2) \(x^2yz < 0\)



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Re: Which two of the following three inequalities must be true xz < 0 [#permalink] New post   24 Jun 2022, 01:55
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(1) Only
Because y^2>=0
We know xz<0
But y can be either positive or negative.
Not sufficient.

(2)Only
Similarly, we know yz<0
But x can be either positive or negative.
Not sufficient.

(1)(2)Together
xz<0, yz<0
So z^2*x*y>0 => xy>0
Sufficient.

The answer is thus (C).
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Re: Which two of the following three inequalities must be true xz < 0 [#permalink] New post   24 Jun 2022, 22:00
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Bunuel wrote:
Which two of the following three inequalities must be true \(xz < 0, \ yz < 0,\) and \(yx < 0\)?

(1) \(xy^2z < 0\)

(2) \(x^2yz < 0\)


Statement 1 Only -
\(xy^2z < 0\)

\(x < 0\) OR \(z < 0\)
y is unknown (can be +ve or -ve). Hence, we do not know about yz and yx. NOT SUFFICIENT

Statement 2 Only -
\(x^2yz < 0\)

\(y < 0\) OR \(z < 0\)
x is unknown (can be +ve or -ve). Hence, we do not know about xz and yx. NOT SUFFICIENT

Combined -
\(xz < 0\)
\(yz < 0\)

\(xz^2y > 0\)
\(xy > 0\)

SUFFICIENT

Hence answer is C.
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Re: Which two of the following three inequalities must be true xz < 0 [#permalink]
24 Jun 2022, 22:00
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Bunuel
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