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Is it true that exactly two of the three inequalities xz < 0, yz < 0

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Bunuel
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Is it true that exactly two of the three inequalities xz < 0, yz < 0 [#permalink] New post   05 Jul 2022, 01:30
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Is it true that exactly two of the three inequalities \(xz < 0, \ yz < 0\) and \(yx < 0\) are true?

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

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


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zhanbo
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Re: Is it true that exactly two of the three inequalities xz < 0, yz < 0 [#permalink] New post   05 Jul 2022, 02:17
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Pre-thinking
If each of the three numbers are positive, or negative, none of the three inequalities are true.
If there is one or two negative numbers, though, exactly two of the three inequalities are true.

(1)Only
xz<0 so one if negative and the other is positive
exactly two of the three inequalities are true.
Sufficient

(2)Only
Sufficient for the same reason.

The answer is thus (D).
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LunaticMaestro
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Re: Is it true that exactly two of the three inequalities xz < 0, yz < 0 [#permalink] New post   14 Nov 2023, 18:42
Correct me if I am wrong, there's a possibility that one of the variable can take value zero in which case the choice C holds true.
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Re: Is it true that exactly two of the three inequalities xz < 0, yz < 0 [#permalink] New post   14 Nov 2023, 20:03
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LunaticMaestro wrote:
Correct me if I am wrong, there's a possibility that one of the variable can take value zero in which case the choice C holds true.


Hi LunaticMaestro

If one of the variable is zero then statement 1 and 2 both will become false, which can never happen. As your statement has to be true in all the case.
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Re: Is it true that exactly two of the three inequalities xz < 0, yz < 0 [#permalink]
14 Nov 2023, 20:03
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