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If \(xyz < 0\), is \(x < 0\)?

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Source: — Data Sufficiency |

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by Ian Stewart » Sun Mar 17, 2019 11:30 am

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If xyz < 0, then at least one of x, y or z must be negative. Notice that means that the smallest of the three numbers is certainly negative, because negative numbers are always smaller than positive numbers.

Statement 1 tells us x < y, but maybe they're both positive and z is negative. Statement 2 tells us x < z, but maybe they're both positive and y is negative. But using both statements, we know x is the smallest of the three numbers, and we know the smallest of the three numbers must be negative, so the answer is C.
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