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

[BTGmoderatorLU]

Source: Official Guide

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

1) \(x-y < 0\)
2) \(x-z<0\)

The OA is C

[Ian Stewart]

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.