KarolPL wrote:

If \(0 < ab < ac\), is a negative?

(1) \(c < 0\)

(2) \(b > c\)

(1) \(c<0\), \(0<ac\), \(0<(-ve)(-ve).\) Sufficient

(2) \(b>c\), \(b-c>0\), \(ab<ac\), \(a(b-c)<0\), \((-ve)(+ve)<0\). Sufficient.

Answer :

DOFFICIAL SOLUTION

(D): By the transitive property of inequalities, if 0 < ab < ac, then 0 < ac. Therefore, a and c must have the same sign.

(1) SUFFICIENT: Statement (1) tells you that c is negative. Therefore, a is negative.

(2) SUFFICIENT: Statement (2) is trickier. The statement indicates that b > c, but the question stem also told you that ab < ac. When you multiply both sides of b > c by a, the sign gets flipped. For inequalities, what circumstance needs to be true in order to flip the sign when you multiply by something? You multiply by a negative. Therefore, a must be negative, because multiplying the two sides of the equation by a results in a flipped inequality sign.

The correct answer is

(D)
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