Question

In the given question, there are two statements marked I and II. Decide which of the statements are sufficient to answer the question. Choose your answer from the given alternative.

If $0<ab<ac$, is $a$ negative ?
(1) $c<0$
(2) $b>c$

• A. Statement I alone is sufficient to answer the problem.
• B. Statement II alone is sufficient to answer the problem.
• C. Statement I and II both are needed.
• D. Statement I and II both are not sufficient.
• E. Either of the statements I or II is sufficient

Answer 1

Answer: (E)

Either of the statements I or II is sufficient

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 $a$s, 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 (E)