Question

If $x$ is negative, is $x<-3$?
(1) $x^2>9$
(2) $x^3<-9$

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is A Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

1. Given that , it follows that $x<-3$ or $x>3$, a result that can be obtained in a variety of ways. For example, consider the equivalent equation that reduces to , or consider when the two factors of are both positive and when the two factors of are both negative, or consider where the graph of the parabola is above the x-axis, etc. Since it is also given that x is negative, it follows that $x<-3$; SUFFICIENT.
2. Given that , if $x=-4$, then , and so and it is true that $x<-3$. However, if $x=-3$, then , and so , but it is not true that $x<-3$; NOT sufficient.

• The correct answer is A; statement 1 alone is sufficient.