Question

If $x=2t$ and $y=\frac{t}{3}$, what is the value of $x^2-y^2$?
(1) $t^2-3=6$
(2) $t^3=-27$

• 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 D Each statement alone is sufficient.

This problem can be solved by determining the value of , and this can be determined if the value of or the value of can be determined. From statement 1, it indicates that and so . Thus, statement 1 is sufficient. From statement 2, it indicates that and so . Thus, statement 2 is sufficient.