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Question

# If x=2t and y=t3, what is the value of x2−y2?(1) t2−3=6(2) t3=−27

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

## The correct option is D Each statement alone is sufficient.This problem can be solved by determining the value of $x^{2}-y^{2}= \left ( 2t \right )^{2}-\left ( \frac{t}{3} \right )^{2}$, and this can be determined if the value of $t^{2}$ or the value of $t$ can be determined. From statement 1, it indicates that $t^{2}-3= 6$ and so $t^{2}= 9$. Thus, statement 1 is sufficient. From statement 2, it indicates that $t^{3}= -27$ and so $t= -3$. Thus, statement 2 is sufficient.

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