Formation of a Differential Equation from a General Solution
If
x = 2...
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 , 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.