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Last Updated on May 10, 2023
GMAT OFFICIAL GUIDE DS
Solution:
Since x = 2t and y = t/3, by substitution, we have
x^2 – y^2
(2t)^2 – (t/3)^2
4t^2 – t^2/9
(36t^2)/9 – t^2/9
(35t^2)/9
So if we know the value of t or t^2, then we can determine the value of (35t^2)/9.
Statement One Alone:
t^2 – 3 = 6
Adding 3 to both sides of the equation, we have t^2 = 9.
Since t^2 = 9, then (35t^2)/9 = (35(9))/9 = 35.
Statement one alone is sufficient. We can eliminate answer choices B, C and E.
Statement Two Alone:
t^3 = −27
Taking the cube root of both sides of the equation, we have t = -3. Since we know t = -3, then
(35t^2)/9 = (35(-3)^2)/9 = (35(9))/9 = 35.
Statement two alone is also sufficient to answer the question.
Answer: D
