Is x^2 + y^2 > 4a?
(1) (x + y)^2 = 9a
(2) (x – y)^2 = a
Official Answer to the above problem.
(1) INSUFFICIENT: If we multiply this equation out, we get:
x2 + 2xy + y2 = 9a
If we try to solve this expression for
x2 + y2, we getx2 + y2 = 9a – 2xy
Since the value of this expression depends on the value of x and y, we don't have enough information.
(2) INSUFFICIENT: If we multiply this equation out, we get:
x2 – 2xy + y2 = a
If we try to solve this expression for x2 + y2,
we getx2 + y2 = a + 2xy
Since the value of this expression depends on the value of x and y, we don't have enough information.
(1) AND (2) INSUFFICIENT: We can combine the two expanded forms of the equations from the two statements by adding them:
x2 + 2xy + y2 = 9ax2 – 2xy + y2 = a----- 2x2 + 2y2 = 10ax2 + y2 = 5a
If we substitute this back into the original question, the question becomes: "Is 5a > 4a?"If a > 0, the answer is yes.We know from the question stem that a is nonnegative.However, if a = 0 the answer is no.
The correct answer is E.
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