M7MBA wrote:Is a < 2?
(1) In an xy plane, point (a,1) lies inside the circle whose equation is x^2 + y^2 = 3
(2) In an xy plane, point (a,4) lies on the line whose equation is 2y + 4x = 10
The answer to the question stem can be NO -- implying that a≥2 -- only if a is positive.
Thus, when we evaluate the statements, we need consider only POSITIVE values for a.
Statement 1: In the xy-plane, the point (a, 1) lies inside the circle whose equation is x^2 + y^2 = 3.
Every point (x, y) such that x² + y² = 3 lies ON the circle.
Every point (x, y) such that x² + y² > 3 lies OUTSIDE the circle.
Every point (x, y) such that x² + y² < 3 lies INSIDE the circle.
Since (a, 1) must lie INSIDE the circle, (a, 1) must satisfy x² + y² < 3:
a² + 1² < 3
a² < 2
a < √2.
Thus, a < 2.
SUFFICIENT.
Statement 2: In the xy-plane, the point (a, 4) lies on the line whose equation is 2y+4x = 10.
Substituting x=a and y=4 into 2y+4x = 10, we get:
2(4) + 4a = 10
4a = 2
a = 2/4 = 1/2.
Thus, a < 2.
SUFFICIENT.
The correct answer is
D.
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