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 OA is the option D.
Could anyone give me some help here? How can I determine if "a" is less than 2 or not? I'd appreciate any help.
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Is a < 2?
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The answer to the question stem can be NO -- implying that a≥2 -- only if a is positive.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
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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Hi nidhips,
Co-ordinate Geometry/Graphing is a relatively rare subject on the GMAT; you'll likely see it just once on Test Day. In that same way, the task of graphing circles is a rare task within a rare category, so you probably won't need any special knowledge on that subject when you take the Official GMAT. The Official Guide doesn't appear to even include the subject in the "Geometry" portion of the book. That all having been said, you CAN physically graph any of the equations that you're given in these types of situations (including circles) - and choosing to work 'visually' (on your pad) can make most Geometry questions easier to deal with.
GMAT assassins aren't born, they're made,
Rich
Co-ordinate Geometry/Graphing is a relatively rare subject on the GMAT; you'll likely see it just once on Test Day. In that same way, the task of graphing circles is a rare task within a rare category, so you probably won't need any special knowledge on that subject when you take the Official GMAT. The Official Guide doesn't appear to even include the subject in the "Geometry" portion of the book. That all having been said, you CAN physically graph any of the equations that you're given in these types of situations (including circles) - and choosing to work 'visually' (on your pad) can make most Geometry questions easier to deal with.
GMAT assassins aren't born, they're made,
Rich
