Hi All,
As complex as this graphing-based DS question looks, the given Facts focus on two equations, so they're relatively easy to deal with/solve.
We're asked if A is less than 2. This is a YES/NO question.
Fact 1: In an XY plane, point (A,1) lies inside the circle whose equation is X^2 + Y^2 = 3
With the given equation and the given (X,Y) co-ordinate (A,1), we can plug in and solve for A....
A^2 + 1^2 = 3
A^2 = 2
Since we're dealing with a circle, there are two possible points that have a Y-co-ordinate of 1: (A, 1) and (-A, 1).
Since A^2 = 2, A = Root(2).
Root(2) is < Root(4)
Root(2) is < 2, so whether we're dealing with A = Root(2) or A = -Root(2), the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT.
Fact 2: In an XY plane, point (A,4) lies on the line whose equation is 2Y + 4X = 10
Here, we have a simple line to work with, so we can substitute in the value of A (for X) and 4 (for Y), giving us....
2(4) + 4(A) = 10
8 + 4A = 10
4A = 2
A = 1/2
The answer to the question is YES.
Fact 2 is SUFFICIENT.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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