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Is a < 2 ?

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Is a < 2 ?

by gmattesttaker2 » Mon May 19, 2014 6:45 pm
Hello,

Can you please help with this:

Is a < 2?

1) In the xy-plane, the point (a,1) lies inside the circle whose equation is x^2 + y^2 = 3
2) In the xy-plane, the point (a,4) lies on the line whose equation is 2y + 4x = 10

OA: D


Thanks for your help.

Regards,
Sri
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Source: — Data Sufficiency |
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by GMATGuruNY » Mon May 19, 2014 8:35 pm
gmattesttaker2 wrote:Hello,

Can you please help with this:

Is a < 2?

1) In the xy-plane, the point (a,1) lies inside the circle whose equation is x^2 + y^2 = 3
2)

OA: D
Statement 1: In the xy-plane, the point (a,1) lies inside the circle whose equation is x^2 + y^2 = 3
The following represents points ON THE CIRCLE:
x² + y² = 3.
The following represents points INSIDE THE CIRCE:
x² + y² < 3.

Since (a,1) lies inside the circle, we get:
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
Here, the value of a can be calculated by substituting y=4 into 2y + 4x = 10.
Thus, we can determine whether a < 2.
SUFFICIENT.

The correct answer is D.
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