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Is a < 2?

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Is a < 2? [#permalink]

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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Oct 2013, 09:17, edited 1 time in total.
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Is a < 2?

(1) In an xy plane, point (a,1) lies inside the circle whose equation is x^2 + y^2 = 3. This circle is centered at the origin and has the radius of \(\sqrt{3}\approx{1.7}\) (check here: math-coordinate-geometry-87652.html). No point inside that circle has x-coordinate greater than \(\sqrt{3}\approx{1.7}\), thus \(a<1.7<2\). Sufficient.

(2) In an xy plane, point (a,4) lies on the line whose equation is 2y + 4x = 10 --> 2*4+4x=10 --> x=1/2. Sufficient.

Answer: D.
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Is a < 2? [#permalink]

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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:
[Reveal] Spoiler:
D


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Last edited by EMPOWERgmatRichC on 10 Apr 2015, 22:42, edited 1 time in total.
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EMPOWERgmatRichC wrote:
Hi All,


2(4) + 4(A) = 10
8 + 4A = 10
A = 2
A = 1/2
The answer to the question is YES.
Fact 2 is SUFFICIENT.

Final Answer:
[Reveal] Spoiler:
D


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Hi Rich!
Nice solution as usual! But please correct a typo. The bold part should be "4A" not A=))
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Re: Is a < 2? [#permalink]

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Hi Konstantin1983,

Good eye. I've made the correction. Thanks for catching it.

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Re: Is a < 2? [#permalink]

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New post 13 Apr 2015, 03:12
EMPOWERgmatRichC wrote:
Hi Konstantin1983,

Good eye. I've made the correction. Thanks for catching it.

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Ah Rich no problem=)). We are human being and even assassins sometimes make typos=))
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Re: Is a < 2? [#permalink]

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New post 15 Aug 2016, 06:34
1. We are told that a is the x coordinate for a point within a circle with radius sqrt(3) its center is origo.

The largest x coordinate possible would be if y=0, otherwise x would have to decrease(if +) or increase (if -) to make sure the distance from origo does not exceed sqrt(3).
If y=0, a can be at most sqrt(3). This is less than 2. As y is 1, a has to be even smaller.
Sufficient.

2.
We can solve for x. Sufficient.

Answer D

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Re: Is a < 2? [#permalink]

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New post 03 Sep 2016, 05:02
Bunuel: Was able to understand your solution, have a query as to how the circle is centered at the origin. Is it a default assumption or its inferred from the equation.?
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Re: Is a < 2? [#permalink]

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narendran1990 wrote:
Bunuel: Was able to understand your solution, have a query as to how the circle is centered at the origin. Is it a default assumption or its inferred from the equation.?


Equation of the circle is given by the formula,

\((x-a)^2 + (y-b)^2 = r^2\), where a,b are the center coordinates and r is the radius.

Now, in the question we are given the form

\((x)^2 + (y)^2 = r^2\), implying a and b are zero. Or the circle is centered at origin.

I think you should go through the basic of Circle once. That would help you in such questions.
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Re: Is a < 2? [#permalink]

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Re: Is a < 2?   [#permalink] 10 Sep 2017, 08:39
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