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The center of a circle lies on the origin of the coordinate plane. If [#permalink]

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05 May 2011, 22:25

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The center of a circle lies on the origin of the coordinate plane. If a point (x, y) is randomly selected inside of the circle, what is the probability that x > y > 0?

Re: The center of a circle lies on the origin of the coordinate plane. If [#permalink]

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05 May 2011, 22:54

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Since x > y > 0. Means that x,y>0 first quadrant is the region concentrated.- probability here is 1/4.

In the first quadrant in half of the cases x>y and other half y>x. As you can draw a line y = x through the region,splitting it into halves. Thus 1/2 is the probability.

total = 1/2 * 1/4 = 1/8 A.
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Re: The center of a circle lies on the origin of the coordinate plane. If [#permalink]

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06 May 2011, 00:34

Alternatively, the step by step manual approach is:

Consider all possible outcomes about sign of x,y and their positions

SIGN POSITION x y + + x sup to y + - x inf to y - + x equal to y - - Go through each of the 4 cases and determine the number of possible outcomes: you will get 3 + 1 +1 + 3 = 8

The number of desirable outcomes is 1 ( + + and x sup to y).

Re: The center of a circle lies on the origin of the coordinate plane. If [#permalink]

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16 Sep 2011, 04:36

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jamifahad wrote:

The center of a circle lies on the origin of the coordinate plane. If a point(x,y) is randomly selected inside of the circle, what is the probability that x>y>0?

A. 1/8 B. 1/6 C. 3/8 D. 1/2 E. 3/4

The favorable region will only be on the first quadrant between lines y=0 AND y=x

The angle formed between these two lines from the center(0,0) = 45 degrees. Thus, the favorable sector within the circle will be 45/360=1/8 of the entire circle.

Ans: "A"

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A picture would have explained it better. I don't have the tool handy.
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Re: The center of a circle lies on the origin of the coordinate plane. If [#permalink]

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16 Sep 2011, 10:16

jamifahad wrote:

I got it. OA is A. One question, will the slope of line y=x matters? Like if a line is y=4x, probability will still be 1/8?

y=x is imperative.

If y=4x For x=1, y=4; but we want x>y. Moreover, the sector formed by x-axis(y=0) AND y=4x won't be (1/8)th of the entire circle; it will be more than 1/8 as the angle formed by the x-axis and y=4x is greater than 45 degrees.
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Re: The center of a circle lies on the origin of the coordinate plane. If [#permalink]

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16 Sep 2011, 13:08

So i guess for condition x>y>0 only line can be y=x with slope 1. Other lines of form y=mx where m is not equal to 1 will not satisfy the condition.
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Re: The center of a circle lies on the origin of the coordinate plane. If [#permalink]

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16 Sep 2011, 18:58

x>y>0

x>0,y>0 can only be possible in first quadrant.

x>y>0 can only be possible in one half of the first quadrant (imagine line x=y line passing through origin , which cuts the first quadrant into two equal parts.)

Re: The center of a circle lies on the origin of the coordinate plane. If [#permalink]

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17 Sep 2011, 22:24

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The probability of x & y > 0 in a circle is 1/4 ( Out of 4 quadrants only 1st satisfies the condition) Now since x>y , so there would be half such points in the first quadrant. Hence prob = 1/2 * 1/4 = 1/8.

P.S This probability also includes half of points for which x=y. IMO this is an incomplete question as nothing is mentioned using which we can calculate the number of points having x=y. P(x>y) + p (x=y) + p(x<y) = 1 But in this question, we are ignoring P(x=y).
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Re: The center of a circle lies on the origin of the coordinate plane. If [#permalink]

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23 Jul 2015, 01:52

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The center of a circle lies on the origin of the coordinate plane. If a point(x,y) is randomly selected inside of the circle, what is the probability that x>y>0?

A. 1/8 B. 1/6 C. 3/8 D. 1/2 E. 3/4

Having a hard time speculating probable scenarios. Could someone please explain this with a picture for species like me? :D

Thanks.

Check the image below:

Equation of the blue line is y = x. x > y > 0 is the yellow region, which is 1/8 of the circle.

Re: The center of a circle lies on the origin of the coordinate plane. If [#permalink]

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28 Sep 2017, 05:46

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The center of a circle lies on the origin of the coordinate plane. If [#permalink]

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02 Oct 2017, 08:39

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kannn wrote:

The center of a circle lies on the origin of the coordinate plane. If a point (x, y) is randomly selected inside of the circle, what is the probability that x > y > 0?

A. 1/8 B. 1/6 C. 3/8 D. 1/2 E. 3/4

1st Quadrant, portion below x=y line is the region which satisfies x>y>0, which is 1/8 of the area of circle and required probability.

Refer image

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