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Combination with co-ordinate geometry question

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nipukumar
 Post subject: Combination with co-ordinate geometry question
 Post Posted: Thu Nov 25, 2010 6:53 pm 
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Course Students


Posts: 11
Circle with center (x,y) and radius r such that r=x+2 or r=y+2 to be constructed in xy-plane. The range of possible x-coordinate is -4<=x<=4 and y-coordinate is -8<=y<6. Given these conditions, how many different circles could be constructed ?

No answer choices given. How to solve this problem ?
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atul.prasad
 Post subject: Re: Combination with co-ordinate geometry question
 Post Posted: Thu Nov 25, 2010 11:48 pm 
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Students


Posts: 34
I assume that x and y are integers.

in that case there are 9 possible values of x and 15 possible values of y.

So we have 15*9 possible "centers" for this circle.
Now, each of these 135 circles could be of radius x+2 or y+2.

So we have 135*2 = 270, different circles
However, when x = y, the circle with r = x+2 or r=y+2 is same.

So we must count out those circles (since we added them twice above).

So the answer should be 270-9 = 261 (since there are 9 possible values when x=y)
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jnelson0612
 Post subject: Re: Combination with co-ordinate geometry question
 Post Posted: Fri Nov 26, 2010 11:30 am 
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ManhattanGMAT Staff


Posts: 1857
I've just worked this through and agree with atul. Excellent work!

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Jamie Nelson
ManhattanGMAT Instructor
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