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# Geometry DS (from club challenges)

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Senior Manager
Joined: 20 Apr 2008
Posts: 316
Schools: HBS Class of 2011
Geometry DS (from club challenges) [#permalink]

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19 Sep 2008, 15:34
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Attached is the question.

I don't fully understand what statement 1) tells us (not sure why the explanation about statement 1 is correct).

Thanks!
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VP
Joined: 21 Jul 2006
Posts: 1495
Re: Geometry DS (from club challenges) [#permalink]

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19 Sep 2008, 16:03
foodstamp wrote:
Attached is the question.

I don't fully understand what statement 1) tells us (not sure why the explanation about statement 1 is correct).

Thanks!

I say that the answer is B.

First of all, when you look at the equation $$(x-a)^2 + (y-b)^2 = 16$$, the radius of the circle is 4. Also, the center of the circle is at (a,b). So we need to know the value of a and b (although a alone will be sufficient to help us answer this question) in order to figure out whether it's location is still within reach to the y-axis when taking its radius into consideration:

(1) $$a^2 + b^2 > 16$$ ---> we can not determine the exact values for a and b because we can't tell whether they're positive or negative. Even if we do manage, the choices are endless

(2) $$a = |b| + 5$$ ----> we know that |b| can be either a zero or positive. So when you rearrange this equation to:

$$a - 5 = |b|$$, you know that the result must also be either a zero or positive. In order for this to be true, a must be at least a 5. When our value of a is at least a 5 and then we look at the center of the circle to be (a,b), the x-axis of 5 is longer than the length of the radius of 4, therefore the answer is no: the circle does not intersect the y-axis.

Current Student
Joined: 11 May 2008
Posts: 552
Re: Geometry DS (from club challenges) [#permalink]

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19 Sep 2008, 23:13
a^2+b^2 > 16.
a, b can be anything. if a=0 , b =5, yes it intersects the y axis.
if a= 2000, b=4000(some random value), it does not

stat 2)when b=0 a = 5. so the min point is 5,0. and here the circle does not intersect.
and b can be +ve or -ve. but x is always +ve.
so the point lies in the 1st or 4th quadrant and the point is 4 units away from the y axis. suff.

ans is B.
Re: Geometry DS (from club challenges)   [#permalink] 19 Sep 2008, 23:13
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