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# In the xy-plane, C and D are circles centered at the origin

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In the xy-plane, C and D are circles centered at the origin [#permalink]  29 Nov 2019, 02:35
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43% (01:36) correct 56% (00:26) wrong based on 16 sessions
In the xy-plane, $$C$$ and $$D$$ are circles centered at the origin with radii $$\sqrt{17}$$ and $$\sqrt{5}$$, respectively.

 Quantity A Quantity B The number of points (a, b) on circle $$C$$ where both a and b are integers The number of points (a, b) on circle $$D$$ where both a and b are integers

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

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[Reveal] Spoiler: OA

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Re: In the xy-plane, C and D are circles centered at the origin [#permalink]  29 Nov 2019, 18:33
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Equation of circle C: x2 + y2 = 17
Equation of circle D: x2 + y2 = 5

The question can now be rephrased as: number of integer pairs of (x,y) that satisfy above equations
For circle C, you have (4,1) and its 3 other variants by interchanging the -ve sign - (4,1),(4,-1),(-4,1),(-4,-1). Similar pattern of roots by interchanging x & y. - 4 more i.e. (1,4),(1,-4),(-1,4),(-1,-4)
For circle D, as well 8 roots obtained by interchanging signs & positions of (2,1)

Thus option C
Re: In the xy-plane, C and D are circles centered at the origin   [#permalink] 29 Nov 2019, 18:33
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# In the xy-plane, C and D are circles centered at the origin

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