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# The circle above has center at the origin and radius 3. How many order

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Math Expert
Joined: 02 Sep 2009
Posts: 52285
The circle above has center at the origin and radius 3. How many order  [#permalink]

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15 Dec 2017, 01:12
00:00

Difficulty:

(N/A)

Question Stats:

4% (02:07) correct 96% (01:04) wrong based on 25 sessions

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The circle above has center at the origin and radius 3. How many ordered pairs (x,y) satisfy the conditions that x and y are integers and (x,y) is inside the circle shown?

(A) 9
(B) 13
(C) 16
(D) 20
(E) 25

Attachment:

2017-12-15_1259_002.png [ 6.81 KiB | Viewed 372 times ]

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Re: The circle above has center at the origin and radius 3. How many order  [#permalink]

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15 Dec 2017, 19:41
1
Equation of circle --> x^2 + y^2 = 9

We have to calculate the number of integer co-ordinates lying inside the circle.

Number of ordered pairs in 1st quadrant that do not lie along the origin = (1, 1), (2, 2), (1, 2), (2, 1) = 4

Number of ordered pairs in 4 quadrants not lying along the origin = 4 * 4 = 16

Number of ordered pairs lying along the origin = 9

Total = 16 + 9 = 25

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The circle above has center at the origin and radius 3. How many order  [#permalink]

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24 Dec 2017, 14:40
Bunuel wrote:

The circle above has center at the origin and radius 3. How many ordered pairs (x,y) satisfy the conditions that x and y are integers and (x,y) is inside the circle shown?

(A) 9
(B) 13
(C) 16
(D) 20
(E) 25

Attachment:
2017-12-15_1259_002.png

I got Answer E, with the same method as Vyshak

But OA says 9.

(0,0) | (1,1) | (2,1)
(0,1) | (1,2) | (2,2)
(0,2) | (-1,1)| (-2,1)
(0,-1)| (-1,2)| (-2,2)
(0,-2)|(-1,-1)|(-2,-1)
(1,0) |(-1,-2)|(-2,-2)
(2,0) | (1,-1)| (2,-1)
(-1,0)| (1,-2)| (2,-2)
(-2,0)

Bunuel , would you please check the OA?
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Joined: 20 Feb 2017
Posts: 88
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Re: The circle above has center at the origin and radius 3. How many order  [#permalink]

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24 Dec 2017, 14:46

Does ordered Pair (x,y) refer to any specific case?

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Re: The circle above has center at the origin and radius 3. How many order &nbs [#permalink] 24 Dec 2017, 14:46
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