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14 Nov 2006, 18:43
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Point (a, b) is on the circle represented by x^2 + y^2 = 10, and a, b are integers. How many such points are possible?
I count 12 points, however, the answer given is 8.
My logic:
Any combination where the x and y coordinates are both/each less than or equal to ten and the sum of the squares of those coordinates equals 100.
So, I counted the following points:
(0,10), (10,0), (-10, 0), (0, -10), (8,6), (6,8), (-6, -8), (-8, -6), (8, -6), (6, -8), (-8, 6), (-6, 8)
Any idea what's wrong here?
Artis
I count 12 points, however, the answer given is 8.
My logic:
Any combination where the x and y coordinates are both/each less than or equal to ten and the sum of the squares of those coordinates equals 100.
So, I counted the following points:
(0,10), (10,0), (-10, 0), (0, -10), (8,6), (6,8), (-6, -8), (-8, -6), (8, -6), (6, -8), (-8, 6), (-6, 8)
Any idea what's wrong here?
Artis
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
14 Nov 2006, 18:57
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I think the key here is that the circle equation is x^2 + y^ 2 = r^2. So if x^2 + y^2 = 10 that means r = sqrt 10. So we need to find combination of integers a and b such that a^2 + b^2 = 10.
I reason that since the circle started at the center, to find the total possible points, i only need to look at the first quadrant, and times 4. In the first quadrant, only (1,3) and (3,1) satisfy the condition. This means there are a total of 4*2 = 8 points.
I reason that since the circle started at the center, to find the total possible points, i only need to look at the first quadrant, and times 4. In the first quadrant, only (1,3) and (3,1) satisfy the condition. This means there are a total of 4*2 = 8 points.
14 Nov 2006, 19:14
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Oh, geez. Silly mistake. I took the radius to be 10 instead of SQRT(10). Thanks for letting me know.
Artis
Artis
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
