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How many points with Integer x and Y coordinate lies within the circl [#permalink]
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13 May 2017, 02:32
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How many points with Integer x and Y coordinates lie within the circle? 1)The circle intersects with parabola y = ax^2 + 4 where a>0 at only one Point 2) The circle has centre at origin Source: http://www.GMATinsight.com
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How many points with Integer x and Y coordinate lies within the circl [#permalink]
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13 May 2017, 06:45
S1. Circle touches parabola at only 1 point. We do not have any idea about where the centre of the circle is. Hence, insufficientS2. We know only the centre. Can't say anything about at how many points does the circle touches or cuts the parabola. Hence, insufficientCombining S1 & S2 Circle touches parabola at only 1 point. So, that means they just touch each other. For the parabola, if x=0, y=4. So the parabola intersects the yaxis at (0,4). This is the point where circle touched the parabola. Even if 'a' is any value > 0. Circle of circle is given as (0,0). Now, we have got the circle with eqn x^2+y^2=16. (4 is the radius of circle). For this circle the integer (x,y) inside the circle can be all those point satisfying x^2+y^2<16 So, all the pairs in the 1st quadrant lying inside the circle will be (1,1) (1,2) (2,2) (2,1) (3,1) (3,2) (2,3) (1,3)  Total 8. Similarly in 4 quadrants it will be 8*4=32. We also have (0,1) (1,0) (0,1) (1,0) (0,0) making the count go to 37. Yes we can say about the number of points lying inside the circle and that number is 37. Hence, C will be the answer.
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Re: How many points with Integer x and Y coordinate lies within the circl [#permalink]
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07 Sep 2017, 10:13
Could you please explain it with a diagram?



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Re: How many points with Integer x and Y coordinate lies within the circl [#permalink]
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31 Mar 2018, 07:45
14101992 wrote: S1. Circle touches parabola at only 1 point. We do not have any idea about where the centre of the circle is. Hence, insufficient
S2. We know only the centre. Can't say anything about at how many points does the circle touches or cuts the parabola. Hence, insufficient
Combining S1 & S2
Circle touches parabola at only 1 point. So, that means they just touch each other. For the parabola, if x=0, y=4. So the parabola intersects the yaxis at (0,4).
This is the point where circle touched the parabola. Even if 'a' is any value > 0.
Circle of circle is given as (0,0). Now, we have got the circle with eqn x^2+y^2=16. (4 is the radius of circle).
For this circle the integer (x,y) inside the circle can be all those point satisfying
x^2+y^2<16
So, all the pairs in the 1st quadrant lying inside the circle will be
(1,1) (1,2) (2,2) (2,1) (3,1) (3,2) (2,3) (1,3)  Total 8.
Similarly in 4 quadrants it will be 8*4=32.
We also have (0,1) (1,0) (0,1) (1,0) (0,0) making the count go to 37.
Yes we can say about the number of points lying inside the circle and that number is 37.
Hence, C will be the answer. Though DS questions dont expect exact answer. just to be sure total number of integer points will be 1st quadrant  (0,0) (0,1) (0,2) (0,3) (1,0) (1,1) (1,2) (1,3) (2,1)....... (3,1).... So in total we will have 16 such combinations in 1st quadrant so total such sets will be 16*4= 64 correct me if i am wrong



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Re: How many points with Integer x and Y coordinate lies within the circl [#permalink]
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04 May 2018, 02:18
GMATinsight wrote: How many points with Integer x and Y coordinates lie within the circle? 1)The circle intersects with parabola y = ax^2 + 4 where a>0 at only one Point 2) The circle has centre at origin Source: http://www.GMATinsight.comAfter combining the two statements the figure will look like as attached. Answer: Option C
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Screen Shot 20180504 at 2.36.15 PM.png [ 194.23 KiB  Viewed 185 times ]
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How many points with Integer x and Y coordinate lies within the circl [#permalink]
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04 May 2018, 02:24
cruiseav wrote: 14101992 wrote: S1. Circle touches parabola at only 1 point. We do not have any idea about where the centre of the circle is. Hence, insufficient
S2. We know only the centre. Can't say anything about at how many points does the circle touches or cuts the parabola. Hence, insufficient
Combining S1 & S2
Circle touches parabola at only 1 point. So, that means they just touch each other. For the parabola, if x=0, y=4. So the parabola intersects the yaxis at (0,4).
This is the point where circle touched the parabola. Even if 'a' is any value > 0.
Circle of circle is given as (0,0). Now, we have got the circle with eqn x^2+y^2=16. (4 is the radius of circle).
For this circle the integer (x,y) inside the circle can be all those point satisfying
x^2+y^2<16
So, all the pairs in the 1st quadrant lying inside the circle will be
(1,1) (1,2) (2,2) (2,1) (3,1) (3,2) (2,3) (1,3)  Total 8.
Similarly in 4 quadrants it will be 8*4=32.
We also have (0,1) (1,0) (0,1) (1,0) (0,0) making the count go to 37.
Yes we can say about the number of points lying inside the circle and that number is 37.
Hence, C will be the answer. Though DS questions dont expect exact answer. just to be sure total number of integer points will be 1st quadrant  (0,0) (0,1) (0,2) (0,3) (1,0) (1,1) (1,2) (1,3) (2,1)....... (3,1).... So in total we will have 16 such combinations in 1st quadrant so total such sets will be 16*4= 64 correct me if i am wrong There seems some mistake. The circle will have radius = 4 so the points must satisfy the inequation \(x^2 + y^2 ≤ 4^2\)The points in the first quadrant will be (1, 0) (2, 0), (3, 0), (4, 0) (1, 1) (2, 1) (3, 1) (1, 2) (2, 2) (3, 2) (1, 3) (2, 3) i.e. 12 Points in one quadrant So in all four quadrants, total points = 12*4 = 48 one point will be origin as well so total points becomes 48+1 = 49
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How many points with Integer x and Y coordinate lies within the circl
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