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How many points with Integer x and Y co-ordinate lies within the circl

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How many points with Integer x and Y co-ordinate lies within the circl [#permalink]

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New post 13 May 2017, 02:32
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How many points with Integer x and Y co-ordinates 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

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How many points with Integer x and Y co-ordinate lies within the circl [#permalink]

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New post 13 May 2017, 06:45
1
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 y-axis 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 co-ordinate lies within the circl [#permalink]

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New post 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 co-ordinate lies within the circl [#permalink]

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New post 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 y-axis 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 co-ordinate lies within the circl [#permalink]

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New post 04 May 2018, 02:18
GMATinsight wrote:
How many points with Integer x and Y co-ordinates 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


After combining the two statements the figure will look like as attached.

Answer: Option C
Attachments

File comment: www.GMATinsight.com
Screen Shot 2018-05-04 at 2.36.15 PM.png
Screen Shot 2018-05-04 at 2.36.15 PM.png [ 194.23 KiB | Viewed 185 times ]


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How many points with Integer x and Y co-ordinate lies within the circl [#permalink]

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New post 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 y-axis 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 co-ordinate lies within the circl   [#permalink] 04 May 2018, 02:24
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