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Point (a, b) is a lattice point in xy-plane where, a and b are integer

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KarunMendiratta
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Point (a, b) is a lattice point in xy-plane where, a and b are integer [#permalink] New post   26 Aug 2021, 01:21
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Point (a, b) is a lattice point in xy-plane where, a and b are integers.
Circle O has a center at (–2, 1) and a radius of 6. Some points, such as the center (–2, 1) lie inside the circle, but a point such as (4, 1) is on the circle but not inside the circle.

Quantity A
Quantity B
Number of lattice points that are inside the circle O
128


A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
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B
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Re: Point (a, b) is a lattice point in xy-plane where, a and b are integer [#permalink] New post   04 Sep 2021, 08:04
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Explanation:

Since the centre of circle O is at (-2, 1) and radius is 6
Let us go 6 units Left (-8, 1), Right (4, 1), Up (-2, 7) and Down (-2, -5)

Therefore,
integer values of x will lie between -8 and 4
i.e. 11 values in total
integer values of y will lie between 7 and -5
i.e. 11 values in total

Now, construct a square will each side 11 units
(Refer to the figure below)

Notice the number of points inside the square are (11)(11) = 121
But, the points inside the circle ) would be less.

Col. A: Value less than 121
Col. B: 128

Hence, option B
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Point (a, b) is a lattice point in xy-plane where, a and b are integers..png
Point (a, b) is a lattice point in xy-plane where, a and b are integers..png [ 41.8 KiB | Viewed 3580 times ]

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Re: Point (a, b) is a lattice point in xy-plane where, a and b are integer [#permalink] New post   04 Dec 2024, 09:41
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Point (a, b) is a lattice point in xy-plane where, a and b are integer [#permalink]
04 Dec 2024, 09:41
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