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Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Location: India
WE:Education (Education)
Point (a, b) is a lattice point in xy-plane where, a and b are integer
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26 Aug 2021, 01:21
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.
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
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
Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Location: India
WE:Education (Education)
Re: Point (a, b) is a lattice point in xy-plane where, a and b are integer
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04 Sep 2021, 08:04
04 Sep 2021, 08:04
4
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
_________________
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
Attachments
Point (a, b) is a lattice point in xy-plane where, a and b are integers..png [ 41.8 KiB | Viewed 2361 times ]
_________________
I hope this helps!
Regards:
Karun Mendiratta
Founder and Quant Trainer
Prepster Education, Delhi, India
https://www.instagram.com/prepster_education/
Regards:
Karun Mendiratta
Founder and Quant Trainer
Prepster Education, Delhi, India
https://www.instagram.com/prepster_education/
General Discussion
Re: Point (a, b) is a lattice point in xy-plane where, a and b are integer
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20 Nov 2023, 12:37
20 Nov 2023, 12:37
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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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