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Point (a,b) is on the circle represented by x^2+y^2=10,

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Joined: 18 Dec 2012
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Point (a,b) is on the circle represented by x^2+y^2=10,  [#permalink]

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New post Updated on: 04 Jan 2013, 04:45
2
7
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

49% (01:32) correct 51% (01:25) wrong based on 192 sessions

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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?

A. 0
B. 2
C. 4
D. 6
E. 8

Originally posted by trex16864 on 04 Jan 2013, 04:41.
Last edited by Bunuel on 04 Jan 2013, 04:45, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Point (a,b) is on the circle represented by x^2+y^2=10,  [#permalink]

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New post 04 Jan 2013, 04:53
1
2
trex16864 wrote:
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?

A. 0
B. 2
C. 4
D. 6
E. 8


a^2+b^2=10 and a, b are integers means that 10 is the sum of two perfect squares.

10 is the sum of only one pair of perfect squares 1 and 9.

So, there can be 8 such points, 4 in each quadrant:
(1, 3);
(1, -3);
(-1, 3);
(-1, -3);
(3, 1);
(3, -1);
(-3, 1);
(-3, -1).

Answer: E.
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Re: Point (a,b) is on the circle represented by x^2+y^2=10,  [#permalink]

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New post 04 Jan 2013, 06:47
X and Y are integers and when squared have to equal 10. X and Y can take values of 1,3,-1,-3. The 1 and the 3 must be used in combination in order to add up to 10 (you cant use 1,1 or 3,3 or -1,-1, or -3,-3).

this leaves you with only 8 choices. answer E
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Re: Point (a,b) is on the circle represented by x^2+y^2=10,  [#permalink]

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New post 04 Jan 2013, 23:20
Very gmatlike question.Can u tell us the source?
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Re: Point (a,b) is on the circle represented by x^2+y^2=10,  [#permalink]

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New post 28 Dec 2013, 09:26
trex16864 wrote:
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?

A. 0
B. 2
C. 4
D. 6
E. 8


Basically (10,0) and (1,3) with all their combinations

Given that each of them can be either positive or negative then we have 2*2 = 4 options each

Hence 8 total

Hope it helps
Cheers!

J :)
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Re: Point (a,b) is on the circle represented by x^2+y^2=10,  [#permalink]

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New post 18 Sep 2018, 10:45
trex16864 wrote:
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?

A. 0
B. 2
C. 4
D. 6
E. 8



Shouldn’t the question be “on the circumference “rather than “on the circle”?
The circle is an area, so we could add all the points inside it; for example (2,2), (2,1),( -2,1), etc.
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Re: Point (a,b) is on the circle represented by x^2+y^2=10, &nbs [#permalink] 18 Sep 2018, 10:45
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