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# In the xy-plane, point (r, s) lies on a circle with center

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In the xy-plane, point (r, s) lies on a circle with center [#permalink]  01 Aug 2006, 10:58
In the xy-plane, point (r, s) lies on a circle with center at the origin. What is the value of r^2 + s^2?

(1) The circle has radius 2.
(2) The point (v2, -v2) lies on the circle.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

What does (v2, -v2) mean?
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Re: geometry question [#permalink]  01 Aug 2006, 18:10
positive_energy wrote:
In the xy-plane, point (r, s) lies on a circle with center at the origin. What is the value of r^2 + s^2?

(1) The circle has radius 2.
(2) The point (v2, -v2) lies on the circle.

What does (v2, -v2) mean?

any point on the circle with center origin always has a length of redius.

so its A as st. 1 is sufficient.
st 2 is not as we donot know the value of v.

r^2 + s^2 = 2.

its A.
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Equation of a circle
(x-a)^2 + (y-b)^2 = r^2
where (a,b) is the center and r is the radius.
Of center is (0,0) then teh equation becomes
x^2+y^2 = r^2

So in this case we have
r^2+s^2 = c^2 where c is radius.

St1: c =1 : SUFF

St2: r^2+s^2 = 2*v^2: INSUFF
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if (v2,-v2) lies on the circle,

=> r^2 + s^2 = (radius)^2 = 2*square(v2)

2nd is also sufficient.

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shoonya wrote:
if (v2,-v2) lies on the circle,

=> r^2 + s^2 = (radius)^2 = 2*square(v2)

2nd is also sufficient.

But 2*square(v2) is not a value. This is a variable.
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Re: geometry question [#permalink]  01 Aug 2006, 21:07
positive_energy wrote:
What does (v2, -v2) mean?

(v2, -v2) might be (sqrt(2), sqrt(-2))
(√2, -√2)
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Re: geometry question [#permalink]  01 Aug 2006, 21:10
freetheking wrote:
positive_energy wrote:
What does (v2, -v2) mean?

(v2, -v2) might be (sqrt(2), sqrt(-2))
(√2, -√2)

make sense. its D now...
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But where did the values for v2 & -v2 come from?
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hemamalinidr wrote:
But where did the values for v2 & -v2 come from?

Its not v2 and -v2
its SQRT(2) and -SQRT(2)
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But where did the values sqrt 2 & -sqrt 2 come from? In the original statement no values are given and even option B does not give any value.
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hemamalinidr wrote:
But where did the values sqrt 2 & -sqrt 2 come from? In the original statement no values are given and even option B does not give any value.

Original statement # 2 is:
The point (SQRT(2), -SQRT(2)) lies on the circle.
The point (v2, -v2) lies on the circle.
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are you saying the question is a misprint..because i saw v in the question and not square root. thanks
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positive_energy wrote:
are you saying the question is a misprint..because i saw v in the question and not square root. thanks

Yes. I've seen this question..
S2 was (√2, -√2), not (v2,-v2).. if so, D is the correct answer..

Clearly, it's another variable unless it's a typo..
I believe it's a typo, 'coz there's no such a statement like this one In GMAT..
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It makes sense now. Thanks dahia.
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