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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] New post 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] New post 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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 [#permalink] New post 01 Aug 2006, 20:24
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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 [#permalink] New post 01 Aug 2006, 20:32
if (v2,-v2) lies on the circle,

square(radius) = square(v2) + square(v2)

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

2nd is also sufficient.

answer should be D.
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 [#permalink] New post 01 Aug 2006, 20:34
shoonya wrote:
if (v2,-v2) lies on the circle,

square(radius) = square(v2) + square(v2)

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

2nd is also sufficient.

answer should be D.

But 2*square(v2) is not a value. This is a variable.
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Re: geometry question [#permalink] New post 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] New post 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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 [#permalink] New post 01 Aug 2006, 22:09
But where did the values for v2 & -v2 come from?
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 [#permalink] New post 01 Aug 2006, 22:31
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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 [#permalink] New post 02 Aug 2006, 09:26
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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 [#permalink] New post 02 Aug 2006, 10:27
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.
instead of
The point (v2, -v2) lies on the circle.
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 [#permalink] New post 02 Aug 2006, 11:08
are you saying the question is a misprint..because i saw v in the question and not square root. thanks
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 [#permalink] New post 02 Aug 2006, 13:31
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..

You asked what (v2,-v2) means.
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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 [#permalink] New post 02 Aug 2006, 20:55
It makes sense now. Thanks dahia.
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