Data Sufficiency

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 (√2, -√2) lies on the circle.

r^2+s^2=radius^2
st 1 provides radius, therefore, sufficient to answer r^2+s^2

any (x,y) point on circle will have equation of x^2+y^2=radius^2
st 2 provides point on circle, therefore, radius^2 can be calculated

d

Its D...
Its the standard equation of the circle with centre at the origin that's being tested here.

For those who are not familiar with equation of circle, it can be worked out simply by using distance between two points formula to find out and match the radius of the circle with center origin.

(r^2 + 0^2)^2 + (s^2 + 0^2)^2 = radius^2
=> r^2 + s^2 = radius^2

So we just need the radius to solve this, which is directly given in statement 1 and can be found out from statement 2 using the same formula [ radius^2 = ((√2)^2 + 0^2)^2 + ((-√2)^2 + 0^2) = 4]. So the answer is D.

both equations telling us the same thing.. i.e. the radius is = 2

since the standard equation for a circle with centre at the origin is

x^2+y^2 = r^2 (replace x and y by r and r resp)

we will get the absolute value in both the cases.

correct answer D.

Circle's Centre is the origin. That gives all relief

Statement 1:

r^2+s^2 = (radius)^2...SUFFICIENT

Statement 2:

the points gives the length of the radius....SUFFICIENT

(D) is the answer

Did this question ever appear in any GMAT exam? I am seeing the circle equation for the first time :-S

Statement 1
Sufficient

Directly gives the value

Statement 2
Sufficient

Gives the length of the radius and thus indirectly give the value of the expression


D

Shabana wrote:Did this question ever appear in any GMAT exam? I am seeing the circle equation for the first time :-S

You don't need to revise equation of circle for this question in particular. Just focus on the Distance Formula. If point (r, s) lies on a circle with center at the origin (0, 0), then the radius of the circle can be given by the distance between the point (r, s) and the origin (0, 0), which could result in appearing as

r^2 + s^2 = x^2, where x is radius

Since, it resembles with (and in a way, it is) the equation of circle whose radius is a and center at the origin, that is

x^2 + y^2 = a^2

so don't worry about that.

Although, revising equation of circle in different scenarios won't be a bad idea either, while preparing for the GMAT.

Equation of circle in xy plane with centre at origin is x^2+v^2 = r^2
s1: radius given, Sufficient
S2: Point given, sufficient

(D) is ans

D

Answer is D.

if (r,s) lies on a circle, and the center is at the origin, then the distance from the origin to any point on the circle will be the same aka the radius. The radius is also the hypotenuse of a right triangle with sides made up of the x and y axis.

The question is asking what is r^2 + s^2. This should look familiar, as it is one side of the pythagoreum theorem. r^2 + s^2 = x^2 where x=radius. All we need to know is the radius of the circle to answer this question.

1) Sufficient. x=2, so x^2 = 4
2) [2^(1/2),2^(1/2)] lies on the circle. This point will have the same distance from the origin as (r,s). Therefore, (2^(1/2))^2+(2^(1/2))^2=r^2 + s^2=4. SUFFICIENT.

D the answer.

Each of the Statements are sufficient.

Answer is D.