Miracles86
My god... Back in High School (or maybe elementary school), here in Portugal, we distinguish a circumference from a circle as being geometry elements completely different from each other. While a circumference is an imaginary line in which every point has the same distance to a specified center, defining thus the limits of a certain circular area and the circle is that area and is defined by the infinite set of points that are in a distance less than or equal to a specified radius. So, a circumference is and equation such as x^2 + y^2 = r^2 and a circle is an inequality such as x^2 + y^2 <= r^2. So the circumference has distance units such as meter, miles, feet, etc and the circle has square distance units such as square meters, etc. This is brilliantly coherent and makes no room for any confusion!
As far as I can understand on the GMAT, according to Bunnel:
"Yes, on the circle means on the circumference, while in the circle means inside the circumference. "
This distinction is SUPER confusing!!! in/on makes all the difference and while for a native this might be even logic for a non native is a pain in.... Furthermore, this makes a person who knows all the mathematical concepts to answer this question right, answering it wrong because of english language issues, which are not supposed to be assessed in this part...
I'm sorry for unburdening my frustration on you guys but I got 2 questions wrong on the same mock because of this and my exam is in 5 freaking days...
Cheers to y'all!
Hello
May I suggest you dont worry about it too much. You are correct that a circle centered at origin (0,0) with a radius of r should ideally be written as:
x^2 + y^2 <= r^2
And I think the meaning of this inequality is that within the circle (inside, not touching the boundary), all points will satisfy: x^2 + y^2 < r^2
While on the boundary (circumference), all points will satisfy: x^2 + y^2 = r^2
Now as per the first statement, since radius of the circle is 4, and since P is a point (x,y) on the boundary of the circle, then definitely the sum of squares of the two coordinates of P, x^2 + y^2 will be = r^2. First statement is thus sufficient.